{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"pygments_lexer":"ipython3","nbconvert_exporter":"python","version":"3.6.4","file_extension":".py","codemirror_mode":{"name":"ipython","version":3},"name":"python","mimetype":"text/x-python"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"# Horse Racing - Big Data Derby 2022","metadata":{}},{"cell_type":"markdown","source":"### Author: Han He\n### Kaggle Id: hanhe2018","metadata":{}},{"cell_type":"markdown","source":"This is a report studying the strategy in the horsing races, my purpose in writing this report is not assembling an excellent machine learning model to improve the predictive accuracy. My goal is to better understand the procedure of horsing races. Thanks to the data from New York Racing Association(NYRA), I have the opportunity to think through the horse racing tactics and verify them.\n\nThis report includes 6 sections. Section 1 introduces my thoughts about horse races and my preferred racing tactics. Section 2 shows the stylized facts found in the racing dataset. In section 3, I introduce my conjecture about the horse racing tactics, and use the data to validate it. Section 4 is the main body of the report, which uses different machine learning models to predict the winners of the 2000 races in 2019. At last, in section 5, I will discuss more about the insights and essence of tactic I conjectured. I list the references at the end in section 6.\n","metadata":{}},{"cell_type":"markdown","source":"# Section 1. Introduction","metadata":{}},{"cell_type":"markdown","source":"### 1.1 A Small Game","metadata":{}},{"cell_type":"markdown","source":"I want to begin my introduction with a small game. I assure you this part is not a digression. Reading the game will be very helpful to understand the idea of my following horse racing tactics. The game could be described as follows.\n\nAssume that 2 players are playing a game. Let's call them Player 1 and Player 2, the two players take turns choosing a number from the set {1，2，..., 10}, with player 1 moving first. The first player who brings the sum of all the chosen numbers to 100 or more wins. Question: Is there any strategy to guarantee Player 1 wins? For example, the following list is one possible play the game: \n\n\"P1\": 10, \"P2\": 9, \"P1\": 9, \"P2\": 10, \"P1\": 8, \"P2\":7, \"P1\": 4, \"P2\": 10, \"P1\": 1, \"P2\":8, \"P1\": 3, \"P2\": 3, \"P1\": 8, \"P2\": 10 \n\nNamely, [10, 9, 9, 10, 8, 7, 4, 10, 1, 8, 3, 3, 8, 10]  In this case Player 2 wins because before his/her last move, the sum is 90, and with his/her final choice of 10, the total sum is 100. Now we come back to the question, is there a strategy guarantee Player 1 wins? ","metadata":{}},{"cell_type":"markdown","source":"The answer is Yes! ","metadata":{}},{"cell_type":"markdown","source":"*Player 1 could find a \"losing position\" for Player 2. Here \"losing position\" means a position that whoever is choosing in that position cannot win, while the other can then win with his/her subsequent choice. For example, 89 is the largest losing position: whoever moves there can take the sum to any number in the set {90,91,...,99}, thus coming short of 100, while the other player can then take the sum to 100 with an appropriate choice. Then what is the largest losing position that precedes 89? The answer is 78: whoever moves at 78 must take the sum to a number in the set {79,80,...,88} and then from there the other player can make sure to take the sum to 89 and then we know what\nhappens from there! Repeating this reasoning we see that the losing positions are: 89, 78, 67, 56, 45, 34, 23, 12, 1. Since Player 1 moves first he can choose 1 and put Player 2 in the first losing position; then, whatever Player 2 chooses, Player 1 can put her in the next\nlosing position, namely 12, etc.*","metadata":{}},{"cell_type":"markdown","source":"Thus, Player 1's winning strategy is as follows:\n\nStart with the number 1. Then, at every turn, choose the number (11−n), where n is the number that was chosen by Player 2 in the immediately preceding turn. \n\nThis is an example I grabbed from Prof. Giacomo Bonanno's Game Theory Textbook, the link for the book is in the reference section at the end. ","metadata":{}},{"cell_type":"markdown","source":"### 1.2 Horse Racing tactics","metadata":{}},{"cell_type":"markdown","source":"The small game provides three crucial hints for the answer we are looking for. (1) Starting position or, generally speaking, the initial performance is extremely important, it is even more important than we thought. For example, in the small game, the one we discussed in section 1.1. The existence of the winning tactic is based on the assumption that Player 1 takes the first move. Strike first is an important experience. it does not necessarily mean that a player should use all his strength at the beginning. Player 1 in the small game does not choose number 10 in the first round, he/she should choose 1 instead. (2) Learn the crucial \"law of motion\". The law of motion touches the essence of a game. how to beat other horses by following a certain smart rule. It should be a tactic somehow based on the decisions of other players. Once again, like the small game in section 1.1, the optimal tactic is \"at every turn, choose the number (11−n), where n is the number that was chosen by Player 2\". Namely, a player should never expect to finish and win a horse game by following his/her own \"perfect\" rhythm. This sounds good, but not feasible, sometimes even not possible. In most cases, he/she will be affected by the move from other players. (3) Looking at the big picture, do not choose local optimal positions, but choose global optimal move. The target of the game is the achieve the goal line first, rather than always taking leading positions. This is exactly what the winners did. They smartly use a draft strategy against air resistance, save strength, and exceed at the end of the race.","metadata":{}},{"cell_type":"markdown","source":"The small game setup is indeed somehow different from the horse race. For example, players in horse races are moving simultaneously, rather than sequentially. Also, it is hard to imagine every player follows the same rule like choosing a number from {1,2,3,...,10}. Such a difference does not matter. Let's think in the following way. You could assume that choosing a number in the small game is choosing acceleration. It could be either 10, use up your strength to speed up, or 1, slow or even no acceleration. Such decisions are based on the speed or positions of other players. Therefore, you, as a player in the horse race, adjust your speed and relative position according to the other player's speed.","metadata":{}},{"cell_type":"markdown","source":"According to the above discussion, the optimal tactic should focus on two keywords (1) the law of motion, and (2) relative positions. Next, I will show stylized facts in section 2 and then introduce the horse race tactic formally in section 3.","metadata":{}},{"cell_type":"markdown","source":"# Section 2 Stylized Facts","metadata":{}},{"cell_type":"markdown","source":"### 2.1 Relative Positions","metadata":{}},{"cell_type":"markdown","source":"I first track the relative positions of racers in each race. I define the relative position of each player by their cumulative distance from the start line. I import libraries in python and create the corresponding functions. To dive into the racing strategy deeper, I focus on the Aqueduct(AQU) races with dirt course type. This is because this type of race has the largest number of races in 2019, a total of 700 races. I also removed the races whose program numbers are non-digit like \"3X\", \"2B\", etc. After this filtering, there are around 620 races left in my dataset. I use the AQU dirt course races on 2019.1.1 as an example to show the changes in relative positions. The records of race 1 and race 2 on that day are shown below. ","metadata":{}},{"cell_type":"code","source":"!pip install utm","metadata":{"execution":{"iopub.execute_input":"2022-11-07T16:59:18.418607Z","iopub.status.busy":"2022-11-07T16:59:18.418058Z","iopub.status.idle":"2022-11-07T16:59:34.034762Z","shell.execute_reply":"2022-11-07T16:59:34.033288Z","shell.execute_reply.started":"2022-11-07T16:59:18.418497Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# prepare library and define functions\n\nimport numpy as np \nimport pandas as pd\nimport warnings\nwarnings.filterwarnings(\"ignore\")\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport heapq\nimport utm\nfrom tqdm.auto import tqdm\ntqdm.pandas()\nimport math\nfrom shapely.geometry import Point\nfrom shapely.geometry.polygon import Polygon\nfrom matplotlib import mlab\nimport plotly.express as px\nfrom plotly.subplots import make_subplots\nimport plotly.graph_objects as go\nfrom sklearn.model_selection import train_test_split\nfrom statistics import mean\nimport cmath\npi=math.pi\n\nfrom sklearn import svm, tree, linear_model, neighbors, naive_bayes, ensemble\nfrom sklearn import discriminant_analysis, gaussian_process\nfrom xgboost import XGBClassifier\nfrom sklearn.neural_network import MLPClassifier\n\nfrom sklearn.preprocessing import OneHotEncoder, LabelEncoder\nfrom sklearn import feature_selection\nfrom sklearn import model_selection\nfrom sklearn import metrics\n\nfrom lightgbm import LGBMClassifier\nfrom sklearn.model_selection import StratifiedGroupKFold\nfrom sklearn.metrics import roc_auc_score, accuracy_score\nimport sklearn.discriminant_analysis\nimport plotly.express as px\nimport geopy.distance\n\ncolor_discrete_map = {\n    \"6\": \"red\",\n    \"1\": \"green\",\n    \"11\": \"blue\",\n    \"9\": \"goldenrod\",\n    \"4\": \"magenta\",\n    \"7\": \"orange\",\n    \"10\": \"pink\",\n    \"3\": \"gray\",\n    \"2\": \"gray\",\n    \"8\": \"gray\",\n    \"5\": \"purple\",\n    \"12\": \"brown\",\n    \"13\": \"olive\",\n    \"14\": \"cyan\",\n    \"15\": \"violet\",\n    \"16\": \"chartreuse\",\n    \"1A\": \"lime\",\n    \"1X\": \"slateblue\",\n    \"2B\": \"indigo\",\n    \"3X\": \"burlywood\"\n}\nsymbol_discrete_map = {\n    \"6\": \"star\",\n    \"1\": \"square\",\n    \"11\": \"x\",\n    \"9\": \"circle\",\n    \"4\": \"cross\",\n    \"7\": \"diamond\",\n    \"10\": \"triangle-up\",\n    \"3\": \"circle-x\",\n    \"2\": \"circle-x\",\n    \"8\": \"circle-x\",\n    \"5\": \"circle-x\",\n    \"12\": \"circle-x\",\n    \"13\": \"circle-x\",\n    \"14\": \"circle-x\",\n    \"15\": \"circle-x\",\n    \"16\": \"circle-x\",\n    \"1A\": \"circle-x\",\n    \"1X\": \"circle-x\",\n    \"2B\": \"circle-x\",\n    \"3X\": \"circle-x\"\n}\n\n\ndef tqdm_pandas(t):\n    from pandas.core.frame import DataFrame\n    def inner(df, func, *args, **kwargs):\n        t.total = groups.size // len(groups)\n        def wrapper(*args, **kwargs):\n            t.update(1)\n            return func(*args, **kwargs)\n        result = df.transform(wrapper, *args, **kwargs)\n        t.close()\n        return result\n    DataFrame.progress_transform = inner\n    \ndef get_speed(points):\n    speed = [0]\n    points = points.values\n    for i in range(1, len(points)):\n        speed.append(4 * np.linalg.norm(np.array(points[i]) - np.array(points[i-1])))\n    return speed\n\ngoal_line_dict ={'AQU':{\n                    'D':[[40.6719205,-73.8319531],[40.6718795,-73.8316874]]},\n                 'SAR':[[43.071816,-73.770390],[43.072480,-73.770883]]\n                }\n\ndef extract_corse_data(df,track_id_,course_type_,furlongs_id_,\\\n                       available_scene_num_=5,goal_line_dict_=goal_line_dict):\n    condition=\"　track_id==@track_id_ & course_type==@course_type_ &furlongs_id==@furlongs_id_\"\n    #col_lst = ['latitude','longitude','scene_id','track_id','course_type']\n    temp_df = df.query(condition)#[col_lst]\n    \n    if track_id_=='AQU':\n        if course_type_=='D':\n            #outer point\n            goal_df = temp_df.copy()\n            goal_df = goal_df.head(1)\n            goal_df[\"latitude\"] ,goal_df[\"longitude\"] = goal_line_dict[track_id_][course_type_][0]\n            goal_df[\"scene_id\"]  = 20\n\n            #Inner point\n            goal_line_df =temp_df.copy()\n            goal_line_df = goal_line_df.head(1)\n            goal_line_df[\"latitude\"] ,goal_line_df[\"longitude\"] =goal_line_dict[track_id_][course_type_][1]\n            goal_line_df[\"scene_id\"]  = 20\n    # slice by scene\n    available_scene_num = available_scene_num_  \n    drop_scene_num= temp_df['scene_id'].max() - available_scene_num_ # max=all\n    temp_df = temp_df[temp_df['scene_id']> drop_scene_num]\n\n    #merge dataframe\n    goal_line_df = goal_line_df.append(goal_df).drop_duplicates()\n    temp_df = temp_df.append(goal_line_df)\n    \n    return temp_df\n\n\ndef cross(row,track_id_,course_type_,goal_line_dict_=goal_line_dict):\n    # Goal line seems to be different if track_id and course_type changed\n    # below is for dart course \n    if track_id_ =='AQU':\n        if course_type_=='D':\n            x1,y1 = goal_line_dict_[track_id_][course_type_][0]\n            x2,y2 = goal_line_dict_[track_id_][course_type_][1]\n    elif track_id_ =='SAR':\n        x1,y1 = goal_line_dict_[track_id_][0]\n        x2,y2 = goal_line_dict_[track_id_][1]\n    \n    return (row['latitude']-x1)*(y2-y1) - (row['longitude']-y1)*(x2-x1)\n\ndef speed(x1,y1,x2,y2):\n    x1=x1*pi/180\n    x2=x2*pi/180\n    y1=y1*pi/180\n    y2=y2*pi/180\n    d=math.sqrt((math.cos(y2)*(x2-x1))**2+(y2-y1)**2)\n    return d*14400*6371\ndef distance(x1,y1,x2,y2):\n    x1=x1*pi/180\n    x2=x2*pi/180\n    y1=y1*pi/180\n    y2=y2*pi/180\n    d=math.sqrt((math.cos(y2)*(x2-x1))**2+(y2-y1)**2)\n    return d*6371*1000\ndef vector(x1,y1,x2,y2):\n    x1=x1*pi/180\n    x2=x2*pi/180\n    y1=y1*pi/180\n    y2=y2*pi/180\n\n    return complex(math.cos(y2)*(x2-x1),y2-y1)*6371*1000\n\ndef all_distance(lat, long, locations):\n    res = []\n    cleaned_locations = [ str(e)  for e in locations] \n    for i in range(len(cleaned_locations)):\n        if cleaned_locations[i] != \"nan\":\n            x = float(cleaned_locations[i].split(\"_\")[0])\n            y = float(cleaned_locations[i].split(\"_\")[1])\n            res.append([x,y])\n        else:\n            res.append(np.nan)\n    total = 0\n    for e in res:\n        if isinstance(e, list):\n            total += distance(long, lat, e[0], e[1])\n    return total\n    \n\ndef num_of_racers(locations):\n    res = 0\n    cleaned_locations = [ str(e)  for e in locations] \n    for i in range(len(cleaned_locations)):\n        if cleaned_locations[i] != \"nan\":     \n            res +=1\n    return res\n    \ndef draft_effect( program_number, lat, long,  disp_vector,  locations):\n    res = []\n    cleaned_locations = [ str(e)  for e in locations] \n    for i in range(len(cleaned_locations)):\n        if cleaned_locations[i] != \"nan\":\n            x = float(cleaned_locations[i].split(\"_\")[0])\n            y = float(cleaned_locations[i].split(\"_\")[1])\n            res.append([x,y])\n        else:\n            res.append(np.nan)\n    \n    #player_idx  = int(program_number) -1\n    for idx in range(len(res)):\n        if not np.isnan(res[idx]).any(): \n            if res[idx][0] == long and res[idx][1] == lat:\n                player_idx = idx\n                break\n    rest_idx = [  idx  for idx in range(len(res)) if idx !=  player_idx]\n    res2 = []\n    for k in rest_idx:\n        if not np.isnan(res[k]).any() :\n\n            a = math.cos(cmath.phase(disp_vector) - cmath.phase(vector(long, lat, res[k][0], res[k][1])))\n            b = abs(vector(long, lat, res[k][0], res[k][1]))\n            if b != 0:\n                res2.append(a/b)\n            else:\n                res2.append(0)\n                \n    positive = np.sum([ e for e in res2 if e > 0])\n    negative = np.sum([ e for e in res2 if e <= 0])    \n    \n    return [positive, negative]  \n\n\ndef relative_positions(cum_distance, all_distances):\n    relative_position = 0\n#     if np.array(all_distances).all() == 0.0 :\n#         return 1\n#    else:\n    \n    a = [e for e in all_distances if not np.isnan(e)]\n    b = sorted(a, reverse = True)\n    num_nan = len(all_distances) - len(a)\n    for i in range(len(b)):\n        if cum_distance == b[i]:\n            relative_position = i + 1\n    return num_nan + relative_position\n\ndef get_trakus_list(data):\n    if data[(data[\"position_at_finish\"] == 1)][\"relative_position\"].min() == 1:\n        return data[(data[\"position_at_finish\"] == 1)&(data[\"relative_position\"] == 1)][\"trakus_index\"].tolist()\n    else:\n        return data[(data[\"position_at_finish\"] == 1)&(data[\"relative_position\"] <=2)][\"trakus_index\"].tolist()\n\ndef final_passby_trakus_index(trakus_list):\n    \n    res = len(trakus_list) - 1\n    for i in range(len(trakus_list)-1,1,-1):\n        if trakus_list[i] == trakus_list[i-1] + 1:\n            res -= 1\n    if res > 0:\n        return trakus_list[res]\n    else:\n        return np.nan\n\ndef pass_by_from_outside(data, pass_by_trakus_index):\n    if not np.isnan(pass_by_trakus_index):\n        candidates = data[(data[\"trakus_index\"]==pass_by_trakus_index)&(data[\"relative_position\"] <=2)]\n        wins = np.array(candidates[candidates[\"relative_position\"] == 1][\"center_distance\"])\n        loses = np.array(candidates[candidates[\"relative_position\"] == 2][\"center_distance\"])\n        if len(wins) > 0 and len(loses) > 0:\n            winner_center_distance = float(wins[0])\n            loser_center_distance = float(loses[0])\n            return winner_center_distance>=loser_center_distance\n        else:\n            return np.nan \n    else:\n        return np.nan\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T16:59:34.039873Z","iopub.status.busy":"2022-11-07T16:59:34.039418Z","iopub.status.idle":"2022-11-07T16:59:37.186758Z","shell.execute_reply":"2022-11-07T16:59:37.185570Z","shell.execute_reply.started":"2022-11-07T16:59:34.039835Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df= pd.read_csv(\"/kaggle/input/big-data-derby-2022/nyra_2019_complete.csv\", header = None)\n\ndf.columns = [\"track_id\",\"race_date\",\"race_number\",\"program_number\",\"trakus_index\",\n                \"latitude\",\"longitude\",\"distance_id\",\"course_type\",\"track_condition\", \n                \"run_up_distance\",\"race_type\",\"purse\",\"post_time\",\"weight_carried\",\"jockey\",\n                \"odds\", \"position_at_finish\"]\n\nprogramers = [ str(e) for e in df[\"program_number\"].tolist()]\ncleaned_programers = [e.split(\" \")[0] for e in programers]\ndf[\"program_number\"] = cleaned_programers\n\nprogram_number_dict = {\"1\":\"1\",\"2\":\"2\",\"3\":\"3\",\"4\":\"4\",\"5\":\"5\",\"6\":\"6\",\"7\":\"7\",\"8\":\"8\",\"9\":\"9\",\n                       \"10\":\"10\",\"11\":\"11\",\"12\":\"12\",\"13\":\"13\",\"14\":\"14\",\"15\":\"15\",\"16\":\"16\",\"1A\":\"21\",\"2B\":\"22\",\"1X\":\"31\",\"3X\":\"43\"}\ndf[\"program_number\"] = df[\"program_number\"].map(program_number_dict)\n\ndf.sort_values(by = [\"track_id\",\"race_date\",\"race_number\",\"program_number\",\"trakus_index\"], ascending =  True, inplace = True)\ndf['xy'] = np.array(utm.from_latlon(df['latitude'].values, df['longitude'].values)[:2]).T.tolist()\ndf['speed'] = df.groupby(['track_id', 'race_date', 'race_number', 'program_number'])['xy'].progress_transform(get_speed)\n\nkey_columns = [\"track_id\", \"race_date\", \"race_number\"]\ndf[\"race_id\"] = df[\"track_id\"].astype(str) +'_'+ df[\"race_date\"].astype(str) +'_'+ df[\"race_number\"].astype(str)\n\ndf[\"run_up_distance\"] = df[\"run_up_distance\"] * 0.3048\ndf[\"furlongs_id\"] =  8 * df[\"distance_id\"] / 600\ndf[\"miles\"] = df[\"distance_id\"] / 600\ndf[\"furlongs_id\"] =  df[\"furlongs_id\"].apply(lambda x: round(x,2))\ndf['track_course_type'] = df['track_id']+ '_' + df['course_type'] \ndf['course_type_miles'] = df['track_id']+ '_' + df['course_type'] + '_' + df['miles'].apply(lambda x: str(round(x,2)))\ndf[\"time\"] =  df[\"trakus_index\"]* 0.25 -0.25\ndf[\"scene_id\"] = df[\"time\"].apply(lambda x: int(x//10))\n\ntemp = df[['race_id','jockey']].drop_duplicates().groupby('jockey')['race_id'].count().to_frame().reset_index()\ntemp = temp.rename(columns={'race_id':'number_of_rides'})\ndf = df.merge(temp,on=['jockey'])\n\ntemp=df[['race_id','track_id','jockey','position_at_finish']].drop_duplicates()\ntemp_pv=pd.pivot_table(data=temp,index='jockey',columns='position_at_finish',values='race_id',aggfunc='count')\nfor x in temp_pv.columns:\n    temp_pv[x]=temp_pv[x].fillna(0)\ntemp_pv['jockey_count']=temp_pv.sum(axis=1)\nfor x in temp_pv.columns:\n    if x !='jockey_count':\n        temp_pv[x] = round(100 * temp_pv[x]/temp_pv['jockey_count'],2)\ntemp_pv = temp_pv.sort_values(by='jockey_count')\ntemp_pv = temp_pv.reset_index()\ndf = df.merge(temp_pv, on = \"jockey\" )\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T16:59:37.189410Z","iopub.status.busy":"2022-11-07T16:59:37.188323Z","iopub.status.idle":"2022-11-07T17:02:15.791586Z","shell.execute_reply":"2022-11-07T17:02:15.790234Z","shell.execute_reply.started":"2022-11-07T16:59:37.189367Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"temp = df[['race_id','track_id','scene_id']].groupby(['race_id','track_id']).scene_id.max().to_frame().reset_index()\ntemp = temp.rename(columns={'scene_id':'max_scene_id'})\ntemp = temp[['race_id','max_scene_id']]\n\ntrack_id ='AQU'\ncourse_type ='D'\ncondition=\"track_id==@track_id & course_type==@course_type\"\nAQU_D_df = df.query(condition)\n\nAQU_D_df = AQU_D_df.merge(temp)\n\nAQU_D_df['use_scene_id']=AQU_D_df['max_scene_id'] - 3\nfor idx in AQU_D_df.index:\n    if AQU_D_df.at[idx,'use_scene_id']>AQU_D_df.at[idx,'scene_id']:\n        AQU_D_df.at[idx,'use_scene']=0\n    else:\n        AQU_D_df.at[idx,'use_scene']=1\n        \n        \nprocessed_df = AQU_D_df[AQU_D_df['use_scene']==1]\nprocessed_df['crossed'] = processed_df.apply(lambda x:cross(x,'AQU','D'), axis=1)\ndrop_idx = processed_df[processed_df['crossed']<0].index\nAQU_D_df = AQU_D_df.drop(index=drop_idx)\n\nidx = AQU_D_df[AQU_D_df['trakus_index']==1].index\nAQU_D_df.loc[idx,'speed']=0\n\nAQU_D_df['accelation']=AQU_D_df['speed'].diff()/0.25\nAQU_D_df.loc[idx,'accelation']=0\n\n\npoly=[[40.6739403, -73.8268994],[40.6750219, -73.8306731],[40.6708878, -73.8325583],[40.6697726,-73.8286816]]\n\ndf_poly = pd.DataFrame(poly, columns =['Lat', 'Lon'], dtype = float)\npolygon = Polygon([tuple(x) for x in df_poly[['Lat', 'Lon']].to_numpy()])\n\nAQU_D_df['Within'] = AQU_D_df.apply(lambda AQU_D_df: polygon.contains(Point(AQU_D_df['latitude'], AQU_D_df['longitude'])), axis=1)\n\nproblem_races = []\nfor race in AQU_D_df[\"race_id\"].unique():\n    Numbers = AQU_D_df[AQU_D_df[\"race_id\"] == race][\"program_number\"].unique()\n    if (\"21\" in Numbers) or (\"22\" in Numbers) or (\"31\" in Numbers) or (\"43\" in Numbers):\n        problem_races.append(race)\n        \nAQU_D_df[\"problem_races\"] = AQU_D_df[\"race_id\"].apply(lambda x: 1 if x in problem_races else 0)\nAQU_D_df","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:02:15.794837Z","iopub.status.busy":"2022-11-07T17:02:15.794425Z","iopub.status.idle":"2022-11-07T17:06:19.741620Z","shell.execute_reply":"2022-11-07T17:06:19.740393Z","shell.execute_reply.started":"2022-11-07T17:02:15.794802Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"center_xy  = np.array([598910.1945129023, 4503049.352680351])\ntest_all = AQU_D_df[(AQU_D_df[\"problem_races\"]==0)]","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:06:19.743706Z","iopub.status.busy":"2022-11-07T17:06:19.743211Z","iopub.status.idle":"2022-11-07T17:06:20.340875Z","shell.execute_reply":"2022-11-07T17:06:20.339552Z","shell.execute_reply.started":"2022-11-07T17:06:19.743659Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"result_df = pd.DataFrame()\nfor race in test_all[\"race_id\"].unique():\n    \n    test = test_all[test_all[\"race_id\"] == race]\n\n    test[\"lat_next\"] = test.groupby([\"race_id\",\"program_number\"])[\"latitude\"].shift(-1)\n    test[\"long_next\"] = test.groupby([\"race_id\",\"program_number\"])[\"longitude\"].shift(-1)\n\n    test[\"lat_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"latitude\"].shift(1)\n    test[\"long_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"longitude\"].shift(1)\n\n    test[\"speed2\"] = test[[\"longitude\",\"latitude\",\"long_next\",\"lat_next\"]].apply(lambda x: speed(x[0],x[1],x[2],x[3]), axis = 1)\n    test[\"disp_vector\"] = test[[\"long_prev\",\"lat_prev\",\"longitude\",\"latitude\"]].apply(lambda x: vector(x[0],x[1],x[2],x[3]), axis = 1)\n\n    test[\"long_lat\"] = test[[\"longitude\",\"latitude\"]].apply(lambda x: str(x[0]) + \"_\" + str(x[1]), axis = 1)\n\n    locations = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"long_lat\"])\n    locations[\"all_positions\"] =  locations.apply(lambda x: np.array(x) , axis = 1)\n    locations = pd.DataFrame(locations[\"all_positions\"]).reset_index()\n    test = test.merge(locations, on = [\"trakus_index\"])\n\n\n    test[\"sum_distance\"] = test[[\"latitude\",\"longitude\",\"all_positions\"]].apply(lambda x: all_distance(x[0],x[1],x[2]) , axis = 1)\n    test[\"num_of_racers\"] = test[\"all_positions\"].apply(lambda x: num_of_racers(x))\n    test[\"avg_distance\"] = test[\"sum_distance\"] / test[\"num_of_racers\"]\n    test[\"draft_effect\"] =  test[[\"program_number\",\"latitude\",\"longitude\",\"disp_vector\",\"all_positions\"]].apply(lambda x: draft_effect(x[0],x[1],x[2],x[3],x[4]) , axis = 1)\n    test[\"draft_positive\"] = test[\"draft_effect\"].apply(lambda x: x[0])\n    test[\"draft_negative\"] = test[\"draft_effect\"].apply(lambda x: x[1])\n\n    maxspeed = pd.DataFrame(test.groupby([\"race_id\",\"program_number\"])[\"speed\"].max())\n    speed_df = maxspeed.reset_index()\n    speed_df.columns = [\"race_id\",\"program_number\",\"maxspeed\"]\n\n    test = test.merge(speed_df, on  = [\"race_id\",\"program_number\"])\n\n\n    pos_mean_df = pd.DataFrame(test.groupby([\"race_id\",\"program_number\"])[\"draft_positive\"].mean()).reset_index()\n    pos_mean_df.columns = [\"race_id\",\"program_number\",\"avg_pos_draft\"]\n    test = test.merge(pos_mean_df, on  = [\"race_id\",\"program_number\"])\n\n    neg_mean_df = pd.DataFrame(test.groupby([\"race_id\",\"program_number\"])[\"draft_negative\"].mean()).reset_index()\n    neg_mean_df.columns = [\"race_id\",\"program_number\",\"avg_neg_draft\"]\n    test = test.merge(neg_mean_df, on  = [\"race_id\",\"program_number\"])\n    \n    trakus_df = pd.DataFrame(test.groupby([\"race_id\",\"program_number\"])[\"trakus_index\"].max()).reset_index()\n    trakus_df.columns = [\"race_id\",\"program_number\",\"max_trakus_idx\"]\n    test = test.merge(trakus_df, on = [\"race_id\",\"program_number\"])\n    test[\"percent_of_race\"] = 100 * test[\"trakus_index\"]/ test[\"max_trakus_idx\"]\n    test[\"round_percent\"] = round(test[\"percent_of_race\"])\n\n    test[\"distance\"] =  test[\"speed\"] / 4.0\n    cum_distance = pd.DataFrame(test.groupby([\"race_id\",\"program_number\"])[\"distance\"].cumsum())\n    cum_distance.columns = [\"cum_distance\"]\n    test = pd.concat([test, cum_distance],axis = 1 )\n\n    all_distances = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"cum_distance\"])\n    all_distances[\"all_distances\"] =  all_distances.apply(lambda x: np.array(x) , axis = 1)\n    all_distances = pd.DataFrame(all_distances[\"all_distances\"]).reset_index()\n\n    test = test.merge(all_distances, on = [\"trakus_index\"])\n    test[\"relative_position\"] = test[[\"cum_distance\",\"all_distances\"]].apply(lambda x: relative_positions(x[0],x[1]),axis = 1)\n    \n    test.sort_values([\"track_id\",\"race_date\",\"race_number\",\"program_number\",\"trakus_index\"], inplace = True)\n    test[\"relative_position_prev\"] =  test.groupby([\"track_id\",\"race_date\",\"race_number\",\"program_number\"])[\"relative_position\"].shift(1)\n\n    test[\"relative_position_change\"] = test[[\"relative_position\",\"relative_position_prev\"]].apply(lambda x: x[0]- x[1], axis = 1)\n    \n    \n    total_rel_pos = test.pivot(index = \"trakus_index\", columns = \"program_number\",values = \"relative_position_change\")\n    total_rel_pos[\"total_rel_pos_change\"] =  total_rel_pos.apply(lambda x: np.sum([ abs(e) for e in x] ) ,axis = 1)\n    total_rel_pos.reset_index(inplace = True)\n    total_rel_pos = total_rel_pos[[\"trakus_index\",\"total_rel_pos_change\"]]\n    total_rel_pos[\"total_rel_pos_change\"] = total_rel_pos[\"total_rel_pos_change\"].apply(lambda x: 0 if np.isnan(x) else x)\n    test = test.merge(total_rel_pos, on = [\"trakus_index\"])\n    test['center_distance'] = test['xy'].apply(lambda x: np.linalg.norm(np.array(x) - np.array(center_xy) ))\n    trakus_list = get_trakus_list(test)\n    pass_by_trakus_index = final_passby_trakus_index(trakus_list)\n    test[\"pass_by_trakus_index\"] = pass_by_trakus_index\n    outside = pass_by_from_outside(test, pass_by_trakus_index)\n    test[\"pass_by_outside\"] = outside\n    \n    result_df = pd.concat([result_df,test])\n    ","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:06:20.343391Z","iopub.status.busy":"2022-11-07T17:06:20.342935Z","iopub.status.idle":"2022-11-07T17:18:42.939398Z","shell.execute_reply":"2022-11-07T17:18:42.938091Z","shell.execute_reply.started":"2022-11-07T17:06:20.343346Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (1) Relative Positions Change of Race \"AQU_2019-01-01_1\" and \"AQU_2019-01-01_2\"\n\nplot_df  = result_df[result_df[\"race_date\"] == \"2019-01-01\"][[\"cum_distance\",\"relative_position\",\"race_id\",\"program_number\"]].drop_duplicates()\nfor race in ['AQU_2019-01-01_1', 'AQU_2019-01-01_2']:\n    dfp =   plot_df[ plot_df[\"race_id\"] == race]\n    plt.figure(figsize =(12,8))\n    sns.lineplot(data = dfp, x = \"cum_distance\", y = \"relative_position\", hue = \"program_number\" )\n    plt.title(f\"race id: {race}\")\n    plt.show()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:18:42.941809Z","iopub.status.busy":"2022-11-07T17:18:42.941402Z","iopub.status.idle":"2022-11-07T17:18:45.757333Z","shell.execute_reply":"2022-11-07T17:18:45.756256Z","shell.execute_reply.started":"2022-11-07T17:18:42.941774Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### 2.2 The trend of Changes in Relative Position","metadata":{}},{"cell_type":"markdown","source":"From the above figures, we could easily track the change of relative positions in a given race. I also plot the total number of relative position changes for all the Aqueduct dirt course races in 2019. The goal of the figure is to show the trends of relative position change in races. The figure is shown as follows.","metadata":{}},{"cell_type":"code","source":"# (2) Sum of the Relative Position Changes in all the AQU Dirt Races in 2019\n\nrecords = [0,0,0,0,0,0,0]\nraces_result = []\nfor race in result_df[\"race_id\"].unique():\n    dfp = result_df[result_df[\"race_id\"] == race][[\"trakus_index\",\"total_rel_pos_change\",\"race_id\",\"num_of_racers\"]].drop_duplicates()\n    dfp[\"distance_group\"] = pd.cut(dfp[\"trakus_index\"],[0,50, 100, 150,200,250, 300, 350])\n    a = dfp.groupby(\"distance_group\")[\"total_rel_pos_change\"].sum() / dfp[\"num_of_racers\"][0]\n    races_result.append(a.tolist())\n\nplt.figure(figsize = (12,8))\nsns.set(style=\"white\")\nplot_df = pd.DataFrame({\"trakus index group\": dfp[\"distance_group\"].unique(), \"relative position changes\": np.array(races_result).sum(axis = 0)}) \ng = sns.barplot(data = plot_df, x = \"trakus index group\", y = \"relative position changes\")\n\nfor index, row in plot_df.iterrows():\n    g.text(row.name, row[\"relative position changes\"], int(row[\"relative position changes\"]), color='black', ha=\"center\")\nplt.title(\"Sum of the Relative Position Changes in all the AQU Dirt Races in 2019\", fontsize =20)\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:18:45.760059Z","iopub.status.busy":"2022-11-07T17:18:45.758968Z","iopub.status.idle":"2022-11-07T17:19:59.638738Z","shell.execute_reply":"2022-11-07T17:19:59.637262Z","shell.execute_reply.started":"2022-11-07T17:18:45.760022Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"We see that the players compete fiercely in the beginning phase of a race. The sum of relative position changes in the first 50 trakus indexes(12.5 seconds) is the highest 6152, while the rest period of races is much lower, the sum is the lowest at the end of a race, only 237. This finding is in line with our discussion in section 1. Strike first is important and even crucial to the results of a game. Most of the players knew it and exactly did it.","metadata":{}},{"cell_type":"markdown","source":"### Winners' Strategy and Final Exceeding Locations","metadata":{}},{"cell_type":"markdown","source":"Next, I study the winners' strategy and final exceeding locations.  It is interesting because we need to know the decisions made by the winners. (1) What is the final exceeding location of the winner? Namely, when did the winner exceed the front horse and be the No.1, and keep it to the end of a race? (2) Did the winners exceed from outer rail or inner rail? (3) Did the winners exceed on straight roads or curve roads?","metadata":{}},{"cell_type":"markdown","source":"Essentially, we are looking for the \"Losing Positions\" of the losers in races.","metadata":{}},{"cell_type":"code","source":"# (3) winner's strategy and Exceeding Locations\nwinners_df = result_df[(result_df[\"trakus_index\"] == result_df[\"pass_by_trakus_index\"])&(result_df[\"position_at_finish\"] == 1) ]\nwinners_df[\"Strategy\"] =  winners_df[\"pass_by_outside\"].apply(lambda x: \"Exceed From Outside\" if x == 1 else \"Exceed From Inside\")\nwinners_df[\"Road Type\"] =  winners_df[\"Within\"].apply(lambda x: \"Straight Road\" if x == True else \"Curve Road\")\n\ngrouped_values = pd.DataFrame(winners_df.groupby([\"Road Type\",\"Strategy\"])[\"cum_distance\"].mean().reset_index())\ngrouped_values[\"cum_distance\"] = np.round(grouped_values[\"cum_distance\"],1)\n    \nplt.figure(figsize =(9,9))\n\ng= sns.barplot(data=grouped_values,   x=\"Road Type\", y='cum_distance', hue=\"Strategy\",ci = False)\nfor container in g.containers:\n    g.bar_label(container)\nsns.despine()\n\nplt.title(\"Winners' Exceeding Point(Strategy/Location) in AQU Dirt Races in 2019\", fontsize =20)\nplt.xlabel(\"Road Type\")\nplt.ylabel(\"mean distance from start at exceed point\")\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:19:59.641757Z","iopub.status.busy":"2022-11-07T17:19:59.640544Z","iopub.status.idle":"2022-11-07T17:19:59.977609Z","shell.execute_reply":"2022-11-07T17:19:59.976327Z","shell.execute_reply.started":"2022-11-07T17:19:59.641705Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"The above figure shows the winners' exceeding location under each strategy(exceed from outer/inner rail) and road type(straight/curve road) combinations. On Straight road, winners choose to exceed the other horses from outer rail  657.1 meters from start point, and they choose to exceed from inner rail in earlier phases, 484.1 meters from start point. As for the winners who exceed on bend rail, they, on average, begin to exceed at shorter distances, 183.8 and 568.9 meters.","metadata":{}},{"cell_type":"markdown","source":"The distribution of the winner's final exceeding strategy & location is plotted for all the AQU dirt course races. It indicates that most winners (202 winners) choose to do the final exceed on a bending road from the outer rail, and 179 of them choose to make the final exceed on a straight road from the outer rail. The rest winners(243) choose to exceed from the inner rail. 130 of them exceed on the straight road while the rest 113 winners exceed on the bending road. It shows that more winners choose to exceed from the outer rail than the inner rail(381 vs 243).","metadata":{}},{"cell_type":"code","source":"# (4) Number of AQU Dirt races in each strategy & road type combinations\n\nwinners_df = result_df[(result_df[\"trakus_index\"] == result_df[\"pass_by_trakus_index\"])&(result_df[\"position_at_finish\"] == 1) ]\nwinners_df[\"Strategy\"] =  winners_df[\"pass_by_outside\"].apply(lambda x: \"Exceed From Outside\" if x == 1 else \"Exceed From Inside\")\nwinners_df[\"Road Type\"] =  winners_df[\"Within\"].apply(lambda x: \"Straight Road\" if x == True else \"Curve Road\")\n\ngrouped_values = pd.DataFrame(winners_df.groupby([\"Road Type\",\"Strategy\"])[\"race_id\"].count().reset_index())\n\n    \nplt.figure(figsize =(9,9))\n\ng= sns.barplot(data=grouped_values,   x=\"Road Type\", y='race_id', hue=\"Strategy\",ci = False)\nfor container in g.containers:\n    g.bar_label(container)\nsns.despine()\n\nplt.title(\"Winners' Exceeding Location & Strategy in All the AQU Dirt Races in 2019\", fontsize =20)\nplt.xlabel(\"Road Type\")\nplt.ylabel(\"Number of AQU Dirt Races\")","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:19:59.983043Z","iopub.status.busy":"2022-11-07T17:19:59.982448Z","iopub.status.idle":"2022-11-07T17:20:00.313557Z","shell.execute_reply":"2022-11-07T17:20:00.312400Z","shell.execute_reply.started":"2022-11-07T17:19:59.983007Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (5) Strategy of Winners Outside/Inside\n\n# races_df = result_df[[\"race_id\",\"pass_by_outside\"]].drop_duplicates()\n# grouped_values = pd.DataFrame(races_df.groupby([\"pass_by_outside\"])[\"race_id\"].count()).reset_index()\n# plt.figure(figsize = (12,9))\n# g = sns.barplot(data=grouped_values,   x=\"pass_by_outside\", y = \"race_id\" ,ci = False)\n# for index, row in grouped_values.iterrows():\n#     g.text(row.name, row[\"race_id\"], int(row[\"race_id\"]), color='black')\n# sns.despine()\n# plt.title(\"Winners' Exceeding Stragies in AQU Dirt Races in 2019\", fontsize =20)\n# plt.xlabel(\"Winners's Final Exceed is From Outside\")\n# plt.ylabel(\"Number of AQU Dirt Races in 2019\")","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:20:00.315052Z","iopub.status.busy":"2022-11-07T17:20:00.314734Z","iopub.status.idle":"2022-11-07T17:20:00.319758Z","shell.execute_reply":"2022-11-07T17:20:00.318713Z","shell.execute_reply.started":"2022-11-07T17:20:00.315024Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"I plot the winner's average distance from other horses for AQU dirt course races in 2019. It shows that the competition is fierce in the early phase of the race, the distance is around 5 at the beginning. But when it comes to the middle or end phase of the race, the winner's average distance from other horses rises up to around 15 meters, and it has much higher variation. This is in line with the figure we saw, the true competition occurs at the beginning phase, and the performance of horses in the last phase(trakus index in [300, 350]) is the consequence, rather than reason.","metadata":{}},{"cell_type":"code","source":"# (6) Winners' distance from other horses.\n\nraces_df = result_df[(result_df[\"trakus_index\"] == result_df[\"pass_by_trakus_index\"])&(result_df[\"position_at_finish\"] == 1) ][[\"race_id\",\"pass_by_outside\",\"Within\",\"cum_distance\",\"center_distance\",\"trakus_index\",\"avg_pos_draft\",\"avg_neg_draft\",\"avg_distance\",\"distance\"]]\nplt.figure(figsize = (12,9))\nsns.scatterplot(data = races_df, x = \"cum_distance\", y = \"avg_distance\", alpha = 0.5)\nsns.despine()\nplt.title(\"Winners' Distance From Other Racers at Exceeding Point in AQU Dirt Races in 2019\", fontsize =20)\nplt.xlabel(\"Distance From Start\")\nplt.ylabel(\"Average Distance From Other Racers\")","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:20:00.321440Z","iopub.status.busy":"2022-11-07T17:20:00.321099Z","iopub.status.idle":"2022-11-07T17:20:00.707602Z","shell.execute_reply":"2022-11-07T17:20:00.706317Z","shell.execute_reply.started":"2022-11-07T17:20:00.321409Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"We could also view a race by using the scatter plot and zoom in by looking at the centered scatter plot. I use the AQU dirt course race at 2019.1.1 race 1 as an example. The race procedure could be viewed as follows.","metadata":{}},{"cell_type":"code","source":"# (7) View a race from scatter plot\ntest = test_all[test_all[\"race_id\"] == 'AQU_2019-01-01_1']\npx.scatter(test,x='latitude',y='longitude',animation_frame=\"trakus_index\",\n          color='program_number',\n          color_discrete_map = color_discrete_map,\n          symbol = 'program_number',\n          symbol_map = symbol_discrete_map,\n          range_x = [test['latitude'].min(), test['latitude'].max()],\n          range_y =[test['longitude'].min(),test['longitude'].max()],\n          title = 'Race simulation lat/long scatter plot', width = 700,height=700 )","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:20:00.709128Z","iopub.status.busy":"2022-11-07T17:20:00.708812Z","iopub.status.idle":"2022-11-07T17:20:07.016260Z","shell.execute_reply":"2022-11-07T17:20:07.015263Z","shell.execute_reply.started":"2022-11-07T17:20:00.709100Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (8) View a race from centered scatter plot\ncentroid = test[test['program_number']=='3'].rename(columns={'latitude': 'centroid_lat', 'longitude': 'centroid_long'}).reset_index()\ntest = pd.merge(\n    test,\n    centroid[['trakus_index','centroid_lat','centroid_long']],\n    on='trakus_index',\n    how='left'\n)\n\ntest['lag_lat'] = test.groupby('program_number')[['latitude']].shift(1)\ntest['lag_lat'] = test.groupby('program_number')[['lag_lat']].fillna(method='bfill')\ntest['lag_long'] = test.groupby('program_number')[['longitude']].shift(1)\ntest['lag_long'] = test.groupby('program_number')[['lag_long']].fillna(method='bfill')\ntest['x_horse3_centered'] = (test['latitude'] - test['centroid_lat']) * (10 ** 5)\ntest['y_horse3_centered'] = (test['longitude'] - test['centroid_long']) * (10 ** 5)\n\n\npx.scatter(test, x='x_horse3_centered', y='y_horse3_centered', animation_frame=\"trakus_index\", \n           color='program_number',\n           color_discrete_map=color_discrete_map,\n           symbol='program_number',\n           symbol_map=symbol_discrete_map,\n           range_x = [-30, 30],\n           range_y = [-30, 30],\n           title='Race id: AQU_2019-01-01_1', width=800, height=800)\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:20:07.018835Z","iopub.status.busy":"2022-11-07T17:20:07.017762Z","iopub.status.idle":"2022-11-07T17:20:12.016502Z","shell.execute_reply":"2022-11-07T17:20:12.015500Z","shell.execute_reply.started":"2022-11-07T17:20:07.018789Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Section 3 Horse Racing Strategy","metadata":{}},{"cell_type":"markdown","source":"### 3.1 Orbit Model","metadata":{}},{"cell_type":"markdown","source":"Now Let's formally introduce the horse racing strategy, I call it the \"orbit model\". I borrow the idea of the movement of celestial bodies. I treat the ellipse-like track as the orbit of the earth. The center of the course is imagined as the location of the sun. The cluster constructed by horses could be treated as the earth. The cluster is orbiting around the center of course in a race. A horse in the model is considered the moon. It is orbiting the cluster, the \"earth\" in a horse race. This model could be summarized in the figures below.","metadata":{}},{"cell_type":"markdown","source":"![game_model.jpg](attachment:game_model.jpg)","metadata":{},"attachments":{"game_model.jpg":{"image/jpeg":"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the setup, I use the phase angle to describe the relative positions in a cluster. The angle could be computed easily by the law of cosines. Namely. Given the longitude and latitude data of every horse in a race, I could easily compute the angle ABC here, where A is the location of a horse at time t, B is the center of the cluster at t, and C is the center of the course. The location of point B could be obtained by computing the mean longitude and mean latitude of all the horses' locations at time t. In addition, the relative positions could be shown in terms of different angles. One is the relative position relative to the cluster. The other is the relative position of the cluster to the course. They could all be summarized by the figures as follows.","metadata":{}},{"cell_type":"markdown","source":"![cosine_angle.jpg](attachment:cosine_angle.jpg)","metadata":{},"attachments":{"cosine_angle.jpg":{"image/jpeg":"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idea of the orbit model is to find the relationship between the angle A'B'A (cluster angle) and angle A'CA (course angle). Since one trakus index change means 0.25 seconds in our dataset. I am computing the angular velocity of a horse relative to the cluster(the group of horses in that race at the same time t). Winners should adjust their angle A'B'A according to the angle A'CA. This means that winners should adjust their relative positions in the cluster depending on the progress of the game. This is the \"law of motion\" I have been looking for.","metadata":{}},{"cell_type":"markdown","source":"### 3.2 Empirical Study","metadata":{}},{"cell_type":"markdown","source":"#### 3.2 (a) Empirical Finding","metadata":{}},{"cell_type":"markdown","source":"Let me use one race as an example to show the idea. I choose the AQU dirt course race, race 1 on 2019.1.1. It is also the first race in the sorted dataset. I compute the angles and plot the trends of different horses in the race, shown as follows.","metadata":{}},{"cell_type":"code","source":"import gc\n\ndel result_df\ngc.collect()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:20:12.018364Z","iopub.status.busy":"2022-11-07T17:20:12.017686Z","iopub.status.idle":"2022-11-07T17:20:13.083419Z","shell.execute_reply":"2022-11-07T17:20:13.082119Z","shell.execute_reply.started":"2022-11-07T17:20:12.018332Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (1) Prepare the dataset \n\ncourse_center_lat_dict = {\"AQU\": 40.67243,\"BEL\": 40.71531, \"SAR\":43.07168}\ncourse_center_long_dict = {\"AQU\": -73.82943,\"BEL\": -73.72266, \"SAR\": -73.76841}\ndf[\"course_center_lat\"] = df[\"track_id\"].map(course_center_lat_dict)\ndf[\"course_center_long\"] = df[\"track_id\"].map(course_center_long_dict)\n\nfrom math import sin,cos,atan2, pi\n\ndef calcu_azimuth(lat1, lon1, lat2,lon2):\n    \n    lat1_rad = lat1 * pi / 180\n    lon1_rad = lon1 * pi / 180\n    lat2_rad = lat2 * pi / 180\n    lon2_rad = lon2 * pi / 180\n    \n    y = sin(lon2_rad - lon1_rad) * cos(lat2_rad)\n    x = cos(lat1_rad) * sin(lat2_rad) - sin(lat1_rad) * cos(lat2_rad) * cos(lon2_rad - lon1_rad)\n    brng  = atan2(y,x)/ pi * 180\n    return float((brng + 360.0) % 360.0)\n\ndef distance(lat1,long1,lat2,long2):\n    long1=long1*pi/180\n    long2=long2*pi/180\n    lat1=lat1*pi/180\n    lat2=lat2*pi/180\n    d=math.sqrt((math.cos(lat2)*(long2-long1))**2+(lat2-lat1)**2)\n    return d*6371*1000\n\ndef cos_angle(latA, longA, latB, longB, latC, longC):\n    \n    a = distance(latB,longB, latC, longC)\n    b = distance(latA,longA, latC, longC)\n    c = distance(latA,longA, latB, longB)\n    cos_angle = (a**2 + b**2 - c**2)/(2*a*b)\n    return cos_angle\n\ndef cos_angle2(latA, longA, latB, longB, latC, longC):\n    \n    a = distance(latB,longB, latC, longC)\n    b = distance(latA,longA, latC, longC)\n    c = distance(latA,longA, latB, longB)\n    cos_angle2 = (a**2 + c**2 - b**2)/(2*a*c)\n    return cos_angle2\n\ndef center_lat_long(locations):\n    res = []\n    cleaned_locations = [ str(e)  for e in locations] \n    for i in range(len(cleaned_locations)):\n        if cleaned_locations[i] != \"nan\":\n            x = float(cleaned_locations[i].split(\"_\")[0])\n            y = float(cleaned_locations[i].split(\"_\")[1])\n            res.append([x,y])\n        else:\n            res.append(np.nan)\n            \n    sum_lat = 0\n    sum_long = 0\n    count = 0\n    for e in res:\n        if isinstance(e, list):\n            sum_lat += e[1]\n            sum_long += e[0]\n            count += 1\n    center_lat =  sum_lat / count\n    center_long = sum_long / count\n    return [center_lat, center_long]\n\nresult_df = pd.DataFrame()\n\nfor race in df[\"race_id\"].unique():\n    \n    test = df[df[\"race_id\"] == race]\n    test = test.sort_values(by = [\"track_id\",\"race_date\",\"race_number\",\"program_number\",\"trakus_index\"])\n    test[\"lat_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"latitude\"].shift(1)\n    test[\"long_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"longitude\"].shift(1)\n    \n    test[\"long_lat\"] = test[[\"longitude\",\"latitude\"]].apply(lambda x: str(x[0]) + \"_\" + str(x[1]), axis = 1)\n    locations = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"long_lat\"])\n    locations[\"all_positions\"] =  locations.apply(lambda x: np.array(x) , axis = 1)\n    locations = pd.DataFrame(locations[\"all_positions\"]).reset_index()\n    test = test.merge(locations, on = [\"trakus_index\"])\n    test[\"center_lat\"] = test[\"all_positions\"].apply(lambda x: center_lat_long(x)[0])\n    test[\"center_long\"] = test[\"all_positions\"].apply(lambda x: center_lat_long(x)[1])\n    \n    test[\"center_lat_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"center_lat\"].shift(1)\n    test[\"center_long_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"center_long\"].shift(1)\n    \n    \n    test[\"angle_course2\"] = test[[\"latitude\",\"longitude\",\"center_lat\",\"center_long\",\"course_center_lat\",\"course_center_long\"]].apply(lambda x:cos_angle2(x[0],x[1],x[2],x[3],x[4],x[5]) , axis = 1)\n    test[\"arccos_angle_course2\"] = test[\"angle_course2\"].apply(lambda x: 180*(np.arccos(x))/pi )\n    \n    test[\"small_circle_angle\"] = test[[\"latitude\",\"longitude\",\"lat_prev\",\"long_prev\",\"center_lat_prev\",\"center_long_prev\"]].apply(lambda x:cos_angle(x[0],x[1],x[2],x[3],x[4],x[5]) , axis = 1)\n    test[\"large_circle_angle\"] = test[[\"latitude\",\"longitude\",\"lat_prev\",\"long_prev\",\"course_center_lat\",\"course_center_long\"]].apply(lambda x:cos_angle(x[0],x[1],x[2],x[3],x[4],x[5]) , axis = 1)\n    result_df = pd.concat([result_df,test[[\"race_id\",\"program_number\",\"trakus_index\",\"arccos_angle_course2\",\"position_at_finish\",\"small_circle_angle\",\"large_circle_angle\"]]])\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:20:13.086096Z","iopub.status.busy":"2022-11-07T17:20:13.085665Z","iopub.status.idle":"2022-11-07T17:50:04.150261Z","shell.execute_reply":"2022-11-07T17:50:04.149022Z","shell.execute_reply.started":"2022-11-07T17:20:13.086062Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (2) Plot AQU Dirt Race 1 on 2019.1.1 \n\nresult_df[\"arccos_small_circle_anlge\"] =  result_df[\"small_circle_angle\"].apply(lambda x: 180*(np.arccos(x))/pi )\nresult_df[\"arccos_large_circle_anlge\"] =  result_df[\"large_circle_angle\"].apply(lambda x: 180*(np.arccos(x))/pi )\nresult_df[\"ratio_small_to_large_angle\"] =  result_df[\"arccos_small_circle_anlge\"]/ result_df[\"arccos_large_circle_anlge\"]\n\ntest = result_df[result_df[\"race_id\"] == \"AQU_2019-01-01_1\"]\nplt.figure(figsize =(22,6))\nplt.subplot(131)\na = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"arccos_small_circle_anlge\"]).reset_index()\nplayers = []\nfor na in a.columns.tolist():\n    if na[0]!= \"trakus_index\":\n        players.append(na[1])\nfor i in range(0,len(players)):\n    plt.plot(a.iloc[:,0], a.iloc[:,i+1],  label = f\"Racer {players[i]}\")\nplt.legend()\nplt.title(\"Cluster Angle Trends of Horses in AQU Dirt Race 1 on 2019.1.1\")\nplt.xlabel(\"trakus index\")\nplt.ylabel(\"cluter angle\")\n\nplt.subplot(132)\na = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"arccos_large_circle_anlge\"]).reset_index()\nplayers = []\nfor na in a.columns.tolist():\n    if na[0]!= \"trakus_index\":\n        players.append(na[1])\nfor i in range(0,len(players)):\n    plt.plot(a.iloc[:,0], a.iloc[:,i+1],  label = f\"Racer {players[i]}\")\nplt.legend()\nplt.title(\"Course Angle Trends of Horses in AQU Dirt Race 1 on 2019.1.1\")\nplt.xlabel(\"trakus index\")\nplt.ylabel(\"course angle\")\n\nplt.subplot(133)\na = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"ratio_small_to_large_angle\"]).reset_index()\nplayers = []\nfor na in a.columns.tolist():\n    if na[0]!= \"trakus_index\":\n        players.append(na[1])\nfor i in range(0,len(players)):\n    plt.plot(a.iloc[:,0], a.iloc[:,i+1],  label = f\"Racer {players[i]}\")\nplt.legend()\nplt.title(\"Ratio of Cluster Angle to Course Angle in AQU Dirt Race 1 on 2019.1.1\")\nplt.xlabel(\"trakus index\")\nplt.ylabel(\"cluster angle/course angle\")\n\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:50:04.152396Z","iopub.status.busy":"2022-11-07T17:50:04.152041Z","iopub.status.idle":"2022-11-07T17:50:21.955739Z","shell.execute_reply":"2022-11-07T17:50:21.954919Z","shell.execute_reply.started":"2022-11-07T17:50:04.152364Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"In this race, the final ranking is Racer 5 > Racer 1 > Racer 2 > Racer 3 > Racer 4. Therefore Racer 5(Program number = 5) is the winner and Racer 4 is the last. From the figure above, it is very clear to see that the purple line(Racer 5) is very different from the red line(Racer 4) in the cluster angle plot. It is not surprising to see that the second subplot has overlapped lines, because the center of the horse cluster is common for all the horses. I then compute the ratio of cluster angle to course angle for each trakus index, it is a measurement of a horse's relative position during a race. It seems like the winner(Racer 5) fell behind a little bit at the beginning. But he started to exceed around trakus index of 200, and finally win the race. The whole race has been shown in section 2.2 above. ","metadata":{}},{"cell_type":"markdown","source":"Next, we compute trends of winners for all the 2000 races in 2019. Then compare them with lower-ranking racers like No. 5th, and No.9th. The figures are shown as follows. ","metadata":{}},{"cell_type":"code","source":"# (3) All races. Winners\n\nplt.figure(figsize =(22,6))\n\nplt.subplot(131)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==1)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_small_circle_anlge\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_small_circle_anlge, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"Winners' Cluster Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"cluster angle\")\n\n\nplt.subplot(132)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==1)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_large_circle_anlge\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_large_circle_anlge, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"Winners' Course Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"course angle\")\n\nplt.subplot(133)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==1)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"ratio_small_to_large_angle\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.ratio_small_to_large_angle, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"Winners' Ratio of Cluster Angle to Course Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"cluster angle/course angle\")\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:50:21.957781Z","iopub.status.busy":"2022-11-07T17:50:21.957308Z","iopub.status.idle":"2022-11-07T17:50:33.795004Z","shell.execute_reply":"2022-11-07T17:50:33.793820Z","shell.execute_reply.started":"2022-11-07T17:50:21.957747Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (4) All races. No. 5th\n\nplt.figure(figsize =(22,6))\n\nplt.subplot(131)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==5)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_small_circle_anlge\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_small_circle_anlge, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 5th's Cluster Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"cluster angle\")\n\n\nplt.subplot(132)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==5)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_large_circle_anlge\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_large_circle_anlge, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 5th's Course Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"course angle\")\n\nplt.subplot(133)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==5)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"ratio_small_to_large_angle\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.ratio_small_to_large_angle, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 5th's Ratio of Cluster Angle to Course Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"cluster angle/course angle\")\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:50:33.796704Z","iopub.status.busy":"2022-11-07T17:50:33.796376Z","iopub.status.idle":"2022-11-07T17:50:45.718617Z","shell.execute_reply":"2022-11-07T17:50:45.717436Z","shell.execute_reply.started":"2022-11-07T17:50:33.796675Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (5) All races. No. 9th\nplt.figure(figsize =(22,6))\n\nplt.subplot(131)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==9)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_small_circle_anlge\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_small_circle_anlge, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 9th's Cluster Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"cluster angle\")\n\n\nplt.subplot(132)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==9)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_large_circle_anlge\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_large_circle_anlge, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 9th's Course Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"course angle\")\n\nplt.subplot(133)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==9)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"ratio_small_to_large_angle\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.ratio_small_to_large_angle, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 9th's Ratio of Cluster Angle to Course Angle\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"cluster angle/course angle\")\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:50:45.720948Z","iopub.status.busy":"2022-11-07T17:50:45.720533Z","iopub.status.idle":"2022-11-07T17:50:57.348455Z","shell.execute_reply":"2022-11-07T17:50:57.347605Z","shell.execute_reply.started":"2022-11-07T17:50:45.720902Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"We observe that the winner's cluster angle trend is more clear than the middle, or the last racers. To make it easier to see, I plot the ratio of cluster angle to course angle only based on their final rankings, and get rid of program numbers. Then I see the following figure.","metadata":{}},{"cell_type":"code","source":"# (6) ratio of cluster angle to course angle vs ranking\n\nplt.figure(figsize =(9,9))\nfor i in [1,2,3,4,5,6,7,8,9]:   \n    a = result_df[(result_df[\"position_at_finish\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"ratio_small_to_large_angle\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.ratio_small_to_large_angle, label = f\"Ranking {i}\")\nplt.legend()\nplt.title(\"Ratio of Cluster Angle to Course Angle Over Ranking\")\nplt.xlabel(\"trakus index\")\nplt.ylabel(\"cluster angle/course angle\")\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:50:57.350621Z","iopub.status.busy":"2022-11-07T17:50:57.350030Z","iopub.status.idle":"2022-11-07T17:50:58.551274Z","shell.execute_reply":"2022-11-07T17:50:58.550072Z","shell.execute_reply.started":"2022-11-07T17:50:57.350588Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"It clearly shows that winners (the blue line with label ranking 1) keep minimal ratio of cluster angle to course angle all the time. It is lower than other racers on average. It means that they are the ones who control their relative positions in the cluster the best in a race. They are not necessarily the ones who always lead in the horse cluster.","metadata":{}},{"cell_type":"markdown","source":"The strong control capacity of winners could be more easily seen in the phase angle figures. The idea of phase angle has been introduced in section 3.1. The comparison shows that winners do follow a better rhythm in a race, while other racers have much higher variation and less control over their relative positions.","metadata":{}},{"cell_type":"code","source":"#(7) Phase angles: Winner vs NO.5th\n\nplt.figure(figsize =(22,6))\nplt.subplot(121)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==1)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_angle_course2\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_angle_course2, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"Winners' Phase Angles\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"Phase Angle\")\n\nplt.subplot(122)\nfor i in [\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"10\"]:   \n    a = result_df[(result_df[\"position_at_finish\"]==5)&(result_df[\"program_number\"]==i)]\n    d = pd.DataFrame(a.groupby([\"trakus_index\"])[\"arccos_angle_course2\"].mean()).reset_index()\n    d = d[d.trakus_index <= 400]\n    plt.plot(d.trakus_index, d.arccos_angle_course2, label = f\"Racer {i}\")\nplt.legend()\nplt.title(\"No. 5th's Phase Angles\")\nplt.xlabel(\"trakus_index\")\nplt.ylabel(\"Phase Angle\")\nsns.despine()\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:50:58.553224Z","iopub.status.busy":"2022-11-07T17:50:58.552876Z","iopub.status.idle":"2022-11-07T17:51:06.818308Z","shell.execute_reply":"2022-11-07T17:51:06.817513Z","shell.execute_reply.started":"2022-11-07T17:50:58.553191Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"del test_all\ngc.collect()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:06.820347Z","iopub.status.busy":"2022-11-07T17:51:06.819779Z","iopub.status.idle":"2022-11-07T17:51:07.842208Z","shell.execute_reply":"2022-11-07T17:51:07.840997Z","shell.execute_reply.started":"2022-11-07T17:51:06.820313Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"del result_df\ngc.collect()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:07.844410Z","iopub.status.busy":"2022-11-07T17:51:07.843785Z","iopub.status.idle":"2022-11-07T17:51:08.609842Z","shell.execute_reply":"2022-11-07T17:51:08.608633Z","shell.execute_reply.started":"2022-11-07T17:51:07.844376Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"#### 3.2(b) Theoretical Insight - Fourier Transform","metadata":{}},{"cell_type":"markdown","source":"The theoretical insight of the \"orbit model\" is essentially called the \"Fourier Transform.\" *A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively.* (Wikipedia) ","metadata":{}},{"cell_type":"markdown","source":"Fourier transform is a method to decompose a time-series signal into a frequency domain. Namely, input a time domain data and output a frequency domain data. Therefore, we could see the main frequencies composed the input signal. The theoretical support of the method is \"Fourier integral expansion.\" Intuitively, it says that every signal could be decomposed to the sum of a list of Sine functions. Their starting phase angle and frequency determine the final signal. I do not want to dive too deep in mathematics in the report. Next, I will use an example to show how to adopt the method to study our horse races. ","metadata":{}},{"cell_type":"markdown","source":"Once again, to make it clear and simple, I use the AQU dirt course race, race 1 on 2019.1.1 as an example to illustrate the idea. We have seen the process of the race in the above dynamic figures. In the following analysis, I compute the \"speed\", \"acceleration\", and \"speed ratio\" of each horse at every trakus index. The \"speed ratio\" is defined as the speed at time t divided by the speed at time t-1. The trends of these variables are plotted as follows.","metadata":{}},{"cell_type":"code","source":"#(8) Race Example: AQU Dirt Course Race 1 on 2019.1.1 (Speed, acceleration, speed ratio plots)\n\ntest=  df[df[\"race_id\"] =='AQU_2019-01-01_1' ]\ntest[\"accelation\"] = df['speed'].diff()/0.25\ntest[\"accelation_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"accelation\"].shift(1)\ntest[\"speed_prev\"] = test.groupby([\"race_id\",\"program_number\"])[\"speed\"].shift(1)\ntest[\"speed_ratio\"] = test[\"speed\"] /  test[\"speed_prev\"]\ntest[\"accelation_ratio\"] = test[\"accelation\"] /  test[\"accelation_prev\"]\n\nplt.figure(figsize=[22,6])\nplt.subplot(131)\nsns.lineplot(data=test\n             ,x='trakus_index',y='speed'\n             ,hue='program_number'\n             ,marker='.');\nplt.title(\"Speed Plot of AQU Dirt Race 1 on 2019.1.1\", fontsize = 10)\nsns.despine()\n\nplt.subplot(132)\nsns.lineplot(data=test\n             ,x='trakus_index',y='accelation'\n             ,hue='program_number'\n             ,marker='.');\nplt.title(\"Acceleration Plot of AQU Dirt Race 1 on 2019.1.1\", fontsize = 10)\nsns.despine()\n\nplt.subplot(133)\nsns.lineplot(data=test[test[\"trakus_index\"] >2]\n             ,x='trakus_index',y='speed_ratio'\n             ,hue='program_number'\n             ,marker='.');\nplt.title(\"Speed Ratio Plot of AQU Dirt Race 1 on 2019.1.1\", fontsize = 10)\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:08.611793Z","iopub.status.busy":"2022-11-07T17:51:08.611138Z","iopub.status.idle":"2022-11-07T17:51:10.486241Z","shell.execute_reply":"2022-11-07T17:51:10.484941Z","shell.execute_reply.started":"2022-11-07T17:51:08.611755Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"\"Speed\", \"Acceleration\", and \"Speed Ratio\" are all time-series variables, I consider them as \"signals\". My target essentially is to find the difference between the signals of winners and losers in a race. Time-series(time domain) data is messy, therefore I use the method of \"Fourier transform\" to convert these data from a time domain into a frequency domain to see the nature of the signals. I plot the frequencies of the \"Speed Ratio\" for all the racers below.","metadata":{}},{"cell_type":"code","source":"#(9) Race Example: Time Domain to Frequency domain\n\nplt.figure(figsize = (16,6))\nfor j in range(1,6): \n    a = test.pivot(index = \"trakus_index\", columns = [\"program_number\"], values = [\"speed_ratio\"]).iloc[2:,:].reset_index()\n    x = a.iloc[:,0].values\n    y = a.iloc[:,j].values\n\n    f = abs(np.fft.fft(y))\n    num = np.size(x)\n    freq = [i/num for i in list(range(num))]\n    spectrum=f.real*f.real+f.imag*f.imag\n    nspectrum=spectrum/spectrum[0]\n    plt.semilogy(freq,nspectrum, label = a.columns[j])\n    plt.legend()\nplt.title(\"Frequency Domain Plot of AQU Dirt Race 1 on 2019.1.1\" ,fontsize = 20)\nplt.xlabel(\"frequency\")\nplt.ylabel(\"log(spectrum of speed ratio)\")\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:10.488348Z","iopub.status.busy":"2022-11-07T17:51:10.487909Z","iopub.status.idle":"2022-11-07T17:51:11.163000Z","shell.execute_reply":"2022-11-07T17:51:11.161783Z","shell.execute_reply.started":"2022-11-07T17:51:10.488309Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"The above figure indicates that racers' signals are very different in the frequency domain. Recall that the result of the race is Racer 5 > Racer 1 > Racer 2 > Racer 3 > Racer 4. Racer 5 is the winner and Racer 4 is the last. The winner(the purple line) is smoother than the loser(the red line.) This tells us the essential difference between winners and losers. **Winners have smoother frequencies in speed evolution. Namely, they prefer to change speed at a constant rate, rather than a sudden speed up or slow down. This is the reason why they have better control over relative positions.** In fact, this pattern is observed in the majority of races.","metadata":{}},{"cell_type":"markdown","source":"**The winner appears to be the first to cross the finish line but is the one who precisely controls his relative position in the race by changing his speed smoothly.**","metadata":{}},{"cell_type":"markdown","source":"If we compare the theoretical curve with the winners' curve we observed. Winners follow the \"orbit model.\" The comparison plot shows as follows. ","metadata":{}},{"cell_type":"markdown","source":"![Fourier%20Transform%20Data%20Comparison.jpg](attachment:Fourier%20Transform%20Data%20Comparison.jpg)","metadata":{},"attachments":{"Fourier%20Transform%20Data%20Comparison.jpg":{"image/jpeg":"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3.3 Interpretation and further discussion","metadata":{}},{"cell_type":"markdown","source":"If you are not convinced by the above findings, it does not matter. Let me give you another example to show the idea. Suppose you're throwing a round frisbee, and you want to use it to hit a bottle on a table 200 meters away. Now you mark a big red point on the edge of your frisbee, you want to hit the bottle by this red point. Is it feasible, or is it even possible? I guess the answer is yes. It is possible. But the hard question is \"how\"? ","metadata":{}},{"cell_type":"markdown","source":"Once you throw your frisbee, it probably will fly in a round track, if we assume you are super lucky and hit the bottle by the red point you marked. How did it happen? I guess you chose a \"correct\" angle, and a \"correct\" starting speed. If you think this story through, it is very similar to horse races. the red point on frisbee is the winner horse. The bottle is your final goal line of a race. The track of frisbee is the course track. Essentially, the red point hit the bottle first means he/she is the winner. Since the frisbee's result can be controlled by starting angle and speed, the horse race should be similar. ","metadata":{}},{"cell_type":"markdown","source":"**Namely, the relative positions at starting line is even more important than we thought, it is not only inner rail or outer rail issues. It indicates that some starting positions may exist an invincible winning strategy. As long as you know it and successfully execute it in a real race, you are always guaranteed to win(like the strategy we see in the small game in section 1.1).**","metadata":{}},{"cell_type":"markdown","source":"Just like the case in the frisbee example, once you know the \"correct\" starting angle and \"correct\" starting speed, and practice it to make sure you could successfully do it every time, you can significantly increase your chance to hit the bottle. This example also shows why we saw more winners exceed others on the bending curve from the outer rail. Because they somehow know that this is more efficient. Just like the direction of the earth's revolution and rotation are the same, horses are easier to exceed from the outer rail. It is also a byproduct of the \"orbit model.\" ","metadata":{}},{"cell_type":"markdown","source":"There are some limitations in the simple model. For example, the cluster of horses is not a standard circle, the course shape is also not a standard ellipse. In addition, racers will not retreat on purpose to circle the cluster when they take the leading position. These are all the limitations of the model. But the main topic of the report is \"relative position\". Firstly, the spirit I want to share with you is that catch the fundamental factors, like the \"law of motion\", rather than focus on too many micro-level details. In a fierce game like a horse race, analysis with a game theory style is more feasible. Looking at the big picture will provide us with more insights. Secondly, winning does not mean a racer should always lead in a race. control of the relative position in a cluster is essentially the key to winning. Lastly, sometimes we take everything for granted and ignore the existence of many fundamental factors. In the example of the horse race, the final goal line is so attractive that everyone rushes to run, and they ignore the essence of the track, horses are running around the center of the course. Thus the distance to the center and the angles shaped with the center are important.These are the things I called \"fundamental factors\". My poor physics knowledge is not enough for me to create a good theoretical model, but the idea is illustrated.","metadata":{}},{"cell_type":"markdown","source":"**In a race where everyone pursues fast speed, the one who can best balance fast and slow is the ultimate winner. This is the philosophy of winning horse races.**","metadata":{}},{"cell_type":"markdown","source":"# Section 4 Data Analysis","metadata":{}},{"cell_type":"markdown","source":"### 4.1 Data Preparation","metadata":{}},{"cell_type":"markdown","source":"I use some mainstream machine learning models to train the 2000 horse races from NYRA in 2019. I manage the data first in 3 steps.\n\n(1) Get the race data\n\n(2) Generate relative position variables in form of angles. Here I compute the \"azimuth\", and \"Phase angle of each horse at starting point\".\n\n(3) Group variables into the numerical variable group and categorical variable group, and generate dummy variables for the categorical variables.","metadata":{}},{"cell_type":"markdown","source":"The \"azimuth\" is the angle between North, measured clockwise around the observer's horizon, and a celestial body (sun, moon). \nThe \"Phase angle of each horse at starting point\" is the angle of each horse at starting point relative to the center of the course. I use the latitude and longitude of each player at trakus index 1 to approximate their starting positions. Also, I checked the latitude and longitude of the center of each course to approximate the central point of the course. More details are shown as follows.","metadata":{}},{"cell_type":"code","source":"# Define the functions\nfrom math import sin,cos,atan2, pi\n\ndef calcu_azimuth(lat1, lon1, lat2,lon2):\n    \n    lat1_rad = lat1 * pi / 180\n    lon1_rad = lon1 * pi / 180\n    lat2_rad = lat2 * pi / 180\n    lon2_rad = lon2 * pi / 180\n    \n    y = sin(lon2_rad - lon1_rad) * cos(lat2_rad)\n    x = cos(lat1_rad) * sin(lat2_rad) - sin(lat1_rad) * cos(lat2_rad) * cos(lon2_rad - lon1_rad)\n    brng  = atan2(y,x)/ pi * 180\n    return float((brng + 360.0) % 360.0)\n\ndef distance(lat1,long1,lat2,long2):\n    long1=long1*pi/180\n    long2=long2*pi/180\n    lat1=lat1*pi/180\n    lat2=lat2*pi/180\n    d=math.sqrt((math.cos(lat2)*(long2-long1))**2+(lat2-lat1)**2)\n    return d*6371*1000\n\ndef cos_angle(latA, longA, latB, longB, latC, longC):\n    \n    a = distance(latB,longB, latC, longC)\n    b = distance(latA,longA, latC, longC)\n    c = distance(latA,longA, latB, longB)\n    cos_angle = (a**2 + b**2 - c**2)/(2*a*b)\n    return cos_angle","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:11.165667Z","iopub.status.busy":"2022-11-07T17:51:11.164702Z","iopub.status.idle":"2022-11-07T17:51:11.179008Z","shell.execute_reply":"2022-11-07T17:51:11.177830Z","shell.execute_reply.started":"2022-11-07T17:51:11.165622Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df[\"race_date\"] = pd.to_datetime(df[\"race_date\"])\n\ndf[\"year\"] = df[\"race_date\"].dt.year\ndf[\"month\"] = df[\"race_date\"].dt.month\ndf[\"day\"] = df[\"race_date\"].dt.day\ndf[\"weekday\"] = df[\"race_date\"].dt.weekday\n\ndf[\"hour\"] = df[\"post_time\"].apply(lambda x: int(str(x)[0:2])  if len(str(x)) == 4 else int(str(x)[0]))\ndf[\"hour\"] = df[\"hour\"].apply(lambda x: x  if (x == 11)|(x == 12)  else x + 12)\ndf[\"minute\"] = df[\"post_time\"].apply(lambda x: int(str(x)[-2:]) )\n\nnum_racers = pd.DataFrame(df.groupby(\"race_id\")[\"program_number\"].nunique()).reset_index()\nnum_racers.columns =[\"race_id\",\"num_players\"]\ndf = df.merge(num_racers, on = \"race_id\")\ndf","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:11.185914Z","iopub.status.busy":"2022-11-07T17:51:11.185226Z","iopub.status.idle":"2022-11-07T17:51:49.559991Z","shell.execute_reply":"2022-11-07T17:51:49.558902Z","shell.execute_reply.started":"2022-11-07T17:51:11.185872Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (1) Get race data\nrace_df = df[df[\"trakus_index\"] == 1]\n\n# (2) generate angles.\n\ncourse_center_lat_dict = {\"AQU\": 40.67243,\"BEL\": 40.71531, \"SAR\":43.07168}\ncourse_center_long_dict = {\"AQU\": -73.82943,\"BEL\": -73.72266, \"SAR\": -73.76841}\nrace_df[\"course_center_lat\"] = race_df[\"track_id\"].map(course_center_lat_dict)\nrace_df[\"course_center_long\"] = race_df[\"track_id\"].map(course_center_long_dict)\n\nmean_long = pd.DataFrame(race_df.groupby([\"race_id\"])[\"longitude\"].mean() ).reset_index()\nmean_long.columns = [\"race_id\",\"mean_start_long\"]\n\nmean_lat = pd.DataFrame(race_df.groupby([\"race_id\"])[\"latitude\"].mean() ).reset_index()\nmean_lat.columns = [\"race_id\",\"mean_start_lat\"]\n\nrace_df = race_df.merge(mean_long, on = \"race_id\")\nrace_df = race_df.merge(mean_lat, on = \"race_id\")\nrace_df[\"angle_earth\"] = race_df[[\"mean_start_lat\",\"mean_start_long\",\"latitude\",\"longitude\"]].apply( lambda x: calcu_azimuth(x[0],x[1],x[2],x[3]) ,axis =1 )\nrace_df[\"angle_course\"] = race_df[[\"latitude\",\"longitude\",\"mean_start_lat\",\"mean_start_long\",\"course_center_lat\",\"course_center_long\"]].apply(lambda x:cos_angle(x[0],x[1],x[2],x[3],x[4],x[5]) , axis = 1)\nrace_df[\"arccos_angle_course\"] = race_df[\"angle_course\"].apply(lambda x: 180*(np.arccos(x))/pi )\n\n# (3) Group variables\n\nrace_df[\"program_number\"] = race_df[\"program_number\"].astype(np.int8)\n\ncategory_features = ['track_id','course_type', 'track_condition', 'race_type']\ndummy_df = pd.get_dummies(race_df[category_features])\nfinal_df = pd.concat([race_df, dummy_df], axis = 1)\nhist_rank_dict  = {1: \"P1\",2:\"P2\",3:\"P3\"}\nfinal_df.rename(columns = hist_rank_dict, inplace = True)\nfinal_df = final_df.reset_index(drop = True)\nnum_features = ['race_number','program_number','latitude', 'longitude','distance_id','run_up_distance','purse','weight_carried','odds','number_of_rides',\n               'P1','P2','P3','year','month','day', 'weekday','hour','minute','num_players', 'course_center_lat','course_center_long', 'mean_start_long',  \n                'mean_start_lat','angle_earth', 'angle_course', 'arccos_angle_course']\n                      \ndummy_features = dummy_df.columns.tolist()\nprint( \"Numerical Variables:\" , num_features)\nprint( \"Categorical Variables:\" , dummy_features)\n\n# Finally, generate the X, y dataset\n\nX = final_df[num_features +dummy_features + [\"race_id\"]]\ny = (final_df[\"position_at_finish\"] == 1)\nX.fillna(0, inplace = True)\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:49.561871Z","iopub.status.busy":"2022-11-07T17:51:49.561530Z","iopub.status.idle":"2022-11-07T17:51:54.187124Z","shell.execute_reply":"2022-11-07T17:51:54.186246Z","shell.execute_reply.started":"2022-11-07T17:51:49.561840Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### 4.2 Random Forest Model","metadata":{}},{"cell_type":"markdown","source":"I begin my explanation with the illustration of a random forest model, one of the most famous and efficient machine learning models. I choose this model because I want to show the feature importance of the variables first. The result is below.","metadata":{}},{"cell_type":"code","source":"# random forest model\nfrom sklearn.ensemble import RandomForestClassifier\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)\nX_train = X_train.drop([\"race_id\"], axis = 1)\nX_test = X_test.drop([\"race_id\"], axis = 1)\n\nclf_rf = RandomForestClassifier(n_estimators = 800, max_depth = 300, max_features=\"sqrt\")\nclf_rf.fit(X_train, y_train)\ny_pred_rf = clf_rf.predict(X_test)\naccuracy_rf = accuracy_score(y_test,y_pred_rf)\nprint(f\"The prediction accuracy of Random Forest Model on Test data is: {accuracy_rf * 100:.3f} %\")\n","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:51:54.189127Z","iopub.status.busy":"2022-11-07T17:51:54.188197Z","iopub.status.idle":"2022-11-07T17:52:15.416243Z","shell.execute_reply":"2022-11-07T17:52:15.414981Z","shell.execute_reply.started":"2022-11-07T17:51:54.189091Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Feature importance table\nfeature_imp =pd.DataFrame(clf_rf.feature_importances_, index= X_train.columns, columns = [\"feature_importance\"]).sort_values(\"feature_importance\", ascending = False)\nfeature_imp","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:52:15.418650Z","iopub.status.busy":"2022-11-07T17:52:15.418165Z","iopub.status.idle":"2022-11-07T17:52:15.549561Z","shell.execute_reply":"2022-11-07T17:52:15.548585Z","shell.execute_reply.started":"2022-11-07T17:52:15.418608Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Feature importance plot\n\nplt.figure(figsize = (12,10))\nsns.barplot(x= feature_imp[\"feature_importance\"], y =  feature_imp.index)\nplt.xlabel('Feature Importance Score')\nplt.ylabel('Features')\nplt.title(\"Visualizing Important Features (Random Forest Model)\", fontsize = 20)\nplt.legend()\nplt.show()\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:52:15.551664Z","iopub.status.busy":"2022-11-07T17:52:15.551011Z","iopub.status.idle":"2022-11-07T17:52:16.628003Z","shell.execute_reply":"2022-11-07T17:52:16.626865Z","shell.execute_reply.started":"2022-11-07T17:52:15.551628Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"From the results above, the random forest model provides a prediction accuracy of 86% ~ 87%, it is not surprising to see that the \"odds\" is the most important variable. But we do find some interesting patterns.\n\n(1) Angle variables like azimuth (\"angle_earth\"), phase angle(\"arccos_angle_course\", \"angle_course\") are more important than other variables like the winning records of the jockey, like winning rate(\"P1\"), second placement rate(\"P2\"), third placement rate(\"P3\")\n\n(2) Schedule variables like \"minute\", and \"day\" are also important to the race's result. these variables are also more important than the effect from jockeys like \"P1\", \"P2\", etc. This finding is in line with the literature. Specifically, Shuang Zhang mentioned the importance of schedule in the paper \"Optimal Model of Horse Racing Competition Decision Management Based on Association Rules and Neural Network\"(link is listed in the reference section). He found that the order of important features is:\n\nrace schedule > age > gender > weight > rating > horse top three rate > jockey > weight load > harness > ranking > field nature > field > trainer.","metadata":{}},{"cell_type":"markdown","source":"Comparing the random forest results with the literature, many of the findings are consistent. The model results agree with the literature that the effect of schedule >  jockey > weight carried > field nature and conditions. I could not check the other features like the age, and gender of the horse due to the lack of horse-level data. But I find that there are some more important features than schedule (1) Odds (2) Starting Angles (azimuth, and phase angle). These angle variables show the relative position of the horses to the course, and the earth.","metadata":{}},{"cell_type":"markdown","source":"Previous literature all focus on the pathing and tracking tactics, like how to optimize their speed during a race, but neglect that effects of nature(schedule, azimuth) are far more important than the effect of humans(jockey winning rate, field, etc.)","metadata":{}},{"cell_type":"markdown","source":"### 4.3 Machine Learning Model Screening ","metadata":{}},{"cell_type":"markdown","source":"I continue to precede by screening around 20 machine learning models. The task of this section is to check the prediction accuracies of these mainstream machine learning models.  I follow 3 steps to proceed.\n\n(1) Train race data by using mainstream machine learning models.\n\n(2) Ensemble models' predictions by majority voting.\n\nI split the race data into train and test datasets. Test data takes 30% and train data takes 70%. I choose 5 folds to do the cross-validation. The corresponding model name, parameters, training accuracy, and testing accuracy are all shown as follows.","metadata":{}},{"cell_type":"code","source":"# (1) Model Screening\nmodels = [\n    ensemble.AdaBoostClassifier(),\n    ensemble.BaggingClassifier(),\n    ensemble.GradientBoostingClassifier(),\n    ensemble.RandomForestClassifier(),\n    \n    gaussian_process.GaussianProcessClassifier(),\n    \n    linear_model.LogisticRegressionCV(),\n    linear_model.PassiveAggressiveClassifier(),\n    linear_model.RidgeClassifier(),\n    linear_model.SGDClassifier(),\n    linear_model.Perceptron(),\n    \n    naive_bayes.BernoulliNB(),\n    naive_bayes.GaussianNB(),\n    \n    neighbors.KNeighborsClassifier(),\n    \n    svm.SVC(probability = True),\n    svm.LinearSVC(),\n    \n    tree.DecisionTreeClassifier(),\n    tree.ExtraTreeClassifier(),\n    \n    discriminant_analysis.LinearDiscriminantAnalysis(),\n    discriminant_analysis.QuadraticDiscriminantAnalysis(),\n    \n    XGBClassifier(),\n    LGBMClassifier(),\n    MLPClassifier()\n]\n\n# Training & cross-validation\n\ncv_split = model_selection.ShuffleSplit(n_splits = 5, test_size = 0.3, random_state = 0)\n    \nmodels_columns = [\"Model Name\",\"Model Parameters\",\"Train Accuracy Mean\",\"Test Accuracy Mean\",\"Test Accuracy 3STD\",\"Training Time\"]\nmodels_compare = pd.DataFrame(columns = models_columns)\n\nX_model = X.drop([\"race_id\"], axis = 1)\n\nrow_index = 0\n\nfor alg in models:\n    \n    models_name = alg.__class__.__name__\n    models_compare.loc[row_index, \"Model Name\"] = models_name\n    models_compare.loc[row_index, \"Model Parameters\"] = str(alg.get_params())\n    \n    cv_results = model_selection.cross_validate(alg, X_model, y, cv = cv_split, return_train_score = True )\n    models_compare.loc[row_index, \"Training Time\"] = cv_results[\"fit_time\"].mean()\n    models_compare.loc[row_index, \"Train Accuracy Mean\"] = cv_results[\"train_score\"].mean()\n    models_compare.loc[row_index, \"Test Accuracy Mean\"] = cv_results[\"test_score\"].mean()\n    \n    models_compare.loc[row_index, \"Test Accuracy 3STD\"] = models_compare.loc[row_index, \"Test Accuracy Mean\"] - cv_results[\"test_score\"].std()*3\n    \n    row_index += 1\n    \nmodels_compare.sort_values(by = [\"Test Accuracy Mean\"], ascending = False, inplace = True)\nmodels_compare","metadata":{"execution":{"iopub.execute_input":"2022-11-07T17:52:16.630116Z","iopub.status.busy":"2022-11-07T17:52:16.629725Z","iopub.status.idle":"2022-11-07T18:08:23.542238Z","shell.execute_reply":"2022-11-07T18:08:23.540622Z","shell.execute_reply.started":"2022-11-07T17:52:16.630084Z"}},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"plt.figure(figsize = (12,8))\nsns.barplot(x = \"Test Accuracy Mean\", y = \"Model Name\", data = models_compare,color = \"green\")\nplt.title(\"Machine Learning Algorithm Accuracy Score\")\nplt.xlabel(\"Accuracy Score\")\nplt.ylabel(\"Algorithm\")\nsns.despine()","metadata":{"execution":{"iopub.execute_input":"2022-11-07T18:08:23.545424Z","iopub.status.busy":"2022-11-07T18:08:23.544558Z","iopub.status.idle":"2022-11-07T18:08:24.037656Z","shell.execute_reply":"2022-11-07T18:08:24.036373Z","shell.execute_reply.started":"2022-11-07T18:08:23.545362Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"From the table above, it is clear that most of the machine learning models have 86% ~ 87% prediction accuracy on test data. This is very similar to the result of the random forest model. In addition, the possible minimum prediction accuracies on test data \"Test Accuracy 3STD\" for these models are slightly above 86%. These models provide similar results.","metadata":{}},{"cell_type":"code","source":"# (2) Majority Voting.\ngood_features = ['odds','angle_earth','latitude', 'longitude','arccos_angle_course','angle_course','program_number','minute', 'hour','day', 'month','P1']\n\nvote_est = [(\"GradientBoostingClassifier\",ensemble.GradientBoostingClassifier()),\n            (\"BernoulliNB\",naive_bayes.BernoulliNB()),\n            (\"PassiveAggressiveClassifier\",linear_model.PassiveAggressiveClassifier()),\n            (\"SVC\",svm.SVC(probability = True)),\n            (\"LogisticRegressionCV\",linear_model.LogisticRegressionCV()),\n            (\"LinearDiscriminantAnalysis\",discriminant_analysis.LinearDiscriminantAnalysis()),\n            (\"RandomForestClassifier\",ensemble.RandomForestClassifier()),\n            (\"LGBMClassifier\",LGBMClassifier() ),\n            (\"RidgeClassifier\",linear_model.RidgeClassifier()),\n            (\"MLPClassifier\", MLPClassifier())    ]\n\ncv_split = model_selection.ShuffleSplit(n_splits = 5, test_size = 0.3,  random_state = 0)\nX_good = X[good_features]\n\ngrid_hard = ensemble.VotingClassifier(vote_est, voting = \"hard\")\ngrid_hard_cv = model_selection.cross_validate(grid_hard, X_good, y, cv = cv_split, return_train_score = True )\n\nprint(\"Hard Voting Tuned Training Score Mean:{:.2f}\".format(grid_hard_cv[\"train_score\"].mean()* 100))\nprint(\"Hard Voting Tuned Testing Score Mean:{:.2f}\".format(grid_hard_cv[\"test_score\"].mean()*100))\nprint(\"Hard Voting Tuned Testing Score +/- 3STD:{:.2f}\".format(grid_hard_cv[\"test_score\"].std()*100*3))","metadata":{"execution":{"iopub.execute_input":"2022-11-07T18:08:24.040365Z","iopub.status.busy":"2022-11-07T18:08:24.039627Z","iopub.status.idle":"2022-11-07T18:10:38.392204Z","shell.execute_reply":"2022-11-07T18:10:38.390898Z","shell.execute_reply.started":"2022-11-07T18:08:24.040318Z"}},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"**Using the selected features, the ensembled model provides a testing accuracy of around 87%. This shows the importance of starting positions. \nWithout knowing the spatial position data during the game, the spatial and temporal data of the starting position alone can provide an 87% prediction accuracy.**","metadata":{}},{"cell_type":"markdown","source":"### 4.4 Insights","metadata":{}},{"cell_type":"markdown","source":"The results show that the effect of nature-level variables like azimuth, phase angle, and schedule is larger than the effect of individual-level variables like winning rate, weight carried, field, etc. It looks messy, but I say that they share the same essential concept \"Relative Position\". Let's discuss them one by one.\n\n(1) Azimuth: It represents the relative location of the horses at the starting point(trakus index = 1). it is a measurement in a spherical coordinate system. It is the horizontal angle from the north. Essentially, it is the relative position vector from an origin to a point of interest that is projected perpendicularly onto a reference plane. The angle between the projected vector and a reference vector on the reference plane is called the azimuth(This is the explanation from Wikipedia) See the figure attached below.\n\n(2) Phase angle: This one is straightforward, it means the position of the horse at the starting point(trakus index = 1) relative to the center point of the course(the center of the ellipse approximately). Here I also compute the mean of all the players' latitude and longitude in a given race, this \"mean start point\" is the reference point. So the phase angle essentially tells us the relative position of each horse to the center of the course at the beginning of the race.\n\n(3) Schedule(day, minute, hour, etc.): This one is little bit confusing? why schedule(date, time) is also relative position? Recall that how we define time originally, people observe the cycle of different celestial bodies. For example, The Earth orbits around the sun every 365 days, people define the concept of \"year\" in this way originally. Similarly, the moon takes about 27 days to orbit Earth. The concept \"Month\" is defined then. My point here is  \"Time is essentially a spatial concept\". We could not see it because we are living in a 3D world, we could only see length, width, and height(only 3 orthogonal axes). We could treat time(like date, minute, hour, second) as the unique identification of the 4th axis, it records the combination of the celestial bodies' locations and their effects on individuals like you and me. So two different dates mean two different combined effects of these celestial bodies(like the sun, the moon, etc.). This effect is periodic, and the effect of the celestial bodies on individuals is so strong that it essentially plays an important role in our destinies. This is the research interest of Astrology. It is not the topic of the report, but I want to emphasize that the schedule essentially represents the relative positions of celestial bodies' locations.\n\n\n(4) Program number： Program number is also counterintuitive. A number is only an id, why it is also informative? This is because it represents the gate position from which a horse will start in a race. Wait, is the program number the same as the post number(gate number)? Strictly speaking, the answer is NO. they are different, but when I look through the 2000 races in our dataset. I notice that majority of the races have horses ordered by their program number at trakus index 1. So I guess that the program number is used as the post number in these races. Meaning a horse with program number 1 starts the race from post1, and a horse race with program number 2 starts the race from post2. Since post 1 is the gate position closest to the inner rail, post 2 is the second slot from the rail, etc. We know that program number tells us whether a horse starts a race in the inner rail, middle rail, or outer rail. The difference in starting positions matters. Because horses in the inner rail have shorter running distances, their space might be extruded by the horses from the middle rail. Horses in outer rail have more freedom to choose their pathing tactics but have a longer distance to run. \n\n\n(5) Odds: odds essentially is the ranking of each horse in people's minds. It summarizes the historical performance of each horse or jockey. It also shows the expectation of people on each horse and jockey combination. So it represents the relative positions(ranking) of horses and jockeys.\n\n","metadata":{}},{"cell_type":"markdown","source":"![Azimuth.png](attachment:Azimuth.png)","metadata":{},"attachments":{"Azimuth.png":{"image/png":"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"}}},{"cell_type":"markdown","source":"# Section 5 Discussion","metadata":{}},{"cell_type":"markdown","source":"### 5.1 Discussion","metadata":{}},{"cell_type":"markdown","source":"The topic of the report is to learn the laws of nature and follow them. Like the small game I introduce at the beginning, once Player 1 learns the invincible strategy, he/she could never lose(of course based on the assumptions of the game). In our realistic world, we may not have such a perfect law to follow and keep winning forever, but I believe there are some critical \"laws of nature\" to follow, at least not violate. \n \n Automatically, we can not help asking： what are the \"laws of nature\"? Honestly, I do not know. My limited physics knowledge is not enough to answer such a question. But I observe the world we live in and have some feelings. I will summarize them by two keywords. \"rotation\" and \"recursion algorithm\". \n \nI believe that if we want to see the essence of the world, we need to look at phenomena that are extremely large or extremely small. Because they are too large or too small for people to affect. they are less manipulated by humans and they are closest to the original laws of nature. By looking at large phenomena like the dynamic path of celestial bodies, and small phenomena like the moving of electrons. We see extremely similar laws. They all show the pattern of \"rotation\" and \"recursion\". In the end, each planet or electron runs in its orbit, coexists, and presents an excellent state of order.\n\nBack to our discussion of horse racing, horses are running on along an ellipse-like track, which looks like the Earth orbits the sun. The horses are moving together like a cluster around the center of the field. Imitating the moving pattern of the Earth might be helpful and interesting. So I introduced the orbiting model in section 3. \n","metadata":{}},{"cell_type":"markdown","source":"### 5.2 Relationship between Nature and Human","metadata":{}},{"cell_type":"markdown","source":"The report emphasizes the a healthy coexistence model between human and nature. It sounds like an empty slogan. Let's come back to horse racing context, and I will provide an example for it. \n\nIn the horse racing, every one is seeking higher speed, what does  the healthy coexistence mean here? Is it really helpful? The answer is YES! Pfau et al. (2009) wrote this finding in the paper “Modern Riding Style Improves Horse Racing Times.” *lifting jockey's leg off the horse in horse racing allows for the 5-7% improvement in race times. By lifting himself off the horse, the jockey is able to compensate for the jerking motion that occurs when the horse’s hooves hit the ground. Using his legs, the jockey is able to constantly keep his momentum moving forward, and thus reduce the work the horse must do.* This is also introduced by Nicholas (2012) in his paper \"Analysis Modeling and Optimization of a Smart Sulky.\" This finding suggests that jockeys and horses have a win-win relationship. Horse is the protagonist of a race. A jockey only plays a guiding role in the key positions of the race. After all, we are studying horse races, rather than jockey marathon races.  According to the dataset. Even the highest winning rate of jockeys is around 20%, majority of jockeys have winning rate far less than 20%, this means that even the best jockey can only win once out of 5 races. Since one race usually has 5 to 9 participants. 20% winning rate is really not that impressive. This is why I propose that jockey should choose the correct \"key positions\" to exceed.\n\n","metadata":{}},{"cell_type":"markdown","source":"### 5.3 Further Discussions about Horses","metadata":{}},{"cell_type":"markdown","source":"We have seen the importance of schedule and relative positions at the beginning of a horse race. It is intuitive to me. Because I know that schedule affects horses more than jockeys. Horses usually have their best state around noon time. This is the best time for a horse race. In addition, if we think it through, we will see that the \"relative positions\" actually affect horses' vision. \n\nLet me show the horse's vision angles. As shown in the figure below. Horses' eyes are on different sides of its face. Therefore they have binocular vision around 55-65 degrees in front of them, and monocular vision around 190-230 degrees on the left and right sides. It means that they have a small blind area in front of their face, and they have a relatively weak feeling of distance. Assume that this horse is running in the inner rail, and it wants to turn right, it means that its right-hand side is rail. Since the jockey needs to turn right, the horse needs to closer to the rail and adjust its head along the tangent direction. It affects the vision of the horse somehow. My point is horses slow down at turning points not only because they face a corner, but also because of their limited vision. Will a horse run at its highest speed at the corner with limited vision? The answer probably will be no. The jockey probably won't instruct the horse to do so. Therefore, exceeding other horses from the outer rail might be a better choice at the crucial point of a race. It is exactly what champions often 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WufgyRZKXWQJSPIzQ6kG+CNYUpJIZ49NGKydSMNUqTgccslwSCz6tD9Nz/z85z//mc98RhA1FUV/pqmTsWQkGIRG5Rg0lRHzFMb83e9+h+lmQQftu1S/OtZ4HHUm94JywHjuDpFMbwq+25DiMK1rH0fzYm5hyXqtUnE4tJKTvbPBtv8lGARspByiwUx/dmk8iNdS0q/xzhCyHVjKSvWQaVqrWbDU472tvt5vkW2gSo9x6ATskfLkOfF1cnuqgZmKw9lhl+bizhUfK3KnnXbKqH1/Rmm8hAkqIy8TiHEi9Se9jphGDUrKa0Yadukhhxyy6aabIp0Jxuq660BTtqbT3kYTfgRU9rA/AUBm36vwRSX3U29HlmJIXURuoR1EbEaDyXIjqI1nKg5nU5wmZ/RlgLTpVEt89atf/ehHP5q1wv0Zt/5X3AS0uGkwhoASXhbeTJDOIAoLVPs2bifSWTR044DptihNj64tR48MgF6HKMOsfdWrXqWowsk6dssNRu/TyOwN3bfBwHZXDPIybFNLmSoOZxMUy8xEhjQDnwItcMhRlOLvU5emggoGNrWmo24yAThaHuQxQikyt6dwaJoOBSfqpKJQA6Mt2v5HNQPyjWPuJS4b8lqUKZfua3cN0XQLIV+2kIubu1J4rXWRVBzOGWQmoaTp6bRtjmJTxFcjiNIUsX5ajn8IObvvvnuCNuqAIYqlp1gB6SyakQr/eFxjRbB0wABmiDqARs/SjY5dJBRj5vG72yUxW04FGmMwTmwT0Q2g6+9YpeJw5iQIXLH++H6sUwATuSl9yLIUPV6F8wk/YZQ2nRGotJlHMD/NY6MbZeS0NuWGKezwOOb3Xnvtteqqq+Jngxz1qGkVJjc8hBZF7nGghWkSA7plJYbXF9kaB97CrUbKPoO0pbavUnE4x/zGzGpQXyjaivp4jGmzRXleICSO0bKNH+NMhsIUaFWFeG5HtNmXYPRs00kkOvCIOgwg11bDAAyKKMh03sKfXEpJS1B0jvLFSOiX7J8XHqBKjPE/dSKVqMimIQHORGmNl1YczgFpEcpCOdAYVFMEEstYThbptaYp9hdQmbV2FYGKvKtu7TVhkSrepww1B8gHgz9QDm+qq6LicA6IVRgthtMbpOuURMkoqu5LBAYPLmhoZXvPdKsyR18Oxw0ia9mpvlR02f40t4OSE9fd3oSub9aNQG52ssoMarYtrqZpxeGcjNNY7gy2nB/sceW5SgdZpzF/IvssZhl7a852jgGOl0fsMUZzlwM60xQMLlsYulH6lLTvMlTTRVSYZErJS3U2PXXDrRExtdSw4nDOh2qi02lpYQZPLdy87G8fGiygkmqwldWI9R1nZlf81lCkTJ+UIcqy0q+cdD2zO0tvOIG64JOeAOGXloNryq2hgrDicNgJPaaZmrYxkZkos47Z8X5YTfxL8zLq/fM+BYGwCFik2D8J7xqPqTgcSXoS8eXjH/+40orWJKaMwQwfWy691hR/qtkXm8FKR4utP2jF4QiT1HLy8tLroJhxlIwuDs8JuOmmhjKMKTEymU0xJ6O2YKs4HBmSRUCWrIL9aEzaW/sNt1qhlsEp8CsXijlgN2l60oPpDdZfueJwBOjDDJPIaqgVDuu06VUZOKxijOVwbBapbm7CM5ktzEBU5ZFWHI4YfVjyTqOlr47dTU9Us5l+WO8wAWHONlXbYS6V2EyAsJzNlGMhq1QcjgApM+n+l8bQMjjyb5lFHG4LOvcO8zBsHLqA5+OZDnmBwzCqVBzOmZWdWUGttVG0Y8rabGjlNMNtoumJJ5Xzg5vOzDZtONRDaopTBm+aojFHudcM0sZO/d870lOOUq1rpuKw+45WubAUYVAy2mfk4p6DHJTQ1WkhZ/VguIXIQIjj+VnKjhtNQUsoqd4D89pybGO2tItvJrORmVMd6snhFYejDoetkbeWOHYYVkqQbFoTRWezZMe3IMeGOcotZD+bBhdtOCJAWrJ8ShJCCapsxDowDvM7Se1Xato8oeKw4rD7LmK5qqxazWn0sEi+25yyxHKPiGb7oc2iYYcxjAmSkoyeOjA/UTxYlgIP8FVk6+S0yVuRqup2VhwOORpzkSkmtNaRVHIpz34oBmySURDKUKs4/W+MplEmUiq6kgOUyjCrQMqP0N+2kt5g+T20mOJZUlyl4rDL3lfZ/ztDFOia4pDq6E866aQykDP7o0cBpCjIUt3PcdVFTvuphGjqqz6hVcJmhsmMVolJWcMVacn0POtQmorDburA0vcre73FKl9uueViEnAzJ6Km+Y5xk7pvsJZNYotxiJAQw6HSYizH15S9/ePPAK2XDODrlmGhAF7Z7zjV6SyMYaw4rDKDtd7yr5oisq99hjbeCy644EUXXTSnNHYea88Ro1GbovNV/B+n6ZIqrb9KR2RfdHxsOs1UWdcaWGmv6k97Co2aVcK9ReO5lVde2XX23HPPvIF8Cy2zdOUxsaeunIrD2aEkE5Oasln9Wrw1RbOpNNuG1GksIyJKliGQMoSrpidumY5fnOYp7QVe/OIXa/YhwqRjovaqFKbWVTkEUg9ljHa95AbQvSZ5OH/JJZcsg1ihRaPxXLBwB5ZWnWfv73buSEJWHA55zCbDJDrZSBIce+yxWVAfHTQioTfU9qo7weTWD45bqC9wy6LOMqi4W70F4ITmNNMbICnzpmfIDD3mbmVH/RlTU7VRZabiA3CGy7BQxKhiKE3ZA9bLJS1f9rKXmVVsFI9H+KtPdsQFw4N1WRdMCoEr20E0zmqK/ErL+qg4rNIvDlPvNZ2u2F/4whe0PwsaZ4Qoy+D+UG8HLEm98ZNtV45VjABm7gWAB34GWvz4xz+2d4QnGbxZSVHMG3jWlUfiUZEU5fajH/1IP5vFF1/81ltvjUnmWrZGD0imbDM9o8hcAHapt/CssK33NfPDRX7ckS233FIbO5dyTAO7PZjUvJyPLcUStZ2pKpu5pV1VxeHs8BtziZtc/5KXvMRk+eyJlo7T0C2miLtwxqggPchTX+VBGaShMyk3+4WTL7/8cgFVvVUNt2h6cjDsUncbXerYpXYThq5j/R1pUR3HzU72CJjxIT2uY3Iq5Agg06iLLbaYVujewpYUjSSdqU7lhBNOoK7f8573AKE5k07wpgbUYcBef/31eD9GwerL3PTwk8LCr3ZplRlHbuL/nFhq1Azvy8IKo6tMoA+dMPxMp1CNRV81xYyqst9M02k9Th0JsXzxi18EDJhxgo1Ds2PPgqUH6T3HBgFkl3HdkKPLuOvL0EQc6HOf+1ygS6imKbKRY8eO5SpDu/d1/qc//ekA5yte8Qp7RNOZuuNVCy20EAUovemLAmywFyV6wxveECo0to9spVX1YZUZxGmSmFLGGyxcQxGjC3jTM4d06O7EOhYsEZvRiThjM7F8S3MUVoVG2YSsSraoFc8QjRHIrERK0oyqqOf6/e9/z+x0rOW+TwEzjmk2AWEHMqUQpeO4yKo/KUZOZuhbOFdqzAr1vnrbvfnNb47mWsTBAgss4EzXedOb3qTZD6OXCc2BpCShlDULt07zZ/iQqWbnguRHxeHQSnRhyqajseJ32GEHC8vsinIxDd090GCWrykxaaamGskYKQCY8aZfuGOZBmCjP42X0dufiegcJ8g60nJMSqO5RV+cwPcDXY9ozAOczl944YVdR0U/55BC86dLRVv+ppPtMMHKdYRkjQlQ5+Eia665pgyH01xk8uTJToPkeBdPxahWx6iwfEgX3HrrrW0ZTVFEUuM0VQarGFsRBQkMzd1E9sux3rmeyo7gM/VGZYl9iOCQxAPPLWYtlqSWVCMBwmhJnk5X9DV+4okn0nClErVUjDFvgWQPYgXEgxnsyZqM+FM0NdRX9k0O5GQ75hgNEI9Ep8am07vxuR7J7czNOPBByvRszVtUmXVkElYW6zSiDqEtc3mVVMzBX7ZkjQUYgJCSoUMyY56wdxBL3Dk0TICwcq8rDkeL5FqXChcCmTBhQgtCzazOuijDITDGzWPdCXVEbCb8wFa9EgMPCI2jyphNrc2tOBwtOEyXhqOIdxpRx7S+slp3lisS4uI8N27hkUce2fRkMiPEn8FSIZAdd9zxqKOOile1qpyqVBzO/cGbxJhQhCGkoJg+JG8q7NKZDQOW/pIwpsvK5sXIjZjgHSCPE4CQKhZ7TFJbDAuoOKw4HEVhm4QZyxBRE8lGuKLp4X8FJJqZLM4oaeWy5CKQ4RZGuVOZ9UYfGzduXPQLzqipc2pNYMXhKMJhq3XSpEmTpDGiLgFUAjOz3CgN8wudhSYMECaRIOZJBQjZw1OnTm2K7vqpDKs+rDgcLVL2TYpHkDYltdHEwkVMW3EWLi4Fxy0UBGoKZmkW8mKujB8//vTTT09PNZ7NzH79dSoOR5FKbB0IaQIPyksGWnp3u+nTCs0oaID2xhtvFCCV746Kijgn+ToSdCZYBAh7G71VGVYcVplmneJzKURoiox8f8DIhks5urTplN6ip3ALIzaTDPIwR4EQv/yUU06JK9RC+IrDKn0LZaUuCeErwdZf74lQgBl9CY0qX48pFpyvVuNQTBTm6PHHH58asqq+isMqfYsiI9apmqNm+mZnvSVAGOdEvlF5sddGgVKmKINQ5gRcVsl6hXxZo1D1YcVhlaY/dB1wwAHq/ZQpZiPDPs+MNGBGX2QLP/nJT3IL8TNzpGEgTeZQikJBg3hpFkPWPGHFYZWB4i4OcFykMRQZNf3nD9O8hCtaVAWtZqQ6RzTTE3GYoxMnTjzuuOPikax4rKHRisMqM8ChUROvfvWrJQAHk1WHPZVEqDMxbrEc7qubi3YSCNzJDUgVWkmkFYdV+payS80RRxyBd6p0PegvZeC0NSkpelVEb/zyBCDkE4qOlj3jEqVzRy+JisMqQ+IcljRr9BpVUbAk31COWyo7u2lFIUaqdF2NXwlCXSf23ntvkZsShFUqDqsMyi4tD9TX6rBkmCnvLr2+KM8N9aj+XWRVwtCZTVFFoaBRmEd0dA6OeatScTiCcVhm5z2iO4vYqdYyYUYm4zT0m7aFWhtqItr0NCYOd1FgRhVF0zOUok63rzisMnM4jFBKOZxMA08Nl7RIkvr7W49ELEeVBoUZiI1AqIYRoqyS9U3RiLGGRisOq8y0XZrNTtP+1JFJJCbaJcU5ujApa9JDLdzCwK0qCi6lVp/ZmLicK1ql4rDKTOCwtDzjf7Rs1Yl6rkkGNp0monzCr371q9FkPsxOTymzUFlfDjAMO7ZCseKwysxJYCYL8zPOyeVDAWedglmoR24h0zSQyWTFEc+xGaEPy07BFYcVhy9IObQO0lRL5yeDEOXswVKrlNogPaUyU9cakNZ603xh66nyhG4pnLRIc95LQlHRoJEskvsCoQBp7IRHaMVoScgcDU1YfpzSyZwF0WhUI23/o8WF/ymlOWXKlKuvvjpOUGTsT723g8QTX0LkVMofJRk8/r/77rs1MnWdCPBGIGqfffaJqFIo8EMPPdQjMU6jnCppXp1pcHacisPZisDBV4j3mRxrvTYWR67U1kuyo+YAt5RapTyt3Bq6ogzLeWyt1omaW7/zne9UjaHDvHWs0y7WKNNUIEd9RtereKU93tORGMCEaidRqZWO/3FZNQg3sIlm1g/OgMSY2ZSjFJO1kw1LHcCtpsPzzDPP61//+rXWWstL9DV25xKkqi59HGlSneNcX0k0jh4fOHdMUxaBMz5pdGGtOJwdOGwZV/ZC/CydlHJamJ9QYPCggw6KXrSUg72ZrjDqJNd0/Pwl/KJnWfxpeSl+1ygpJ2nihbmC9LdFlmvRn/qdZTY8FOPNN9+svTQ/ren2dIqyDCKVYTzi7QxgYZGqjaIWqEdjHugWtLVobJMjyl74PcRX+o53vCNGXOCOm1ph4gVPNW5ATw0HFNTaa6/90pe+FIk8TZIcWROh3aSbM6qNssBi9790i5eIPEl1Mq3nn3/+D3/4wyqY5513XsWTMZ1mzJgxuSljC0VLO71Y59Qg19Fol/rlYm3FL2HBadJOFQgGesTK04F344039r+lgDsCFaYm2K09kmuixHNp+3nQ2vKS+eabzxrykosvvthEFCCMcV/f+973QNG7KGzX5dqAIe5ZTPYDDGV+NgV9uEHU7Icu2qXpGbpJH7/VwtRMiBd1xMgXGuljH/sYPLDi3LaRL9GAtCulTKnwDatAN2f6UmXe9xvf+MYVV1zhQKd9cHJgH4zWjJmujBqRlmkTu5jvNpr2S4fKfMJ22CAA5hMJMult5VL2F5rfgZ78Tc+kKsgEY/pfW51s+F1xOOQgjH0021rnKvTzNz2jZI3gY6cxnFQbcJzso35mj5t/kvZM0ilLxdL0lMyCUwwPYybRtJEQN1TMIwBmoF/MTtE2BtUzPRMrnjHWdBrjr7HGGi1v8wWCMC3S4K/lZc3Nffe7382uM/hFOtFn5CUaBbPJJpvwDI1ziR2hi+Ei/3sjY88YDsBAO73vfe+LX8Fs4BjJBEIK/GOwTG8F3vQ0oQq/Ny9r6BojM98LW0g0GA7NwAm0x2SbnBJFYbqCb8DeF75oxeHss0tTz8T+asH5bWz/jpG5HAsYWCive93rcCz9ueiii8JMTp8dOF5vbQVZjH0FyX7jeCNXeP/7329YCu0HqK5m5p53oTkjSdB0ZieJi1CntBBmWfY768oHp9vt+rGsQ6688kqf3XQXbli4RpSD6gpJfP6S4yh9sohBBee7i98/4LEXQv/YhvgCbBBK0nsJz/pyBHJCH2b/Rd8b20Hhf6gvKLVNpLHN5aPDKXDjNBKuPAv6kNEhNuNSDJ/Qh8suu2wGb+amOYcjA4flnlo2Dox9N6ax8xBYZaussgq/wopkpNFX8mkxNTqmt8dvDDzMqpizGbNQQnex+gLeVokfPt9dfxdDwjhC9l0GkqtZHIDKUyonTnsWZ4Up2xSzKLry8Xme9B57mH6Ied0Mb8ZhLFDbkC5sdgGfmsMWq5mACitOCCSK8bviH/q6fHCOnFY34RiLdirFEp7xrB/CLbkTsxydI2WSPxkU+VMglHnCj+DWppeufMQcAax0OwsrlFL1hfuNcPfMafN9Ur8+phoRFzftMK4Z6rSMHlccztY4TSYePLjZZpulPiR+MwqNxciLM8HLU2rwQh9GBVCgl7qgJbyWm7dxRyJiHuwTs/ts5/RqDCqK9UftuIjFxPh04I2AEOAjU5fTI3Kz6G53CQsO8CxWIRlGoPUqORFuIdub3qCZzTD1v3N8KLarbjR8WtuQ+aFhy3UlXs10ZPoq+KDZGO32QTcGXVzEpkOgY17qhUNRu086rfxmctRcGNih0ITBbHBo675MwHMpmw6dycoFeIaJ07wpdx3UxWNiJkdGjOd6NsJwxGFrFgqQiA3EBuwpWzUzSahTETp4WIjWpV9OtMA5rMp0TgR4mGoiopxJWpTCzHK+MH54mPQneDP/ABtKmbUvf/nLRW6ss2CTQbvTIo3WnwnXRQlt7393aFOgDBmH/rd82aJuif4JZJraaTIhoAKDL0FcVwikW7dhe2Iec9WwBdgU7idzerEHUcLndISebKZnHTTT51fjKdo7fgKX9UuFp8ew9w0Lw2aQFj79XvRkM8pkOOIwna74Of1+jBnbs2XnF7J3Mof8eGybOJ+jgm/pWX2sbd65JjIJ2bo+GNvFrWPXNOpZtMZphkVvuumm3EJK0rIQRo85m3Z90ZHZUEMU+gT8srjeYrUBAZ5H5NbCMSa8YiqFbjHYkGdFsbC0BZbM9+yWPdLiOWT6oSl4sGkxlvmbDI/lC1vtG1s/dG9exOiU4Zi3yExdrAlqza5p7wRI9iSkWayhoLLjAwPSszF3ur+5RWnkeC0Nacu33O2+gjGeolI8YsOOgYTEnHfPxjVnQzuJuDc3Y2tIC1POALpkZTzCWKUYpdp4UEw4W4nYSeS7fRxqnIHaFf+wNRc1vuT8VjMxW05N7c9uLCkQJd6CapNXiOP80XuDtuJwDoAwWc5JE8lMYO8fO5ReadM206fXy9hPpphbKy96meVO38qDRUJvqPVhLkTmN4pJxug5Y/YCOKQJjfWVOAnfKT+Xewv/ma/VLbXcchNa95kh4pL600zf/rgEc2K4zw50rUBXGReoOJxjkqm/3GVjHXAFM+DZGsucuO1tgpa803Lp5FNZ0RemV14/kRyYDObkkG7SuUYjOMTMpuuy4YV4CQMVx0AuGxeMro5Pze8Sh0QWozbDVXvhapnBD/kCYIKlYXxCvmOhaTZwaRq09rvWt1c+1dsKzUcioO0d+QKskgz5VBzO+XhpicBSojFuS5sFVFJhpmXV4oWWWjE5paWyjUdKMOd+38XkxAA4zJaHlJ64qCQK5lo8u8EGG4iRSnlLG8rXCSpKNtKE4lIRbUo63gu/DYErgBeClkUQO8EFZfHK0H7nO98RYmmhqNR7LbXW55dW0vTztbYbqUVOftDZRqHHOEzjpbkp2pVFL23/fDkWWjDL+IrCd3JTOSSwzHO0HLnSOSlVaEIuX5LrxvX5ivRS9Mzuzdgaik8d754d7yk9pqawbVAIeKri+6Ao+s8KBQzRJgrQOZJv3V27HPIPfehDriwQ7ZbgMOJDkgqDUbm9GeeD2cKCswqKNU4zXPzD6IYUIEFbs9kLXVptQTQR3uQmCV1glmVv+d6RgD5DBbFEUuPljp6uS5wmvy9nLVIazPKWfdXbBeoWAMrruAfrUswmuaOoBcGkEbUKnp2QkqT/u971rggmdVF8vdJC3g7+JWaD1SAcHQ6CGxAqC26DwJITpDcwe4WL8ku2kUnl20ZT4/lTGMzL3a2TEaH80H5fB7HhegsmQNMhYIiHY+3T+U2nW7m3k1vyf26+pX07FwR1hqk+LB8J8hQJI01RTPzp529tw7333d4PDqZ1krVi7w9e2wz39a7UW6S/mm8hIhofU74+HmElSmZSiQil8Y4+C7hKMAb7pIu23EILLSQqKzYrSMvzFIt2J9gCMbkNWUJGR1jIdiCpg9xrl/QnU9ar2A7MVzRgSRdeLscyIkmOWbZKEJEB5HsVXgCkdIt8jJcEDh1TvxJR2L+eWn311f3pLWwBfhFv4SCZTOlTVBwOCQ6bYlKKY5EJuz5/SUWFvRNxRO2F5RiDjezN9KT9uOmQP3FobOG2UnaOkGNcjVmLiRb0y4BNvEogJIpTvcrVJAkQdCJQ6fcWFxE5aDplVpQSY7XpjNF2jn3d4rDa5DO74je2imgtviASEGo/zkErd0vQSFHHrN/QFc6hu5pZnVvap38OD7a5sE4Ryn1RDjilIITZo9wJGtHQfMkw5t096wsBWiQEZi2arteGqWkf8XV5lUSLHcS3511AOnZSLFYfCrwDh75237A9iA/M9pansdHIM0F4FHbIo/o1m+lLauYCZ3LY8UvT08u4PN8dJU3uXvLaNBV7c5CwGY0QwmTFULMl8xg5kGoR/LTYp9Yr3HqETrM3i2fYg1VssIXwHq0Djyy11FJQh5yJ1YnuiL78tre9DSZjoVgfrCYbvKcsO3qYUQQhNmmbApxYKGjNXYzT5HriEkeOngWeoQur36e2mhmrYcuRqEWKEVHdops3nUo/2MM7Q20DJD65jQ/ZKEoQ7YxRcuEEJ8NncHF5d9gFcBIWZlDwqbU42atys1BXEbRBipSl3XRIC6FyKXmlwN4rUjV44Z6NbiBiBM92JCLnSfaYC5IcwzFvkUZgeAKsEfXgQfWOoiTOmwOqwErlHcXiYCk52c/m2Mlw6wfmk8CwR+zNagU4PDSYgIcqCqACPC/BnHSCuIi9NsoIPCgcEm9h/8a6hjd/BmElLEYBTHt2UJy76BuHiWV/8Rb4pTDAH45nrUVhTDXpLIIswwuCXuCwW+IbBnXpEJqNJeIbYyV6F7sVheabUUDIyAQh2PMV0X7xu1CGDpRor7zyyk52/7ZOSky2wy9FpwFkuLKY4mK/VL2Mi5f4IVDYQ/fa+NCnWKHeImDstws3wc9KN5YBtrmmUfIwzVuUJbyUm+VINYGcX4gTTx9yikQCkEigi/XoR/JLOxnN0rHgvsG6AT/gcWCTjt/Snup/Kyb3fnV0HlHXC+0Ooto4SGQWmXVPE6rl8SeXxlNBZKWEm04OvYt1wMlJiJp0jjEarfLIOIHNJmRlmwDCfEern962rQQDuyviS0Px822IAwGMYAmc+Lxgw57nAoCoLyTsfJuRjdKtMixtWNS1k/mENguwgdv4Ee2VXm6XDE0OSOBKnSofs/05jmoyaVI+hQ/l5R7hVdoBVR5aAE5jleSU1WitMHcEaZrh3J8mDvy61h9zRUhADQRdxGZDsLRM/YR2XH6IeEDEFRmNQgie2rkjURZsWbBULSNRB7+069CQahesiVhJdmuoY7sCeTDFXcp2HkaR1SA6EkRzVit3JexD7OoIBkZHmW7pQ5eC7dhEWKRWYepDCLRe7UHhIIVYtTYju1IUfHVFhKl8SyiEz3XEXfkzeBShjrhz2YzDpuDZiIf5KjweRS3O91QkhOIrEl8VNfV4pGcc+DPq0eIpr43ZAREyJc6JCzrwlN83CMMt/kDF4ZCLNWeXBT/EEbBh1XDuo9hUhYQfhh6zZ0dwX9DFn3QIpSeswpqyoL3Qnu1x9meU0lphnnJN7P54Fz4nyHkjj1vubFEvBGARWmCzGXMsGa7RI5T+dDUniKQ3XWqYnVnTplMG+amOiHwooQgcetAHtyJZwu4kAvoRpooKDB5Xd/2CAXaKPO7v5Fa9ResrgqUBinpn+GUmm6q0IyoOh0SSNmU7tF+W/deCiRY0mqbDsMmEkoOo8Y0THGS90jMdyRS/Z+3B5WrIjdZTWY4Yu37cQ9YQ57DrsolOVwAQV+a4RkGzbULYg4kYHqOoEjvNbsIEYDDHq3hTopRMdym+/OrKuMXM0tNbn6VkZgfqynqLVh4oe8wlY7s8v2z80XLtenMtZgjLuYxwM0zt0gBSSUrMDm5J/y+XWjN9J9KSA1munt7htWFFZYybiQYtgr08VQecsbDT2MOiGiIZDPLYAqLPkngvhc+JLfuJNP3XncxQmJ1BpYj/I0HnOPuvxX0mkTCQH1tVWfrUTF+XmKVSgdI+872jVoZvPX65r/dGTomfODPyb2UL3bxOarN08UOXDiuTJu+EMQx+mgWznHmDUVHZdLruKpjk4jKSg//tg0gGyNCgpwgFi2c0PV0CXkhuTaxLUERAmGUuVCPoxQ9nDwufCoR6l/x6k+7HYudCRxQ3QFhywfN+Svr+XN/qYsTbpVl1GrWCnCLbP4+Is+5P/3PwnBBhg1wNsWcH6ticSdQsaWgJ0VSew20d8GCFmoRepGGkKC3upqd9IDUory11wX2NR3xGwJDri6hpZG5eeN2Qqyn4kKbndbuOmKcAFc6akKz4lvRp7+1DClFddVRmt5yL3omZRGkF4bDWh2VfDBkqYXEmGT0gm8wA4wuJX4vQcJwkfMMDLP0NyoFzJbGWVmtpAmXflOHpZsiea4EhPkz/RAv9XNBgJi4aVcIRcLIlwSoOQ/TIil51qWdmubW+14pRR5696cx4U2wB+ZxSpnLQCV3cTxARUfFSaQm5wWC9Mmsl5e2V4VrLNNDe/nR+fPP55deZcMNaH6Zn4keiDPk/1oRt2INMI2U+IqKetf7kDP26rZcznJwTzd1KHdtnDc7w8Q/j9oKDAlGylHgIwUGJvcaxAgiZOiCRa2k687e//e1vAwmTNYozMuCU/tispTf1ktQFT9ZHCFpwiDIEJAdujNns+lAnrUJdg6VYkc1RntPu4JY26IjcoG1CtFkmUCpI1NdmKsRdTtGZa1hpc60+DP8tQMId0nGdDoz4J3fIsuC3CCHKIoSFZmNGuXyiI8wnHk4k2YQ3QDf8FlcW/XfstR7McdbDCocAAFHKHSTEhV7izuPbsJSxNH185wTSPIvbQHnSovSk/GfZLmSWDb8ABlvU1+7L1BwgtsVg1VDR9FvwXUyDo7fdRjBpUAgZKdKtkjpgLN/jp/RIJHLtpMzdmEcQIZ/uTiWoOOzycsyqwviF2DkWH/IUaOnmxGmxLsUw7M32Y7aQLVnrTsuUnmS7OsahYSm5jkyjwKOlw7jyk1sfXqVHrQ1b7CFb0QwTYcW5MZROTqB8YNiZKZYyMi0l6RtIOjjeGVanL4q2FErlyzXFuKtZa2+VFFCGsRwmvEXbSNtf4NAFqTjkB0ovCC6o54FDXqLbsM35Ewu36eEG2UYlXaMLeEK9bFFTcTgCBFnUT0gBKpyJ6ie40kvXr24tQprNWxiDJ+l3jW75EMhewm/Ez6JeLBpWk5Uk1GF50bEWtMUxrD4ma1Nmghqk59EvkbxKbPB4ETspIgSxHLAj0e/TNR1ijU/NPmx6Wvo2A3ZwGgCEOXXYt8cGjo6JNG0QAIVkFOwLqIoPIXPf05GYgcOWRv3FdvIbCfPQliJJNsfg6CVJiDrNsFnF4UjCofCA+gM8Er9iTJIhLB/GmPVhWSi9oeVQ3poevqgHhXYcQKw58g4imqdmCs0tyhS6xUHpltAn7koZB4YnLqv1nesVtDCErHvbDT5twMzOgjyNedP0UMOjpXcOPJuFhR5eZbhtvp+oOWw6BV82ON8zTcgRhTFxXTfjNPrZBkEtU482C/fPVxRVwmRicTBHPWUojRib+xdkQhWuwBuROLQsBCQ4HsoIg6yIuUahKcbhCgrkWH/CjHQCM9WxFSkqgI3JoWKw+fk5OdEZMeoGovk3W3eYtKwNFRQ49EmVRMY0m3CfAnVMceYAkzWL3Jl/jAJQceybiWhWU0zwnLXETDBIXSF6NyW1CH6Y/d7dfdrU/EkhOzn6R3mE4+BkX6lXRVM5J9zYEd64YyeIwfqNWhzRKiNmLrcJh7yjmMrk97O//qgjDB7eIFPNHszgsQjUy4pYSGkICTCfPG7/FlGkIrxKdNEjVoMt3Ast32HyAZlwApI2DkrGXQVPreTExHw4oY60CKx12MNQbzo9dRiHNFhST1O/zaxd2vQa4TZAyKfVI688LeLe/b0qo+IVhCMGh5HQt/2Lf8aaUFlDvzF7bM9i6+AXyX0nCJxai06wqUe8NIaluAhuCmPJs9GI4e6ODJPP6MbYzIpCfC4VQ4HDMrOilpJlziCMpEXow+zpQnjCps0IZTWd1H+fI8cHg8MAYbJtg6iUbUvj/5YLmvPV0utLHmLsBWHFhMVbjhKqCBxhOCyP+ys5a83EbfUCHuZdMQNUiGxghrYSTJq8Z7acRJw8fuRv4sGYEAq68afsXBjkTc+4sllLHmafrqh8TzpoAiw47uX4g7INV7bbKxne2YQ/b2kwQ9crDoedJIm0HKXQu7t7NvwtycR5fnK+Wg3ahoNEE0RBSGYnxRiV/nnPzAFpQ3HjmIIcOw4TQOAk4jRNTw102QJ01vIWZXu75NAnWTRAGGW4ZXv83mTg3o2eyy7D+WtWEI4kHGbApqyRafktvSviWi0VW4zTZs7x2pJgmfcf5U4apcl86j0hqpF7TYCBByjMy3tUgZFzwunAyFtkoFiVc1NMYu1i05ryS84I0ACzYvp8995U7wrCkYfDuUCSz1Xqc5pBYEnwU2JTBgJlr3S9QvvBocyBPgM0ZwlO6XKB4qaTfqRORbOi+/3wN8WrVBwOC183kSl0xBaVRxHfF++VumiKUsyAk1ix4A3qgmhNhmGYpqLBKC9xKU/xIRHQmhfAa6tScTiKVGLpTYET/Ci0Z3miGSCmJJDSeKMnsVXEb3DZoutZZAU0Yo0GVk3PxGwRnd5vVKXisEo7ENIqgNQBGa0UaRsrSOglw/2lKytkSlUKhyrMjaEXYa+CLrJR1Jeo3I0OWgnjWtBQcVhlIOs0G0yAE3q3rqqayiFJR8fr7CuRsV/xG82slHqp022KVDtMIouJmrqOJlc4RvgAAwdLqlQcVnneYkyDE01UwhAvTykDknf5bGizSNaBHxo3wg0KUatZo052MvhQ6lJKH2AypgDUgGTFYZXBGqVyg3CosYUqPsM5mun7l8X/0Rgq2tFL5cefaXNiDonWaKkKn9ENWY6xhfYqFYdVptOErQAM8KhyUi4k4hLZiLIzSKYBFQHiecOYbH4UBCZppumU+VGVUvl4bc5RZFTjNBWHVWbgHJaDTdWOACH/MKIv5Yydpkg/QCmYKQiEtHI+eZwPmQqRlGLKQMKhBmpVH1YcVhlIH5bAgJOYwKGcMvIQyZZucVYUUnL/lOdGO6bsExkEMY/QgSuuuKKcPj6AGuKAegVhxWGVfnGYCg3qlDLBoVkxUXHbFKy0Fv+rJLhnaWLWZGhBoOc3+CnSRwnAR63fdsVhlYGgGISYwI/EfeAwWKOtJmul/RkNkTM80+o3B4cxGU41pguqG25q3qLisEp/EnUGocqUqKOqSfrJHIY+DOppkrzLRGLvKpOmqBhEZwuCW7RIi45MVSoOq/QdpIm62MgBsiRVV+jFZqxnzCTL+EpW05aVhGUpbXavCazKHwYOo1NWDHKsFNOKwyp947Ap2kmo4tUVSnMA2b/oNlBCK3ltmb1oNSYvH5QzFDJ1oP2HRIgCqC6OSa1ScTi3SdnnXy8zpG0WKa52+IeDqaNvITNAa2Rq4NB1dO4BRX0im7luRFnFYZUuSDkLCUUbt1u/MwMhFNonDnsPBuxTqaZijD+j7308qB0401Qf1PqFVxxW6UNKXRejnbRdU/fEP4xpaiXYBlBl2fg8hE3raso14s8YJK5av37hFYdV+lWJAbBPfvKTyg45h3q0cRRj5MYgcZgR1DBKRX0Ee2QO41nV/XAYpRtVKg6r9AHCTPppLRONxo1kMaMqiDKDxGGeEPkPf+q2mDjEqkEPgMawdatUHFbpWxkSXRLpQ/6h/LupG8He7s8P7P1UOXK86QwqzQYZVKVrmtN20UUX1e+84rBKHxJpd027hTSVFOJ5m8Ch23/y2gYZp2l1nVOnny0zms58KMrWwKb6hVccVukXRZpBwYl2iWholKG5SFFVWDK8ZyrlYOCE3t4KMrQk9qeYjeufe+65JW6bYTZ9tUrF4Zw0Tf1vwAacGAAsWmPCmRY15SiyWWuvauAZilwMbFN7obZYN41m+lqqVtVVlYrD0esf+l8DC/4b5GhAipLW9IzxCMD0NztgYAFmkx51u3FstI7kpHGFObq8dlKsOKwynVFqGKAxcmYSsx7V0RsyU+KkpLPN7JU1mzKiMI7NvQrTt9wFKhQrDqs8jxZqCkJ0c9LTyTTVUmWlRTqz1NAwNcePH68PqkmPjg1L9C6GPZYmbhf77VepOBypEgZn1OAfcsghWs6Ic0aEJlPzRF5+Zk3TAJjo69vf/nbdojxi2GNMRC63gKYyTisOqzSdYosYb6zi6eCDD26FTHKsRUkHHyQO41L6Lyp9cqBdjTn1bOCAdMvorT9ExeGoFrEZIETF1hQ4DMi0FUtztPf4qsFA0f/YOVowmoaNIWAgOcybxNpMPxCySsXhaBdVEcxFeQs1h/o+Nd2r1o26YTX+cLjHHns0PdmRaCs8wIy0KhWHo05WWGGFF3XEQJisdXrhl422N1GEIQwbU580CPdGUvxp9NY8fsVhlWmy8sorBw4jo9CtMfFlt1JEUyRvB9KJQSVPz7NsUlyl4nCUilGHiy22WODwggsuaKbvhvjCoRhX08t0wQUXRNZZf/31lTia8p1GaZxQcVhxOKpl7733NnIUCHXEMLi36WpuPXoKu6CSYs7noYceimGDQW7ct5L/ppjlVn+IisNRLWYYhjI0Iy1QkcN9X6CE2Zl6j2lKGTowUNHbqfpvZpW2WqXicG4TvLPAYVRCRFlw1vK+QMk+i471azOflGmqAsPbRRFG1g130RiuUnE43CXjk6HxDKiQSMBlU30fzWPKxvhdsUtTH55yyilmDKu3iJDpbbfd1hSdUatKrDgcLQiMRR8DYUL/aG34qle9ykimpZde+uijj2562rd1ERXZd+PCCy/UGgMOzUv0pvzSeLzySysOR6MyLPMEbEWqCTbk97Bqmq6OKGy14vcuyotPO+00Kcp3deTuu+9ues11q1JxOPfjsJm+weHWW28dbUV/9rOfRXPRbgVpSuTHsb767FI4bDpdw71vVFeFBq6/TsXhaAFhzqhIpqiCQ8RrCMHD1p8mUdotlRjKMICtaaIyf3OCHRtyCoeqq2q8tOJwlEIxI5Nonxq0qQlU7vSVr3wlOlZkqKaLcZp4R5pQH6poYYpuql9GsL1nocK4SsXhCJYkkcWi32mnnSilSZMmxYF4ZtPD8O4KKspJif43mlt4JvShEsfXv/71rGJBo+jqX1VixeGog2IAQxMa8FMGoRxJqa4AZo467C7s44IbbbRR2TdR7HT++ee/9957S9+1SsXhqABhxEtDU22++eaonvvtt5+nUEz5bCX9ulvvmHn8EocehEONcKJ1fwVhxeEocg4hMH2/K6+8UknuIossgvDZ9LDbzjnnnKZoh9Et0zRQjdQWOZKmM4FYF5zXvva1wrPd9UirVBwOd4EujWciUspDg4roLAoD119/PX1oCsUQ6WH/jxkzxjvGWwCeFsP45cFuq6S2isPRpQ/TCMShgQojCpue/hToZt2dx1Q2enOgTXjpH3JHpRNXX331sldNlYrDUeEfZjYPuWyeeeaBxsQAHOrg1HSPUtPqeuq9XvnKV0ZUlojQ8A/1xYnecFUlVhyOFsnk4cUXX/y+971Pi0SZ9EQdwncYjUFA7fq7S1cyfQPq7kSn8AUWWICXGC5i9Q8rDkeRaRrL/cADD2QibrjhhqX2+8Y3vpHBzK4ETlqth132S1/6UrDnPG64InoNxmlNHlYcjkYo+l9pBRyqPMzHFQG/7nWvixLELlqJWfdEx/rz61//+jHHHBNPMUexauhDoZrKp6k4HHWmadOZZgGHYiSJTIN7P/rRj0ZfjK5Tvf/WkabTzxt3J+M3+HQ8xuWXX77apRWHo0gThrX5zDPPaOz71re+lQ5MAHzrW9+aOHFinACH3UoeJmcgHllrrbWUO2XTRC1qEAmUIIe2rFJxOCok8GAyNm6nib8iJfmUmI0eak1Pk6gu9qeJ/yMYI0sJh2eeeWacoBuAMeDvfe97q4tYcTjqnMOpU6cySs3fLoM0mjipfmo6wdLkhXZFH7YAqWtbphDvu+8+k0m1b6v6sOJw1OlDzDI4XG655cqnzF2LevwuTn3J65RNuzVrywKrO+64g39oKlutA644HF1C8+C1qAM88sgjS3Aimh5++OFNV8mlTU8dcLim8Ub6eSO4hZmqQYak5dve9jZk1/rTVByOIjF78BWveAXtF9opVdY3v/nNCNt0t+4ph37H23EIOaJ8wpgzQwyBYpp+/vOfrz9NxeEokvPOO49Ruswyy6TqC4TAoWbbTU+D7W65ownCUIZcU4X/6GyJQ6ap+2Gs1p+m4nAUyWWXXWbd64XRdIoe2IeBQxn2fffddxaGbw9GK6ZRKlUYecuHH3443kUSv+Kw4nDUiaSFda87WzN9k9+f/OQnNFX22O6iSmw67JxwCH/wgx949xh1GvhX/ajq4tOf/nTNW1QcjhYx7MWINWTryByUXTDYq0ofoqlht3je5XyL6F+8+OKLzzvvvNdee23Tk6jEbtMzTlIxuhhXqTic+0VYkjr67ne/G39mMDP+/OIXv3jSSSc13a6O/3tHEuqrrrrqY489lsj0OHpNNU0rDkeRmLltxXMFwyhFcAsKW6Duy1/+shYyTzzxRLferozT+FN5h1BtpChK01eXKnfFKq4/UMXhqBBlh1a8URZpFpYjZWik97///bfcckvT7b6JRJWTzCG/VGOobCseb43slrtDlYrDuVMSaUKUcnc8MaGaFloCGL/85S/nm2++yCgEflqEmEFGZUoYZ0GTLhhKnOKtM68YdinkS+VrV0M/l4q0Rm4qDucSiQZtgYSbbrqpNP/SaMz2MFdddRXKtUR/U1TuJ0c0khwDm6AR+Ik3be0CaHT0MAJNU7QVjy0A3XzXXXfVy1RJVFNMCM4L1t+x4nDE4zCNQ/MG4VCGoClG0qdxuMMOOyyxxBJU1v77799Mz0eLE7KGcAAcpqGbbbzjjR588EFGL5XY2gKydZUIaum4lo3AKw4rDuce09T/l1xyiWK/pZZaqumr3F7/UnQzYOAihvUY8Es2TMBshnX66W0mMqF37Nix0hVRz5F8usBYYPuKK67w1szmpshq1mKoisORLcmSSTHRRVpCZcP555+flmE5a8koQs1jgEF3DKVJ4SWGTZvl+QNYiRkULT3DONAIwzhuxf6RNsykiMxhauNLL700WT6piuuc4IrDkS2xjkOxRCwk6GOM0gzAlEs8zkExdc64cePoJZO6swYi1ODAyf1IEraiO0SjfhzuULPAljhsjf7mu5qIqHGjZooVgRWHc5UtWjqH1B0waKTfwknpjOnX5hwmopPlGD7zmc8ohkhUz7BEMBpqlMiUJvnRj37kTT/4wQ8yeoMxkz5kNuCIwKmqK/zv6Gvc29WsUnE4gqGYeAMtSGAcxp9lPDPP+drXvgaHcv1NJ5fAOhU4iV4yg6yXD8xAFzb5BhtsoCfiBz7wAVw5A21c+eCDD26mJ/Gkpm16iK9oriUOq0qsOJwbYjOhlxxrEGyoizZN0fYiFVdvHF5zzTVpKxoCRTFCZihGGUgAE++5qiP8PUkO5qtEvGNtgp3JsdQclZEpUaHXRvQL33HHHV3Z402vVGT+efbZZycOm66WX1WpOJxjIIxQTaxyfE4F+Bq0xRzsjIKUwwl745Boo6hGSck8SiooIqZF5983vvGNwjmaTfn/LW95i7bcDjxulNpXv/pVjxgwikCDVv7kk0+6TuhDXRJzX+h9z0ZNJdcnlWHNH1YcjngoWsHRkQ0eDMHWjqkpps3kLMRMRfTGYRiZVN9KK62EbSPW4oSPfOQjKjbm6ciLe8Tj/odMoaBPfOITrfRGTFwLu7Q/XInoeCH1K88Zpwmo1r41FYcjPkiTuQQsFoQ1rlqao33m6Fo4LEM4rNm77rqLnRlZPhkOqk/f0X/rCEDKTAYg6UZ9UL0ESS0xL/pS2qX93fPxxx/vCjKZZZyp/poVhyNVwCYQGKk/gUqTBmN9J/ya6Yf19sZhNjKNjAVUhHkJcqxc8IMZBiq30yParnkKIHfeeeeEcV5chaFnDzrooGbAvt2mvjmN4i0/QpWKw5EqJWWMdQcz2Jsx9zfTd1kp359dmo3bUi9NnjzZCZgx8vIULFsXAoVh/Y8Q5ylKMrjamXWIi8dE7oH1IdHIuOz2Xyk1FYcjXpLhTSWCDX2Y481Cy6W6608fJhKiTLHpFCjJMVJ99J5KQjgEwpe97GX/3hFm6oILLujMYKLG9UOnhT6M2OkAEg2OFQo3RUONappWHI5s0zRCpvQhZcWSjHGfHglQ9R6u1jtOkx5mmoj77befc17akRd1BA5f9apXidCoLTRTMcqIvXvo0kDRxhtv7MxgkKeUAItjpB+UGnlL+Y+qDCsO5waBMXoMGCZMmMCF+/nPf57ASOew5Jc2/cRLW8JFpPdQbZwpJMM6jQgN01cUR1GFdEXTk/dP9AYOUx9mTqJMosRTMRBu7bXXbnrYrfWnrDgcqRJB/1jKjFI4iRZpibrkiw2cP+wtyqMEP83GcKYDWQqcNfrQn7vvvrtxbhAYajYLpvrDYdMzgqq8Mec4kz9ZmtD1B604HKlxmqanA42kH3cuzMUMnMRB5DZmCoeyfMKeUhcipZho66yzDjMSXQ6BRpFhGd0peeEtHDZFfXAGjQJvgcOtttqq6QR7q0qsOBzxdikBBjhkOmLSlGqnxfMePA4DiieccIKYCuCJ3JiTgQpzwQUXoM5knUTpHPapD0udXErYpeutt17TV/VWlYrDkacSLXfW6dvf/naMM92ZPEgrht0YegZyoghw8DgcOHDSO67Tnz7s05b2qnvuuYefKf9xyimn1B+x4nAuEbl76T7dXyxxUBRlYUmuttpq+KJYo4KTMVtmpvRh6VhmHUZZsx8WaVm83xuHxlpQp/YFXB9677ke8ZT2/k42lKqpbO+Kw5Eep4kDiQRrWjG+Y1xTBqROwbjUHpQApCd32223mcJhKLrx48dPmTKFUgUnyQYli6orsoQ3PM8yCtrCoReK96y55pp4pwos5CT1CrBBxG3vueeeTtZKo+nq8KkqFYdzJk5DcLKtacaeYwRRClC/NixtD/70pz9VQmEQ2izgEOpU98rO06u/+MUv/CmPH41PI0yaBmqfOIRS0FWKxc8EwhjNHSM3CO3t5O23377+jhWHI1tCh4jNiGRCiCLgiK989rOfFd7kfUWFEYMwCjJmyi4lyy67rFJGfbjNjTGtDZ4B/tZbb216AqEtPdbbLl1yySUlIYEQx0CZxe233x7hViLwA5kRqmm61NG4SsXhHIPiCiusILPHJwwCjRwGjCnkjSokKXg9hSX9Zg2HUnxUnwPk7Pvvv18XYAZq+oQlubTpK15q3M1CCy2k3j86CNPVHMWAHKdRmZXtI/q7VRxWHI5ssb6tfmXysZqhZd111+WGAQ919K1vfYu2DO71zOJwn332YdZCl0tx80SDVlxxxfvuu6/pSb7HoLUB8ocK+VXumzyD1R0RXbfUdHIVTU/9/i677FJ/xIrDES9cQas5zMUgfD/UI9IVkhb6XESV4EzhMIr91fgr4HAF8OZ/nnvuufRYdp1pUWF641B5FAD/6le/4l5C4Le//W3nZMqRcxgEnfojVhyOeFl44YWtZr0t4k/YEx2J2CldxBRsetjeg8dh4IQ2M0ERV45CE4PVWgazVD+bPGFg/zCQrEsAMqqNIFh4UXAYN7PNNtskL7zapRWHI1ggjdmJgJbxD9wXFuB2222ngZqCeiZl6yWDt0vDmKTNBHt0RmTiUmjUbDAHml79UXvrQ7d33XXXOQBmNxZgS0qq5AriuHcJ1niVisOREZJpCqJm/KkpsKijkGaeppgIJ1s7Q/YqR1EspKW4Bs+nkW8AFU4g45ZdyvTlHGbjqezyNACvjf5EJ7AjSFdIgZQGbdMp1wDCbC1VpeJwuEsERXLcZxbORlPgaGUfi1vARoDUul9mmWUUTORo7kz0iV7mSwYWdikoimfqKMNRbDqzfvF1shdGq2l/4DBjQk4z81RB1sc//nEhGRzxsltp+ZKS7lOl4nD4asJynkTJAosm+WXTJ3wXHdPKMGaLBTp4HIKxrlNUll4yEY9FgomAUEsllv1pyjz+Jz/5STVTwCatoh1j7iPZzsODXiKXWH/lisMRgMOcx1QqNxVJTFCDJSKDH4tbPFM1gyDkQR3RDjgnEA4eh3EyKkzMq2k9VSYPy674m266aakPxWZM0RBibXo6i+ed5P2MGTPGS4477rj6K1ccjgxJPmeqR3Qzi9igpfI0+oqS5B9KGGgt8/3vf78ppi/NFA5NjMHGhqtJkybJ8kVRlXsAsHKsWhrJvfvTyEDu3REdh4844ohIG2bjHMcsXiWOTOiI61apOBwBdmkehHoJJjfqTFOMpkBhE5lsOrMrItoZqikt28HbpfShFB8iKK2luDHeqM/5oaWzV+IQG84V9thjDxEjNxOlklm7GGjUy8OrALL+0BWHIwCHZYQjlIlho1bwWWed1XQYKsAGgWE0sk55dLSZXGKu+LjaIossknNmBq5yyGZwwjO0VgxUK0cIlxN/W3GaVl99cVf4j9Kn7A8QGEb98apaiFhxOGJwmNgIVaN8QRf96EnjWTObcFYsdLFNi1sXJvhpilm/g8dhPM7JXHzxxXl9DGBjMyITWLaciYx8Xjns0uir35r6ZjYbGkDuBZn8cExje5XC//pDVxwOdymrb0PjgZzlq8AvnC6pcKl2ZRYcLWl9bTLoJYQVHlozfXOKSHUEDvtjsQRCpP6WX355+pYLeuqpp0bzm2xjUTaJ6t3Pmy0akVX3wFPViDGvHBLtApqe6TRyjE3RcWcwkxirVBzObn1YBmli0aNcW75cuDgHfUy5EwUop+9xSfymk2ag/ZrpMx8lDgewSz2FHCf7JxUZPcKbnp5O5fDTbOmddql23Wil4EctQ6YRUdL0QriqisvBGxndcc/qmLHzuKz5eGs2TpWKw+GiD8PHSy0RODz99NPT0uMKWve0InvVQCWpOSD0f6niZsoupUu5oPifop0MVPoteTCpBkPTxl2FPpSEoEg5hHaEmIoRWc0PfehDEUyKV+UHcSComyoxe5A3lXRacTjc9GEgLRIGsTojzBj5vQyWyhYyIzljqDBUpdydIgn2ZEngLHHYnwTMtHICLQcqgJUscfCQacAm0w9pl8YtRTKQ9pPPBF17gfSmsiwVkkK7iy66aKkMS1NZdZUXhjfb4spVqTgcdmiEQwRrByIoGgcLxsQA0NLMk+VD7+bXWf1iOU2n8t1U+pnCYVzKFVxKPbFyXjlJHqnxo/zPDJamARkbQTlnhvKc0hHoxa0Ta6Ue5VQirhOho1SJutckDiOUGhOsqotYcTjs7FJrPdsfMvws3Khkj+qHZJ+qS+IcSsdRYpShR2gnDl7qzMHnD7fccku8UI02lE3wFSVF1FvobdH0JDCjlVtqxTJeGs/+8Ic/ZCfzMAVj3CR1zW8sozXxQt03vJA3m6HdwHnta1pxOOyUYTkxRlsXCxdDpSlYb3EsOsJYZUAq3o3OUS3/cDA4DJXlUoneEMq2nOiWI8FLHIY+jC0DAi+88EK7gL3AaZpixC2lLo1txTm6WqmBSi1dJjyrVBwOIxCm58a6s75x1sRCml4t6xUES1oIiqJoK3cIbk0pg8Rha05TAqPET9bjx59hl0beIrYG1qntwA0rm8pgaavXeFjUihu9NqgCYffWoRcVh8MUitlOQldSZYTRwrAlDEgkMvBjmmrZxsdrpo+LDrIen6gtZtxG2rApZhXm1co8StMXr40/qQRRVlOfKCTVplfxRwrz1WuFfJtiWHdtalpxOOxwmEwa41ksWYnyPs8Uy0EEBTMQQqmReGit/sHXAYuyiAZheKPIIesktTXSepnP7K+PMDErCod7iSWWiHZVA+DKOV575ZVXVqO04nC4x2kCAIHDZKi0RJwG2c3qpwmBMKfVz9R8i9RF0oaacIujaHAIlqzZMC9jU2jN8e1djy8EKoniVZIZ6oAHQJdmcEadyvVHBDhBXn/6isNhpAwjMxFRk2hzZop9nyczJlu1C60FPfj5FiAHyZQqLH3sYx8TSsFQ058mOj6Fih6gb6LHvQo3FYxlOz07gKnJM9RGgNN71VVXpXtZ8xYVh8NLGWZaQuRDHg9jRoyxz5MFRdQuCDxSLPKHDlpm3uDtUrRS1fS0q7AQtjc0xrMBD9eMfaG//jRO8Krod1puKH2+Iy8UL8/Lo9cOeFdSW8Xh8JXovct+6+8EuT41Sk4DQil7LfFnIU4T58sEYs8dddRR+XiWUAWiWvqq93wL9NQgmkefm2ZARivOgJeXAd4aL604HI6mqYO99trLYrW+B8AhT4wBiVPG6XJQQquZmf6lXM3QeAZxY8Zl9iLThq0iw95xGqQ2KlFG0Z0ImQ6MKw0+vDx4As302ZoqFYfDRUL5xNjAAXAoTAqBnDottBHfooi+lEHmD/2vnwX8CMz+53/+J8Uoid/KWLT0W2//kEJGOVC76CmY7HM2cIpeHq985St1Xi2n4lSpOBxGyjAMQuCxsjUCRRDrT11g0oQj5yWxoDE8y0ZMg+SXkjPPPNOcUGEhtiWyS38e6QD6kHtJOQvSbLvttkqfBn5HE2xwD1zBQTVKKw6HIw4DclSTZSpN30zfkrSFQ1k7nQ5VPNBFaiAMS6MYZxaHrYvLyAP/TOHQRURBb7vttuwBZZ6p0sQBNPCnPvWpclZHzVtUHA4vieChfrs5y7o/dRFxGvpHfyehEdWD3LPsaT9IHPYOqPAno6P+TOlDutRGINxqR5C9QPuG5wHAT3+WLmL1DysOh5fEiixx2J8IqPT2CZt+6oAHFgBGN0MJ4GrqKYwxN1M45NDCFeBJQrqU+K3Qq21igCtgwMnmR/l/mZmsUnE4LOxS/+Ne8gwxS4VPmhm1Wss6iWy8nem4weNQmbxcpa74Wnq/853vvOCCC2bKLgUk70K5oXoPUuEL1ZipisQTFVv1p684HHY4lFW3ymXwxV0G40+WQC0T6IOvA6YDaTDoEoC1BZTTbAaDw9ZOMXCVffaqEZt1kehQXvk0FYfDTgKH8geioANwL+kfKTsHONOooQxL/4cKHTwOQxcBnr4ySpa8RFH/DAkuvf3DpoehFhmLpKr3t30gqesZRSVG7/AaMq04HHb6EGs0g6Vl1V/TE1oMBrbONLwyj4iaaqFtBoYGofkq/+uqOJi+idkBwJ9RyNuqCe4Ph8EsD+EZ6j1ja8CV0e3GW2uxMXBYSDup+eabT9S3/u4Vh8MxThNMmmjclA0Lo162rAMW2DRlSVzk1a9+tcSdR9buSK71wGE5qq0/Udgh+yfqQ50ieUcf4QFQVNYBh8u34IILsqKlLpjT2DmCt7L5/V0hthLdpbRadHI03ag/fcXhMBKd117zmte8+c1vRjFrevphN0XperbMkKMTX2GLAiElBgaf+MQnwlaME6LyPXhtA+OQKpNsoMewVT/zmc8kz7u3a1f2Ly3nH4rxaBKl5AJZHKiodI0C+rxItCf2EpyBeeaZxwsFfmu8tOJweIkSCkscJKIKsRw8mCoxkOlPNbucQ5anGijn65SRjYDTPxwMDsVp3vKWt8glsCrV6UL4wDfZe96TflZaS9kUZD5oRW8Nq/2BOT4FRb3AAgtQ5oOJslapOJytQhdZ4rohNj2dBbNLRSjDrH5QOz/vvPMyCAFAKt8jSG3ZQ63pMGMG2a9N037KTexE1ETPqBkmElr6kNgR3LkO31FALOqD/trna7N7twIo/XXQ6LIfR5WKw2EhVqSegmpkY4hapCWyFr6cxNZ0GoeKqUZv7DKikyGZwOHA/bx7t/ptph+i2Nu1a+EwHhEfYpSK2VKt9JsAbH/6MLo/hlbXs3j++eevSYuKw+ElCNbWt9UZfYGzZ1RK9k0ULOVWUUFy7hwzrUebniREQmgwOHyuI9GYNFvjDNCEv3ecpvfJA/e5SCVPbSoIFjLVmLz6hxWHc1hKXYcLZn3z09S2twqOSrtUpwwZC7QbJwvqqADWittUtrLxadNT9zTDOTOpQluUgEHqQ139OaV43m5AbCkM47RsS0zGQbZjhMOY7y1UW+OlFYdzEoE57YhgV0f8A0k6B10kSNI6ZbsK90OC4gYn61zadGYkLrbYYs30tQuDnPc0eMmUSdwnEiyFjArHUxVlFSllJ6+66qonn3xy2eItO6CW7RjDRcSqUYio6WO2PK1ScThbJdZ0znjwyOWXX25xi1vqGpyt9ZOektAVTdHg0NwLdbTOl8GnHrFDo29iKYPnlw5+4whFF3Yp7fe9731PT3GPu42YHC736CPkDpLbR3YiLjWwdAv/UMqxtqipOJyT5miEYWIVopXRM1HIC4T0XkZQMueWSDA9wiQJNfsK9pVlUI8xEKqUwc+3GKRkMtOMN1dW72toaQxOlAl88YtfjDkgaSl+GzeZc7mbolN49sJywMVFbeMPVxxWHM4xydZs/dmNnD2KMTVJOa0+QixoK9KDkgS3d8QYjBxXmvqwizhMCX3o3R0rfZTtlPmQTsSMpaujR3Bpi5ZR3PzIHrH1iNOo8Kj+YcXhHJMcfJ0aMofvphpJlyy9xHwk5gFjS5v6pLxd8yVKqazHH8xc7heCQ+2G40/aGxEH/Bil/jcFgGkNkC2DNjP48dFsKHQ+zxZ6a+lTxeGcdBFLvDU9Oe7IIpTzA3NEmQqMdLccSx7qU4hExjIUdaSgRFxzTZf+YVdwmBDCLM94aZiU3l3LGZFe3Dr/cxFFbjRWzRrfkhn7bEeqLVpxOCxAmBZm1u9mxVAMxI7kXmrIbFQTr2KOrtER/FKqb+zYsaXnORT+YV488g3Ba4ttgnksTMoqNgUAW03xlLQKPZnD20q79G8dSbO8Jg8rDuewMmwt8dbUzpZbVb626fRNFGkUGmGUyh8++uijrdOGAodx/cBhWfe00047aaDqcfcjt9mfIu0N6SoVhyPevQRFrQel0Y3jHjduXDN9/7WhwGFIi18KYwsvvLDkIZqrKG6QgapUHI4KYZcaN2+cPbwZdabt0m677VZagF3HYYtPkzVWhF+q5kNuky0qVLP00kvX0EvF4agQ8dKFFlqIJyaPp1shQKqpLTnTQ4HDkk+T+lDYU+oCWZRFKn8YvUmZyvU3qjic+wXkorlLICGq+MpBhUOtD8s6YLkTG8HEiRMxzqdOnbrooouWlZBVKg7ncinp4FFPNHT6MCX4NJHHD7EjCBRlOr52nak4HF0gTGZc1O+XSbmY9zQU8dJWHj+M4WDJlhya+gNVHI4WHOZEtCR/pijFgBblSF1/X8xy3daQS/ORkkcard+qVByOdolUpGiKnmjK9qtqqlJxOAeUZJTYJyalEyoUKw6rzG5lGD5bHGTFRv1mKg6rzG6nMdtPNNMnM6pUHFaZTRIVG/lnkMXr11JxWGUOaMXWQZWKwypVqlQcVqlScdgNK4uTM1Rdn4eJ5fb7P9x885/v6u/Zp5565sQzLrzm99Oa1asH7n2CB6/83R9bfuDd9z7wl3vuH/h9veTUsy85/5Kr+j1hWuVuH7Xzzw1BH+4bb779iSef6u41b7ntrocfebx85LKrrjv+1HOfefa5isMZyMFHn7LBtnttuO0e/j3+xJPHnXLunlN+3d07s7ZOOPW8jbfb0xKf2dfuOvmI2+68O47Pu/iqw489/YXfz9KrbnbWBVf0+RSMbbD17nsdeOxvr7nBW594+vm9z/njn25beb2x/5x+T9lqwr4n9XVyKTvuech2uxzwm/Mu6++E/Q878cAjT249+Lsbbt5o2z3+2dUt7Jlnnltp3e0eeOjRQZ5/3wMPPfX0jH+71Tfa0R6Xf55+7qWrbbjD0See+dcnnqw4HEi0f1j2V1tcfMXv/3zH3bfdcbcf+7G/PpFbml4tg9RjQvcJudZTTz/z7O77HbXF+MkrrLXNzOrDRx/76zKrbe7/+HO7XaYccMRJ/4J3/21X/t5rhnZGNY+devZOex1a7hHlC2+48c9rbDKhZ/E9/NcejVEqRngbt+uB5Xv5f61Nd6IN2htQcYePPv7XFdfeZuDP+/Ajjz3S82Gf67mxZ5997p77HhzgUw/wrfb31B133eOGy91nRgAb/5d7H+jvSwtVz4xadYPtn376X32K19l84u9u+FNL4fd8in8MbDiMLhzefte9q22wffnIXgcc88BD0yj8hx172mY7TN5p70Opx1tuv8svOmHPQx7vbGzHTj0nNvUjj//NAUeevP5Wu/mRHv/rk+P3OHj73Q8et+sBDz78r4322eeee+yvT553yVVbT9h3Zm/vqt/9cb0t/9WMbM1NJnjEwdW/v3HLHffdaqf9d9nniGc7VjStvv/hJ66/1a5/feIp90btbLPz/nfdPc1QPOPcS7fd5YCtd9r/9HMusQ5OOfOiMPNuuvWObSfuP3bXg1JB3Xr7X1bfeMIyq21x4JFT2Wx7HvDrWKB01NhdD9xix8nXXj9tVU3c53B7vAPvZWvYfPxkj7i3Zwt73t6xw+4Hbb3TFKrMbThzg212/9GKG+2yz+GpWHbf78hbO9C1A07Y6xAHvuqnnn6WmvLa7Xc/5MgTprVm/PVJZ13y29/FtxGfmqKOj3DQUVOPOfnsLcbvu/n4fbxF69vzwTceu/fYXQ6YdNBxl/z299MM8htuZvVQ3dtMnOJOPHLvAw9tvsM+m+2wz+SDj3M1j5x53uWHHXOaZ9fdctdA0YS9Dv3ecuv5Sm+48VZ/7nfoCb6NLXecfN0fb/HnnX+5b7Pt93YD4/c8ZIvx+5S6/fs/G7PVhP3uuOteZsXz6+Se+x97/Am72NY7T9lk3F533n2fM087+5LDjzvd5uiE62+89ZBfn7rR2Ek+9SjC4UWXX2vZ/frks4495Vzf0ZNPP/PzNbe2sVmy9raHHnnMClhs6XX8xnZQlkxsVOtuucuFl02b9ffjFTf0M9/xl/s4AH7g8zqejxced8o5rTfyu8bP3Ic/9vQzTz71dPkvd/GTzrjgp6tsbo1C+IS9D6MbaVd7Bx3+h5v+DPnswzPOnYaiRZdcY9JBx951z/033XI7s9N9UiwuxRnbcJvdqZTr/nDLEr/YqNxofZyLr7iWNqP3UvNYlIcec5rXWmSrbbDDtPV0+In0uQPrIzYFaL/6umne46bj9tr3kONBbvvdD7T355XZEWtvtvNR0+yxpyzHjbbb0/tCNbv0gQcfyU8HmaeeNW0O6R77H7XnlKMhf8W1t/Wn1QwJDkINQjg83PmXzqf+023TPvW6Y8/s7B3/u9Rakw857sGHHvVZ4hdJufb6m5z/l3seoKW/u9x68UJf4DXX3eTzLrf6Vieedn4ouuNPPc/n3XCbPUAr7srV7B0eX7NjGkCRj3zv/Q9hKex94DGTDz7eg/scfFygzskAT5OzI3bb98i8gUuvvM4X6L0ozyVX2tiWd2dnnbimK/tm9jrg13EF3+oqY8ZxsPeYcvRiy6zju7XjLLXKpqMIh8y89bfa/cCjph541Cm+CBvemK128zizPvZCunHNjgHju956p/3CZvD92tU8tcyqm4cS4I4vufImYLP3QcduN3H/Uh+miRJbcktAZfMdJo3Zene/tH8bbLPn+N0PSnt4/B4H7TL5yHMu/K1/+x124ipjtu88eHAs02mqadLh7Mzb77rH9hGPeOufrbnVlMNPDvvtVxvuMH6PaYqFepx65oXlW9M5G267p9eWD1oTlqwDWwktR3/+aIUNIPCgo0/ZbPtJ9GFYX48+/gQltsJaz7/pCaedB0t5kUuu+F0at9dcdyNMOth+twPtbuV7WcrhDcIVMF9+9fWbbr936PZfjtkhHC2blLfzncMwpREvZKQIfrjzFXoM3XW32CW0U4olzicP03SNjXf0bRxx/Bk+cjzrO7/x5tvsZb/aaHw8Qh+GkvdN3nTLHWF0rNW5c/fjWQd+9O//bP3DjzuDcqMD/3TrnX73dbeYmJ78SadfUGjjy8buMiV2E+vkmU6t1rkXX5nnWw8w72D5NbYKk36XyUfssf/RDnyWcl+b+3G4wda7UYn555HHn+GL4Er9fK2tI8Z12LGnx6ZFJ/ghOwvrpti2YWOrHlNzr85mf8NNfw5TsLe3Ztd85NHH+4wQWmpPP/3MU51/1F0ZG/zVhuP/2EFFx3q5eLuJ037XVdYfl2tu1THb/+nPd558xgW7Tv7XTmy5MJwsFFf72ZpbX3P9TWKDjnu/+9QzL/rJyptknFM4wcb8xJNPB9rBxvoAEhbszX++8/kgzc23r73ZtI3p5N9caDX3GMw7nXn+5XlZmtmiTPNs50mHTTtn0wl5kRAWsu+NSowTnBnLnVx42bU/WXnTG266FdjW6YDBp76+YxaSX64/zo351KF/uPRu245WXtwXzufvLPffxf5Fe9tMHfghmAz6tAJY3if4+ZbsYukIsD/jxticsUj871I33nLHzT2esJfvd9gJ8Tsut/qWkJk34N5i45i2TnZ8fp3stt9R+/R8Rtpv30OnWRNr9uxZIBq7z9EnnWWvGS04tLUvu9rmrIV8xMKyLDhFP1pxQ4vGcl98+fXDUqcNDjvm9NvuvMdLApl2r/07v8E0vXr4SRwhekw0ggFTxgn8yWRaepXNGI0zlRGxJthRGVuH+VCD62y+88FHT2VlUVNjtpo2nZdBFYFNGLZY/X/uRVf6dYEazOg3N8ZLKRHu09Fp1i7jjVuY+YxYhW6bFrLWhWp/svLGjCh3zjL0FH9s252nVceLuIq7PPTwY78+6cxFfvyru4qkBRVtg3CHQp2uz9BgIjMinp0+fG+LcXvuMwJRzAFflJN9Y0DiBlhop551EYsu4kA+r2sy70ON+NSg6OCKa26g8VrhGUaB8DIoLrHSRqEGwQkGaKcxW+8Wmtwma+n7nicdeOy3frKmV11x9Q1LrrypjclnZxn6uZ3mZLrLdyWXs9QqmzmwWYZrZ+OwZji0Eycd9r3l1i3jN95FzDmwCm/xoHdkKfgULM/lVt/i4UcftzXEcvIlU4z20OeV+WnnjRYc+gE4x2WsbM/9jw47zWa/2Q77HnHcGQwe9pJHZMzGbL3HbvsdKX7Duujs3ydYZ/FCK1rEQjhk+90PojDzgr5x+OE6WmSCATPMsJUCHqW/IYZx4y23x+Mbj91r24kH2DIDpWzCWDHWh5eM2/3gbSdOiUcAcqPt9hq320FWTBlHoV2FEBirZ57/rywCY49W74T1n7WwnuqE/qx+kZhxux3s2cDY2Z2cB1CJSG05YT/71JTDTyox5pgmEYrYaqf9YoO37GLLaCUq195sItMukOPOKWR+nWCMb/KoTpBm2ttdeEVsHIIunU99WGhslovNxcEFl17TO50D0mO22YM7R+mFNgOt9bbcFSZZ6fFZLPpNxu7F3RAgcFrHBJ3qZ/K5fMMXX/H8+CpqbbPx+7kxx1OOOMnt+T6tkFhCvN9tdtrfl5DOQgRgac6I/VonEd+aFjx/+tkd9zzYN+NNw9Lhpoa5Th9YXT0RrKNCmY+i/GFvYcIxL6dFRO68hwmUaYMZ5wlnY//2AULtvZ/q8+QyZiN0YnFz5CJ22gr3t4Zp95mwGeA2fJNWNjNv8J+uv1aI6TkPkTAHQokNeG//HDiZSSuy0su8yOB/u1GaP+xTWAjb7LyfgL7g4ZWdPMFcL1KmMpy24a5nrixKINxqwuSW/zYMBcAYNSK6L/A69O26W+x6U8d4GYXSZX7pqOIi2d+fHTI239DxBLv9JXSHstMnNa/isEqVKhWHVapUHA7eN6jfYJUqcxKHott/uvUOUeZMdsu8y4zlCcLTjH4MkshEY2zdfOudQhpTDj/R41JemWLuriB8ZGokRNrqsqtvKLmUqK2XX32DXHZ5mvv3eMTlsGEvv+r6uj6qDGscSjRh1XDRxcqm/uai55F5wDEIGXH8yGOPI9CAqMyhvBNvXv4a9uTx0DudIJs8pSiD6IpIwcl0oSOvttGOiCChrtF9ZMAkr/C5MCc9ctzUc6TgkMuXX2PL23oyTu5w47F7IhlHdvGoE85M1kiVKsMUh/hWkWu27g84Yhrd8YknnkKqhL0I4k8+5PggGeHy+v/e+x9E2gz4BVGDIv17T77rmuv/hA4iDx4YoKYoJdd/uENqu/W2v5Tcro66+9OzfQVmPRhJalzzby6x+pNPPfPHm29bfvUto1hBGkDi2F6A3BO1be4E4zleizWCayJvHgFAWewtizqAKlWGHQ7xPJISRachRjpAowE8nGMlcPBA+7FLhfVx81HD8D8oKKehjCB5OcAGZgQ6E5Vphz0OQZVYCSfzljvAgPpSLUFf4ROrY4AWLMRzLppGx0FwmbDXYbvue9Rvr/3DAHcIRXSdA/SuqANqptEUj1Sv3OFJP1/DYbNgXTedEg0H5196dbDPmmnE/99vvv2kuj6qDF8cwlIWgNMwEzoFsmglVA0+BNQxRKNqFoc7GBJKNBT7NNO4F7tG8VHQiHEUx+95cGiwn66yqaQZFts3l1w9ONkqX6LgDbPZP5r2u8uu67UD354TfvrLTZAeQfoX62ybhbZK+0875xJcuev/+LxfusUOk9CjkPI22m6P8HizgA0Da4uqD6sMZxxmZS3BY+RH0SQTO4DBAOZx+f+uDqNXEY0qpKbDwXUOIOH4I7IJgWw6blq1Dh0YHpoCiKhtweGMkjZhFSgKQgm1dlqHT4h2uNJ643CR+7s3dVVYdSd1qMwUsoKA4FV6a4+jLCpB4LvGyVjR9KrHEdPAVd0WtzBS87vue0RsHFWqDEcccuos37t7ei4gFuLOszkDTiA0brcDs6yOpXpsp7qXhQkhgjRR/kOdqnzhBLIewx9TnaTWrplW+3tEKCXM7/W2eL6ahhmcao3Lp54t0NUSZcco5jRh/Em1qr2IYyxzNEjYnla80/FLWZ5rb76zy24ybm/mKG1J2br/Rzvkfd5s8oyrVBl2OOTRAdWDPc2CVO58a6l1t9vl+VF7/MNvLLlm1KoD2C/XHzutPu2hR6PiVs3oNp2yYNapArMotDnihDMBT/3+yWdcGDrq6k7XM6bs9rtN06XM3Z+tsSU1xdzl+CkzE9hsOqVuCgvyxoB8kSVWtyNM/c2Fx0w9Bwin8ffXH7fvYSeefs6lPEz2cNPpSqSLh3pTj8QbhaiCW6kTyCXcVGZz7bFdZfjiEHjCFYw/eXTiLvmneEzWtlrHwEZ/qjSL/guqYKJuhWEZBRnU0X6Hn6xYRgg00OslkZBk+kaJNw5xdA1US7X/4SeLuzBWaTZFeho05Y1x844+6WzhIvHbTqOAaRrbNfc//CT/Mj/BERWn2f+wk1pNEAVas2bHtiJ/WBdHlWHtHzJE9RGZs/fNeSuL2bsoelJwgOfuKpsqcwMOmZqtBi2zWXiUDz3y2BBdnFt4+5331JVRZbjjsEqVKhWHVapUHFapUqXisEqVisMqVapUHFapUnFYpUqVisMqVSoOq1SpUnFYpUrFYZUqVSoOq1SpOKxSpUrFYZUqFYdVqlSpOKxSpeKwSpUqFYdVqlQcVqlSpeKwSpWKwypVqlQcVqlScVilSpWKwypVKg6rVKlScVilSsVhlSpVZpf8f5g7L2XWcc/cAAAAAElFTkSuQmCC"}}},{"cell_type":"markdown","source":"### 5.4 Conclusion","metadata":{}},{"cell_type":"markdown","source":"I show the interesting finding in the horse race's dataset, and introduce the idea by the \"orbit model.\" The starting position is more important than we thought, it is not only inner rail or outer rail issues. This suggests that some starting positions may have an invincible winning strategy.I illustrate the idea in section 3.3 already. In fact, the winners are often those who have the most control over their relative positions. They have good rhythm of their \"frequency\". They adjust their cluster angle according to the procedure of a race. Exceed from outer rail is prefered by more winners. ","metadata":{}},{"cell_type":"markdown","source":"I did not use any mathematic models in the report, but I show that the theoretical support of the \"orbit model\" is essentially the Fourier transform, which says that every signal could be decomposed to the sum of a list of Sine functions. Their starting phase angle and frequency will determine the final signal. I highly suggest you watch the youtube video of Eugene Khutoryansky. The link is in the section 6. ","metadata":{}},{"cell_type":"markdown","source":"**Borning in spring, growing in summer, harvesting in autumn, hiding in winter, learning the laws of nature, and keeping obeying them is the only theme the report wants to express.**","metadata":{}},{"cell_type":"markdown","source":"Although I did not provide other evidence or give a specific mathematical solution due to my limited ability, I feel that the orbit model touches on some essential rules. How do I know?","metadata":{}},{"cell_type":"markdown","source":"Well, I learn from nature.","metadata":{}},{"cell_type":"markdown","source":"#  Section 6  References","metadata":{}},{"cell_type":"markdown","source":"1. Prof. Giacomo Bonanno Textbook \"Game Theory\", Page 91.  http://faculty.econ.ucdavis.edu/faculty/bonanno/PDF/GT_book.pdf \n\n2. Shuang Zhang  \"Optimal Model of Horse Racing Competition Decision Management Based on Association Rules and Neural Network\" https://www.hindawi.com/journals/sp/2022/4240244/\n\n3. Nicholas C. Noble \"Analysis Modeling and Optimization of a Smart Sulky\" file:///C:/Users/hanhe/Downloads/Analysis%20Modeling%20and%20Optimization%20of%20a%20Smart%20Sulky%20(1)%20(1).pdf\n\n4. Pfau, Thilo, et al. “Modern Riding Style Improves Horse Racing Times.” \n\n5. Eugene Khutoryansky, youtube video about Fourier transform https://www.youtube.com/watch?v=q31UcMOuds4","metadata":{}},{"cell_type":"markdown","source":"I also study the code from public resources on Kaggle. They are listed below.","metadata":{}},{"cell_type":"markdown","source":"1. LichtLab https://www.kaggle.com/code/lichtlab/race-detailed-observation-with-animation\n2. Meskine Hocine https://www.kaggle.com/code/meskinehocine/draft-effect\n3. Omu_com https://www.kaggle.com/code/hkhiroshima/let-s-analyze-the-jockey-s-drafting-strategy\n4. xxxxyyyy80008 https://www.kaggle.com/code/xxxxyyyy80008/derby-2022-eda-speed-analysis\n5. VK https://www.kaggle.com/code/venkatkumar001/big-data-derby-explore-eda-approach-try-it\n6. xxxxyyyy80008 https://www.kaggle.com/code/xxxxyyyy80008/predict-and-visualize-winning-with-lightgbm\n7. aldparis https://www.kaggle.com/code/adaubas/tps-jul22-lgbm-extratree-qda-soft-voting\n8. LD Freeman https://www.kaggle.com/code/ldfreeman3/a-data-science-framework-to-achieve-99-accuracy\n\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]}]}