\nThe most pressing issue in horse racing, from my point of view, is the determination of the expected position of the participant. Of course, mathematics and statistics don't see the future, but they can predict the likely outcome, based on which there can be drawn important conclusions.\n
\n\nThe main points of this work are:\n
\nThe main idea of this work is that in determining the position of participants in future races, not only the final results of previous races are important, but also intermediate results: the time of holding certain positions, the deviation of speed from other participants, the distance to the leader, horse health indicators and many others. There were used only data provided by the organizers.\n
","metadata":{}},{"cell_type":"markdown","source":"#\nYou can get acquainted with the code for preprocessing in the code block below. The preprocessed race tracking data you can find here.\n
\n\n
\nDuring the initial data analysis there was found a considerable amount of missing data that needs to be recovered or deleted. There was found 2 types of missing data:\n
\nIt is necessary to recover data and the main reason for this is correct determination of the position of each horse during the race, as well as to get rid of anomalies in the movement of horses (rapid acceleration and unreal high speed). Having considered the distribution of time moments of implicitly missing values, there was found an interesting moment that more than 95% of observations were missed in the first 5 seconds when the run-up occurs. This deprives us of important information about the start of the race, however, a small number of missing values allows us to recover them. For the purpose of rational data recovery, it was decided to recover the data of those horses that missed no more than 10% of observations. The rest will be deleted. Thus, data will be recovered in 301 races. To recover the movement of horses, it was decided to use interpolation. \n\nLet's take a look how it works:\n
","metadata":{}},{"cell_type":"code","source":"exp = df[df['race_id']==18]\nexp = dist_and_speed(exp)\nexp['utm_lat_lon'] = np.array(utm.from_latlon(exp['latitude'].values, \n exp['longitude'].values)[:2]) \\\n .T.tolist()\ncolors = ['#'+x for x in ['e8e8e8', 'e8e8e8', '1e56c7', 'e8e8e8',\n 'e8e8e8', 'e8e8e8']]\nlim = exp[exp['time_sec']<=2.5]\nfilenames = []\n\nmt = [0.5, 0.75, 1, 1.25, 1.5, 1.75]\nrec_time = {9: mt[:1], 10: mt[:2], 11: mt[:3], \n 12: mt[:4], 13: mt[:5], 14: mt[:6]}\nmt_for_plot = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75]\nfor i, sec in enumerate([0.25]+mt+[2]*8+[0.25]+mt+[2]):\n data = exp[exp['time_sec']==sec]\n fig = plt.figure(figsize = (10, 10))\n if i > 7 and i < 15:\n ndata = exp[((exp['time_sec']==0.25)|(exp['time_sec']==2))\n &(exp['program_number']==12)]\n sns.lineplot(data=ndata, x=\"longitude\", y=\"latitude\", \n color='#3d3d3d', linestyle='--')\n plt.annotate('Missing interval', xy=(-73.830355, 40.666860), \n xytext=(-73.830400, 40.666900),\n arrowprops=dict(facecolor='steelblue', arrowstyle=\"->\", \n connectionstyle=\"arc3,rad = 0.22\", \n color='#3d3d3d'), \n fontsize = 13, ha='center')\n ndata = exp[(exp['time_sec']==0.25)&(exp['program_number']==12)]\n sns.scatterplot(data=ndata, x=\"longitude\", y=\"latitude\", color='#1e56c7', s=150, \n linewidth=0.5, edgecolor=\"black\", alpha=1, zorder=10)\n \n if i == 8:\n exp = no_miss(exp, 18)\n if i > 8 and i < 15:\n ndata = exp[(exp['time_sec'].isin(rec_time[i]))&(exp['program_number']==12)]\n sns.scatterplot(data = ndata, x=\"longitude\", y=\"latitude\", color='#1e56c7', s=150, \n linewidth=0.5, edgecolor=\"black\", alpha=1, zorder=10)\n plt.figtext(0.58, 0.285, 'Passed distance at \\nmissing moment time', size=11, ha='center')\n plt.figtext(0.8, 0.3, 'Total distance of \\nmissing interval \\n/ ', size=11, ha='center')\n plt.figtext(0.8, 0.26, 'Number of \\nmissing moments + 1', size=11, ha='center')\n plt.figtext(0.7, 0.295, '=', size=15, ha='center')\n \n a = sns.scatterplot(data=data, x=\"longitude\", y=\"latitude\", \n hue=\"program_number\", palette=colors, s=150, \n linewidth=0.5, edgecolor=\"black\", alpha=1, zorder=10)\n \n plt.xlabel('')\n plt.ylabel('')\n a.set_xlim([min(lim['longitude'])-0.00005, max(lim['longitude'])+0.00005])\n a.set_ylim([min(lim['latitude'])-0.00003, max(lim['latitude'])+0.00005])\n plt.xticks([])\n plt.yticks([])\n plt.legend(title='Horse №', frameon=False, \n title_fontsize=12, bbox_to_anchor=(1.018, 1.02))\n for j in ['right', 'top', 'bottom', 'left']:\n a.spines[j].set_visible(False)\n \n plt.figtext(0.14, 0.86, 'Date: 2019-01-05', size=15, ha='left')\n plt.figtext(0.14, 0.835, 'Track: AQU', size=15, ha='left')\n plt.figtext(0.14, 0.81, 'Race №: 2', size=15, ha='left')\n plt.figtext(0.14, 0.785, f'Time: {sec}', size=15, ha='left')\n \n if i < 8:\n plt.figtext(0.55, 0.855, 'REAL DATA', size=20, ha='center')\n if i > 14:\n plt.figtext(0.55, 0.855, 'RECOVERED DATA', size=20, ha='center')\n \n filename = f'{i}_{sec}.png'\n filenames.append(filename)\n plt.savefig(filename)\n plt.close()\n \nimages = list(map(lambda filename: imageio.imread(filename), filenames))\nimageio.mimsave('gif1.gif', images, duration=1)\n\nfor filename in set(filenames):\n os.remove(filename)\n \nImage(open('gif1.gif', 'rb').read())","metadata":{"_kg_hide-input":true,"jupyter":{"source_hidden":true},"execution":{"iopub.status.busy":"2022-11-10T13:20:26.935061Z","iopub.execute_input":"2022-11-10T13:20:26.935628Z","iopub.status.idle":"2022-11-10T13:20:37.618156Z","shell.execute_reply.started":"2022-11-10T13:20:26.935578Z","shell.execute_reply":"2022-11-10T13:20:37.617153Z"},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"#\nDetermining the position of the horse during the race is the main task for further analysis. I created not the fastest way to determine the position, but accurate and understandable for any person. A perpendicular line is built to the vector of the direction of movement in a quarter of a second, then two more perpendicular lines are built to the first perpendicular line in the opposite direction of the direction of movement, as a result of which a polygon is formed. The position is determined by subtracting from the total number of participants the number of participants inside the polygon. \n
","metadata":{}},{"cell_type":"code","source":"data = exp[exp['time_sec'].isin([10, 10.25])]\nfilenames = []\n\nfor i, sec in enumerate([10]+[10.25]*8):\n fig = plt.figure(figsize = (10, 10))\n ndata = data[data['time_sec']==sec]\n \n if i < 4:\n colors = ['#'+x for x in ['e8e8e8', 'e8e8e8', \n '1e56c7', 'e8e8e8',\n 'e8e8e8', 'e8e8e8']]\n else:\n colors = ['#'+x for x in ['c71c1c', '34675c', \n '1e56c7', '34675c',\n 'c71c1c', 'c71c1c']]\n a = sns.scatterplot(data=ndata, x=\"longitude\", y=\"latitude\", \n hue=\"program_number\", palette=colors, s=150, \n linewidth=0.5, edgecolor=\"black\", alpha=1, zorder=10)\n if i > 1:\n ndata = data[data['program_number']==12]\n sns.lineplot(data=ndata, x=\"longitude\", y=\"latitude\", \n color='#3d3d3d', linestyle='--')\n\n plt.annotate('Direction vector', xy=(-73.829795, 40.668087), \n xytext=(-73.829828, 40.668042),\n arrowprops=dict(facecolor='steelblue', arrowstyle=\"->\", \n color='#3d3d3d'),\n fontsize=12)\n if i > 2:\n sns.lineplot(x=np.array([-73.8298013, -73.829806]), \n y=np.array([40.668085, 40.66808765]), \n color='black', linestyle='-')\n sns.lineplot(x=np.array([-73.829806, -73.82980355]), \n y=np.array([40.66808765, 40.6680933]), \n color='black', linestyle='-')\n \n x = np.array([-73.829950, -73.8297037])\n y = np.array([40.66818, 40.668035])\n sns.lineplot(x=x, y=y, color='black', linestyle='-')\n if i > 3:\n plt.fill_between(x, y, color='#f7f7f7')\n plt.figtext(0.5, 0.2,\n 'Position = number of participants - number of participants behind',\n size=13, ha='center')\n \n plt.xlabel('')\n plt.ylabel('')\n a.set_xlim([min(data['longitude'])-0.00003, max(data['longitude'])+0.00003])\n a.set_ylim([min(data['latitude'])-0.00003, max(data['latitude'])+0.00003])\n plt.xticks([])\n plt.yticks([])\n a.get_legend().set_visible(False)\n \n for j in ['right', 'top', 'bottom', 'left']:\n a.spines[j].set_visible(False)\n \n filename = f'{i}_{sec}.png'\n filenames.append(filename)\n plt.savefig(filename)\n plt.close()\n \nimages = list(map(lambda filename: imageio.imread(filename), filenames))\nimageio.mimsave('gif2.gif', images, duration=1)\n\nfor filename in set(filenames):\n os.remove(filename)\n \nImage(open('gif2.gif', 'rb').read())","metadata":{"_kg_hide-input":true,"jupyter":{"source_hidden":true},"execution":{"iopub.status.busy":"2022-11-10T13:20:37.619722Z","iopub.execute_input":"2022-11-10T13:20:37.620300Z","iopub.status.idle":"2022-11-10T13:20:41.190725Z","shell.execute_reply.started":"2022-11-10T13:20:37.620262Z","shell.execute_reply":"2022-11-10T13:20:41.189480Z"},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"#\nTo begin with, it's interesting to evaluate how often the expected by odds winners and underdogs compliance with the actual results. The expected position by viewers is quite easy to calculate based on the distribution of their bets.\n
","metadata":{}},{"cell_type":"code","source":"full_df = pd.read_csv('../input/derby-full-data/derby_tracking_full.csv') # Main file (tracking info)\n\ncols = ['track_id', 'race_date', 'race_number', \n 'program_number', 'weight_carried', 'jockey', \n 'odds', 'final_place']\njok_info = pd.read_csv('../input/big-data-derby-2022/nyra_start_table.csv', names=cols)\n\njok_info = race_id(jok_info)\njok_info['program_number'] = le.transform(jok_info['program_number'].astype('str'))\njok_info['race_date'] = pd.to_datetime(jok_info['race_date'])\njok_info.drop(['track_id', 'race_number'], axis=1, inplace=True)\ncols = jok_info.columns.tolist()\njok_info = jok_info[cols[-1:] + cols[:-1]]\n\n# Expected finish place\njok_info['expected_finish_place'] = jok_info.groupby('race_id')['odds'] \\\n .rank(method='min').astype(np.int16)\n# Reality equals expectations\ndef ree(row):\n return row['final_place'] == row['expected_finish_place']\njok_info['REE'] = jok_info[['final_place', 'expected_finish_place']] \\\n .apply(lambda row: ree(row), axis=1)\n\n# Count of horses and dist\njok_info = jok_info.merge(full_df[['race_id', 'num_horses']].drop_duplicates(),\n on='race_id', how='left') \\\n .merge(races_info[['race_id', 'dist_furlong']], \n on='race_id', how='left')\n\n# Favorite or underdog\ndef fav_und(row, col):\n if row[col]==1:\n return '1st'\n elif row[col]==2:\n return '2nd'\n elif row[col]==row['num_horses']-1:\n return 'pre-last'\n elif row[col]==row['num_horses']:\n return 'last'\n else:\n return 'middle'\n \njok_info['fav_und'] = jok_info[['expected_finish_place', 'num_horses']]\\\n .apply(lambda row: fav_und(row, 'expected_finish_place'), axis=1)\n \njok_info['act_pos'] = jok_info[['final_place', 'num_horses']]\\\n .apply(lambda row: fav_und(row, 'final_place'), axis=1)\n\n# ##############################################\n\nstat = jok_info.groupby('fav_und', as_index=False) \\\n .agg({'REE': 'sum'}).drop([3]).reset_index(drop=True)\nb, c = stat.iloc[2].copy(), stat.iloc[3].copy()\nstat.iloc[2], stat.iloc[3] = c, b\n\nstat['REE_rating'] = round(stat['REE'] / 2000 * 100, 1)\n\nfig = go.Figure()\nfig.add_trace(go.Bar(x=stat['REE_rating'], y=stat['fav_und'],\n marker=dict(color='#34675c',\n line=dict(width=0.5, color='black')),\n hovertemplate='%{x}'+ \"\nViewers are more likely to guess the winners at short and long distances than at medium distances. The more participants in the race, the less chance to guess the winner. They are 5% more likely to correctly identify the current underdog at long distances than at short ones. Also, they correctly identify the underdog in almost half of the races, where the number of participants is no more than 5.\n
","metadata":{}},{"cell_type":"code","source":"jok_info = jok_info.merge(races_info[['race_id', 'track_condition', 'race_type']], \n on='race_id', how='left')\n\ncompl_tc = pd.DataFrame(columns=['Expected position', 'MY ', 'GD ', 'FT ', \n 'SY ', 'FM ', 'YL ', 'SF '])\ncompl_tc['Expected position'] = ['1st', '2nd', 'pre-last', 'last']\ntc = ['MY ', 'GD ', 'FT ', 'SY ', 'FM ', 'YL ', 'SF ']\n\nr1, r2, r3, r4, r5, r6, r7 = [], [], [], [], [], [], []\nfor position in ['1st', '2nd', 'pre-last', 'last']:\n for t, res in zip(tc, [r1, r2, r3, r4, r5, r6, r7]):\n info = jok_info[jok_info['track_condition']==t]\n l = info['race_id'].nunique()\n info = info[(info['fav_und']==position)&\n (info['expected_finish_place']==info['final_place'])]\n res.append(round(len(info)/l*100,2))\nfor col, res in zip(compl_tc.columns[1:], [r1, r2, r3, r4, r5, r6, r7]):\n compl_tc[col] = res\n \n###################################################\n\ncompl_rt = pd.DataFrame(columns=['Expected position', 'AOC', 'MCL', 'ALW', 'STK', \n 'CLM', 'MSW', 'STR', 'SOC', \n 'SHP', 'WCL', 'SST', 'WMC'])\ncompl_rt['Expected position'] = ['1st', '2nd', 'pre-last', 'last']\nrt = ['AOC', 'MCL', 'ALW', 'STK', \n 'CLM', 'MSW', 'STR', 'SOC', \n 'SHP', 'WCL', 'SST', 'WMC']\n\nr1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12 = [], [], [], [], [], [], [], [], [], [], [], []\nfor position in ['1st', '2nd', 'pre-last', 'last']:\n for t, res in zip(rt, [r1, r2, r3, r4, r5, r6, \n r7, r8, r9, r10, r11, r12]):\n info = jok_info[jok_info['race_type']==t]\n l = info['race_id'].nunique()\n info = info[(info['fav_und']==position)&\n (info['expected_finish_place']==info['final_place'])]\n try:\n res.append(round(len(info)/l*100,2))\n except:\n res.append(0)\nfor col, res in zip(compl_rt.columns[1:], [r1, r2, r3, r4, r5, r6, \n r7, r8, r9, r10, r11, r12]):\n compl_rt[col] = res\n \n#####################################################\n \ndef style_df(df, title, size):\n for col in df.columns:\n df[col] = df[col].astype('str')\n \n df = df.style.hide_index().set_caption(title)\\\n .set_table_styles([\n {'selector': 'th.col_heading', 'props': 'font-size: 12pt; text-align: center; font-weight: bold; border-collapse: collapse'},\n {'selector': 'td', 'props': 'text-align: center; font-size: 11pt; border: 1px solid black !important'},\n {'selector': 'caption', 'props': 'font-size: 14pt; font-weight: bold; color: #303030'},\n {'selector': 'th:not(.index_name)', 'props': 'background-color: #34675c; color: white;'}\n ], overwrite=False).set_properties(subset=['Expected position'], **{'font-weight': 'bold'}) \\\n .set_properties(**{'background-color': '#fafafa'}).set_table_attributes(\"style='display:inline'\")\n return df\ndisplay(style_df(compl_rt, 'Compliance by type of race', 10))\nprint()\ndisplay(style_df(compl_tc, 'Compliance by track condition', 11))","metadata":{"_kg_hide-input":true,"jupyter":{"source_hidden":true},"execution":{"iopub.status.busy":"2022-11-10T13:21:07.926220Z","iopub.execute_input":"2022-11-10T13:21:07.926617Z","iopub.status.idle":"2022-11-10T13:21:08.273545Z","shell.execute_reply.started":"2022-11-10T13:21:07.926581Z","shell.execute_reply":"2022-11-10T13:21:08.271940Z"},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"\nThe data contains information about only 40 races with types WMC, SHP, WCL, SST and SOC, so it is useless to make any conclusions about them. Most often, viewers guess the winner in races with \"Starter Allowance\" type - 46.75%. The least often, they guess the winner in races with \"Maiden claiming\" type - 35.38%. This difference is easy to explain: \"Maiden claiming\" races are for horses that have never won a race. Therefore, it is harder for viewers to predict the outcome. In 40.15% of \"Maiden Special Weight\" races, the underdog justifies it's position. \"Maiden special weight\" races feature top quality horses that are expected to quickly break their maidens and move on to more prestigious competitions. This means that it is easier for viewers to single out the worst among promising horses. Most often, viewers manage to guess the winner in races with a sloppy track condition. This is quite strange, given the increased complexity for all participants.\n
","metadata":{}},{"cell_type":"markdown","source":"#\nEveryone is interested in the final result, but let's see what part of the time the participants hold the expected and actual position depending on the stage of the distance (the first 30% of the distance, 30-70% and the final 30%) and what was their finish position:\n
","metadata":{}},{"cell_type":"code","source":"def positions(df, position):\n if position == 'expected_finish_place':\n suff = '_efp'\n else:\n suff = '_act'\n info = pd.DataFrame(columns=['race_id', 'program_number', \n 'compliance_0_30'+suff, 'compliance_30_70'+suff, \n 'compliance_70_100'+suff])\n r, h, res30, res70, res100 = [], [], [], [], []\n for i in df['race_id'].unique():\n r_info = df[(df['race_id']==i)&(df['completed_dist']<=100)]\n for horse in r_info['program_number'].unique():\n h_info = r_info[r_info['program_number']==horse]\n place = jok_info[(jok_info['race_id']==i)&\n (jok_info['program_number']==horse)] \\\n [position].values[0]\n r.append(i)\n h.append(horse)\n for c_dist, list_ in zip({30: 30, 70: 40, 100: 30}.items(), \n [res30, res70, res100]):\n h_info2 = h_info[(h_info['completed_dist']>(c_dist[0]-c_dist[1]))&\n (h_info['completed_dist']<=c_dist[0])]\n try:\n list_.append(int(len(h_info2[(h_info2['position']==place)]) \\\n /len(h_info2)*100))\n except:\n list_.append(np.nan)\n for col, list_ in zip(info.columns.tolist(), [r, h, res30, res70, res100]):\n info[col] = list_\n return info\n\npos_df = positions(full_df, 'expected_finish_place')\njok_info = jok_info.merge(pos_df, on=['race_id', 'program_number'], how='left')\npos_df = positions(full_df, 'final_place')\njok_info = jok_info.merge(pos_df, on=['race_id', 'program_number'], how='left')\n\njok_info['compliance_total_efp'] = jok_info['compliance_0_30_efp']*0.3 + \\\n jok_info['compliance_30_70_efp']*0.4 + \\\n jok_info['compliance_70_100_efp']*0.3\n\ndef positions2(df, act_efp, suff):\n stat = df.groupby(act_efp, as_index=False) \\\n .agg({'compliance_0_30'+suff: 'mean',\n 'compliance_30_70'+suff: 'mean',\n 'compliance_70_100'+suff: 'mean'}).drop([3]).reset_index(drop=True)\n for col in stat.columns[1:]:\n stat[col] = stat[col].round(1)\n b, c = stat.iloc[2].copy(), stat.iloc[3].copy()\n stat.iloc[2], stat.iloc[3] = c, b\n return stat\n\nstat_efp = positions2(jok_info, 'fav_und', '_efp')\nstat_act = positions2(jok_info, 'act_pos', '_act')\n\ncolors = ['#'+x for x in ['34675c', 'b7b8b6', 'ebc91e']]\nfig = make_subplots(rows=2, cols=1, \n vertical_spacing=0.1,\n subplot_titles=('Expected', \n 'Actual'))\n \ncols = ['compliance_0_30', 'compliance_30_70', 'compliance_70_100']\nnames = {col: name for col, name in zip(cols, ['0-30', '30-70', '70-100'])}\ndfs = [stat_efp, stat_act]\nx_ = {1: 'fav_und', 2: 'act_pos'}\n\nfor info in zip(dfs, ['_efp', '_act'], [1,2]):\n for col in cols:\n fig.add_trace(go.Scatter(x=info[0][x_[info[2]]], \n y=info[0][col+info[1]], \n name=names[col],\n mode='markers',\n marker=dict(color=colors[cols.index(col)],\n line=dict(width=0.5, color='black'),\n size=10),\n legendgroup=col, \n hovertemplate='%{y}'+ \"\nThe last 30% of the distance becomes decisive - on average, 55% of the time leaders and losers holds it's actual finish position. The first 70% of the distance leaders and losers hold less than a quarter of the time of their actual position. But looking at the graph, there is definitely no clear conclusion, why so? It is not so easy to take and hold a good expected position, especially with a large number of competitors. In addition, the goal of jockeys is not to hold the expected position, but to win. \n
\n\nSo, it is important to evaluate the actual finishing position depending on how long the expected leaders remain in the TOP 3, and underdogs in the LAST 3. For this purpose, were considered races with 6 or more participants:\n
","metadata":{}},{"cell_type":"markdown","source":"\nOf course, there is the fact that the higher the horse hold a position in the TOP 3, the higher the compliance of the expected and actual finish position. The results are quite obvious, but even long-term hold of leading positions doesn't guarantee leading positions at the finish. The expected leaders of the race, holding the leading positions for more than 2/3 time of the race, finished in fourth position and worse in 15.8% (expected 1st) and 27.7% (expected 2nd) of such races.\n\nIt is also worth considering similar statistics for underdogs:\n
","metadata":{}},{"cell_type":"code","source":"display_html(pre_last_stat._repr_html_()+space+last_stat._repr_html_(), raw=True)","metadata":{"_kg_hide-input":true,"jupyter":{"source_hidden":true},"execution":{"iopub.status.busy":"2022-11-10T13:25:17.338666Z","iopub.execute_input":"2022-11-10T13:25:17.339002Z","iopub.status.idle":"2022-11-10T13:25:17.365167Z","shell.execute_reply.started":"2022-11-10T13:25:17.338972Z","shell.execute_reply":"2022-11-10T13:25:17.363780Z"},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"\nMost of all attention should be paid to the fact that the expected underdogs, who spend almost all the time of the race in the last positions, get into the TOP-3 in ~10% of the races!\n
\n\nHow does this happen and what does it depend on? During the race, the change in position determines the difference in speed from the average speed of competitors. Speed changes can occur for a variety of reasons, which, unfortunately, it is not available to us to determine for all races in general. In case of slowing down, it may be a jockey's mistake, sudden deterioration in the health or fatigue of the horse, slowing down of competitors running ahead, etc. \n
","metadata":{}},{"cell_type":"markdown","source":"#\nBefore I start analyzing all races in general, I want to demonstrate an example of a race where the underdog Joey R. Martinez, running in the last position throughout the race, took first place at the very last moment, overtaking the expected winner Reylu Gutierrez, who held the leading position 92.5% of the race! At the finish straight, the distance to the leader was 60 feet, there was 25% of the distance left, but Martinez snatched the victory contrary to any expectations.\n
","metadata":{}},{"cell_type":"code","source":"exp = full_df[full_df['race_id']==32]\nexp['text_scatter'] = 'Distance (feet): ' + exp['passed_dist'].round(2).astype('str') + '\nNo statistical model could have predicted such an outcome even during the race. Of course, this is an exception to the rules, but this race serves as an example of the fact that the actual finish position depends not only on the horse's own position during the race. It is important to take into account the speed of competitors. \n
\n\nThis race is also an excellent example for analyzing the speed of the expected winner and underdog in comparison with the average speed of all participants:\n
","metadata":{}},{"cell_type":"code","source":"exp_plot = exp[(exp['time_sec']>0.25)&(exp['program_number']==0)]\n\nfig = make_subplots(rows=3, cols=1, \n vertical_spacing=0.05,\n subplot_titles=('Speed',\n 'Deviation from the average speed',\n \"Distance to the leader\"))\nfig.add_trace(go.Scatter(x=exp_plot['time_sec'], y=exp_plot['gen_avg_speed'],\n name='average speed', mode='lines',\n line=dict(color='#344d90', width=1, dash='dot'),\n hovertemplate='%{y:.2f}'+\"\nWe can see that the distance between Martinez and Gutierrez steadily increased throughout the race, but at 48 seconds, as soon as Martinez reached the finish straight, he abruptly shortened the distance, overtaking everyone and taking first place. There may be many reasons for this outcome, but from my point of view, Martinez, holding on to the last position, retained a lot of strength of his horse to the finish straight, thanks to which he was able to overtake tired competitors. It is also worth noting that there were 4 more similar situations in his career in 2019. We'll leave this race for now, but we'll come back to it later.\n
","metadata":{}},{"cell_type":"markdown","source":"#\nOur task is not to thoroughly study one race, but to try to find a common solution. Let's look at all the races depending on their distance. The distance of all races is different and each takes a different amount of time, so it is incorrect to take into account the speed during each quarter of a second. Thus, the analysis will be performed based on each 1% of the completed distance. Many analysts consider the speed of each participant individually, but it is more interesting for me to look at the difference in speed between winners and losers.\n
","metadata":{}},{"cell_type":"code","source":"def percent_races(df):\n pr = pd.DataFrame()\n for race in df['race_id'].unique():\n exp = df[df['race_id']==race]\n exp['completed_dist_round'] = exp['completed_dist'].apply(lambda x: math.ceil(x))\n info = exp.groupby(['completed_dist_round', 'program_number']) \\\n .agg({'speed_mph': 'mean', 'dist_to_lead': 'mean'}).reset_index() \\\n .rename({'completed_dist_round': 'dist'}, axis=1)\n info = info[info['dist'].between(1,100)]\n ms = exp.groupby('completed_dist_round') \\\n ['gen_avg_speed'].mean().reset_index() \\\n .rename({'completed_dist_round': 'dist'}, axis=1)\n info = info.merge(ms, on='dist', how='left')\n info['race_id'] = exp['race_id'].unique()[0]\n info['sdm_num'] = info['speed_mph'] - info['gen_avg_speed']\n info['sdm_%'] = round((info['speed_mph'] /\n info['gen_avg_speed']*100)-100, 2)\n pr = pd.concat([pr, info], axis=0, ignore_index=True)\n return pr\n\npr = percent_races(full_df)\npr = pr.merge(jok_info[['race_id', 'program_number', 'final_place',\n 'expected_finish_place', 'dist_furlong', \n 'num_horses', 'fav_und', 'act_pos']], \n on=['race_id', 'program_number'], how='left')\npr = pr[pr['dist_furlong'].isin(sorted(pr['dist_furlong'].unique().tolist())[2:9])]\n\n#############################################################\n\nfig = make_subplots(rows=4, cols=1, \n vertical_spacing=0.05,\n subplot_titles=('6 furlongs',\n '7 furlongs',\n '8 furlongs',\n '9 furlongs'))\n\nfor i, furlong in enumerate([6,7,8,9]):\n info = pr[pr['dist_furlong']==furlong]\n for line, color in zip(['1st', 'last'], ['#34675c', '#c71c1c']):\n for col, name, width in zip(['fav_und', 'act_pos'], \n ['expected ', 'actual '],\n [1, 3]):\n info_2 = info[info[col]==line]\n fig.add_trace(go.Scatter(x=sorted(info_2['dist'].unique().tolist()), \n y=info_2.groupby('dist')['sdm_%'].mean(), \n name=name+line, mode='lines', legendgroup=name+line,\n line=dict(color=color, width=width, \n dash=('solid' if width==3 else 'dot')),\n showlegend=(True if i==0 else False),\n hovertemplate='%{y:.2f}%'+\"\nRegarding races at middle and long distances (7-9 furlongs), horses keep approximately the same speed for more than half of the distance. The speed deviation from the average does not differ by more than 1% on average: 50% of distance for 7 furlongs, 55% for 8 furlongs and 60% for 9 furlongs. This is quite understandable - there is no need to frazzle horses at the beginning or in the middle of the race, when you can stick to the average speed. All participants try to leave the explosive power of horses to the end of the race. With increasing distance, endurance becomes more important than explosive power. But it is also important to note that before the participants begin to hold the average speed, the leaders start with a considerable deviation from the average speed of the other participants. As for short-distance races, all is the opposite - the participants start the fight earlier and explosive power is already becoming more important.\n
\n\nIt is also necessary to consider the difference in speed on turns:\n
","metadata":{}},{"cell_type":"code","source":"full_df = full_df.merge(jok_info[['race_id', 'program_number', 'fav_und', \n 'act_pos', 'dist_furlong']], \n on=['race_id', 'program_number'], how='left')\nfig = go.Figure()\nfor fur in [6,7,8,9]:\n info = full_df[(full_df['not_turn']==False)&\n (full_df['dist_furlong']==fur)]\n for pos, color in zip(['1st', 'last'], ['#34675c', '#c71c1c']):\n fig.add_trace(go.Scatter(x=np.array(fur), \n y=np.array(info[info['act_pos']==pos]['speed_diff_avg_%'].mean()), \n name='Actual '+pos,\n mode='markers',\n marker=dict(color=color,\n line=dict(width=0.5, color='black'),\n size=10),\n hovertemplate='%{y:.2f}%'+ \"\nThe results are quite obvious, but I propose to consider in more detail how the distance to the leader changes during the race:\n
","metadata":{}},{"cell_type":"code","source":"fig = make_subplots(rows=4, cols=1, \n vertical_spacing=0.05,\n subplot_titles=('6 furlongs',\n '7 furlongs',\n '8 furlongs',\n '9 furlongs'))\n\nfor i, furlong in enumerate([6,7,8,9]):\n info = pr[pr['dist_furlong']==furlong]\n fig.add_trace(go.Scatter(x=sorted(info['dist'].unique().tolist()), \n y=info.groupby('dist')['dist_to_lead'].mean(), \n name='average dist', mode='lines', \n legendgroup='average dist',\n line=dict(color='#344d90', width=1, dash='dot'),\n showlegend=(True if i==0 else False),\n hovertemplate='%{y:.2f}'+\"\nThe results of the change in the average distance to the leader during the race also confirms that the culmination of middle and long races occurs closer to the finish. In the first half of the race, the distance of the actual leaders to the leading position does not exceed 16-23.5 feet, depending on the race distance. Difference between the leaders and losers to leading position is no more than 9-17 feet for 7-9 furlongs distances, but with 10% remaining until the end of the race, the difference is more than 120 feet! In addition, it is also interesting that a small difference in the results of speed and distance to the leader between the expected and actual leaders and losers persists for quite a long time from the start.\n
","metadata":{}},{"cell_type":"markdown","source":"#\nBased on the graphs describing the change in speed and distance to the leader, there could be a misconception that in races with distances from 7 furlongs and above, from the start to the middle of the distance, there is almost no change in positions. This is partly true, especially if we compare the distance interval of 20-70% and last 30%. However, the change of positions occurs throughout the race.\n
","metadata":{}},{"cell_type":"code","source":"def overtaking_stat(df):\n res = pd.DataFrame()\n for race in full_df['race_id'].unique():\n exp = full_df[full_df['race_id']==race]\n exp = exp[exp['time_sec']>=1]\n exp['completed_dist_round'] = exp['completed_dist'] \\\n .apply(lambda x: math.ceil(x))\n ot_stat = pd.DataFrame()\n time = sorted(exp['time_sec'].unique().tolist())[1:]\n overtaking = []\n for sec in time:\n positions_aft = exp[exp['time_sec']==sec]['position'].tolist()\n positions_bef = exp[exp['time_sec']==sec-0.25]['position'].tolist()\n if positions_aft == positions_bef:\n overtaking.append(False)\n else:\n overtaking.append(True)\n \n ot_stat['time_sec'] = time\n ot_stat['overtaking'] = overtaking\n\n winner = jok_info[(jok_info['race_id']==race)&\n (jok_info['final_place']==1)] \\\n ['program_number'].values[0]\n dist = exp[(exp['program_number']==winner)&\n (exp['completed_dist_round']<=100)] \\\n [['time_sec', 'completed_dist_round']]\n ot_stat = ot_stat.merge(dist, on='time_sec', how='inner')\n\n ot_stat = ot_stat.groupby('completed_dist_round') \\\n ['overtaking'].sum().reset_index()\n ot_stat['race_id'] = exp['race_id'].values[0]\n \n res = pd.concat([res, ot_stat], ignore_index=True)\n return res\n\not_stat = overtaking_stat(full_df)\not_stat = ot_stat.merge(races_info[['race_id', 'dist_furlong', \n 'track_condition']], \n on='race_id', how='left')\not_stat = ot_stat.merge(jok_info[['race_id', 'num_horses']].drop_duplicates(),\n on='race_id', how='left')\not_stat.rename({'completed_dist_round': 'dist'}, axis=1, inplace=True)\n\n###########################################\n\nfig = make_subplots(rows=4, cols=1, \n vertical_spacing=0.05,\n subplot_titles=('4-5 participants',\n '6-7 participants',\n '8-9 participants',\n '10-11 participants'))\n\nfor i, p in enumerate([4,6,8,10]):\n info = ot_stat[(ot_stat['num_horses'].between(p, p+1))&(ot_stat['dist_furlong']==9)]\n x = sorted(info['dist'].unique().tolist())\n y = info.groupby('dist')['overtaking'].mean().reset_index()\n ma = y['overtaking'].rolling(5).mean()\n \n fig.add_trace(go.Scatter(x=x, y=y['overtaking'], \n name='Every 1% of distance', mode='lines', \n line=dict(color='#344d90', width=1),\n showlegend=(True if i==0 else False),\n legendgroup='Every 1% of distance',\n hovertemplate='%{y:.2f}'+\"\nTry to change the interval of the completed distance (20-100%) and you will see the difference in the number of overtaking. From the above results, the number of overtaking in the last 30% of the distance in all races increases by ~28%. Interesting that the change of positions with 6-9 participants throughout the race is quite stable. The analysis of speed, distance to the leader and the number of overtaking tells us that the last ~30% of the distance are the most important. \n
","metadata":{}},{"cell_type":"markdown","source":"#\nThe whole analysis above rested on the fact that the most important and decisive stage of the race is the final one, where the participant, who holds the last positions throughout the race, can become the winner. But how valuable is the information throughout the race and what does the expected position depend on? To answer this question, it will take something more than statistics and graphs - machine learning algorithm!\n
\n\nFrom the point of view of machine learning, calculating the expected finish position is a multi-class classification task, but there is one big nuance: the number of participants in each race is different. A participant whose expected position is the third among 3-4 participants is a bad expectation, but among 9 or more participants is already a good one. Therefore, I decided to use binary classification, where the expected position of all participants will depend on their chances of winning in the ranking order. There will be used XGB algorithm with AUC metric. What is AUC and how to understand it's results will be explained immediately after learning the algorithm.\n
\n\nInformation that will be useful for learning the algorithm:\n
\nThe model will be trained at intervals every 10% of the distance, which will allow for a better evaluation of the impact of various factors on predictions throughout the race. In addition, the model will not use the individual speed of the participant, but only his speed deviation from the speed of other participants. You may have noticed that information about the type of race and the condition of the track was not added to the model. This information, as well as the length of the distance and the number of participants, has no effect on improving the quality of predictions. You will see the results below:\n
","metadata":{}},{"cell_type":"code","source":"#################\n# PREPROCESSING #\n#################\n\njok_info.drop(jok_info.columns[-7:].tolist(), axis=1, inplace=True)\n\n###########\n# Statistics on previous games of 2019 didn't show big improvement, so I decided not to take it into account.\n###########\n\n# lej = LabelEncoder()\n# jok_info['jockey_id'] = lej.fit_transform(jok_info['jockey'])\n#\n# def jockey_position_time(df):\n# res_df = pd.DataFrame(columns=['race_id', 'program_number', \n# 'time_in_top3', 'time_top1', \n# 'time_last'])\n# rid, pn, top3, top1, last = [], [], [], [], []\n# for race in df['race_id'].unique():\n# info = df[df['race_id']==race]\n# for horse in info['program_number'].unique():\n# h_info = info[info['program_number']==horse]\n# rid.append(race)\n# pn.append(horse)\n# top3.append(len(h_info[h_info['position']<4])/len(h_info))\n# top1.append(len(h_info[h_info['position']==1])/len(h_info))\n# last.append(len(h_info[h_info['position']==h_info['num_horses'].values[0]])/len(h_info))\n# for list_, col in zip([rid, pn, top3, top1, last],\n# res_df.columns):\n# res_df[col] = list_\n# return res_df\n\n# jpt = jockey_position_time(full_df)\n\n################################################################\n\n# jok_stat = jok_info.groupby(['jockey', 'race_id'])['final_place'].count() \\\n# .reset_index().rename({'final_place': 'races'}, axis=1)\n# wins = jok_info[jok_info['final_place']==1].groupby(['jockey', \n# 'race_id'])['final_place'].count() \\\n# .reset_index().rename({'final_place': \n# 'wins'}, axis=1)\n# top3 = jok_info[jok_info['final_place']<4].groupby(['jockey', \n# 'race_id'])['final_place'].count() \\\n# .reset_index().rename({'final_place': \n# 'top3'}, axis=1)\n# last_place = jok_info[jok_info['act_pos']=='last'].groupby(['jockey', \n# 'race_id'])['final_place'].count() \\\n# .reset_index().rename({'final_place': \n# 'last'}, axis=1)\n\n# jok_stat = jok_stat.merge(wins, on=['jockey', 'race_id'], how='left') \\\n# .merge(top3, on=['jockey', 'race_id'], how='left') \\\n# .merge(last_place, on=['jockey', 'race_id'], how='left').fillna(0)\n# jok_stat.sort_values(['jockey', 'race_id'], inplace=True)\n# jok_stat = jok_stat.merge(jok_info[['race_id', 'jockey', 'program_number']], \n# on=['race_id', 'jockey'], how='left')\n# jok_stat = jok_stat.merge(jpt, on=['program_number', 'race_id'], how='left').drop('program_number', axis=1)\n\n# cum_stat = jok_stat.groupby('jockey').cumsum()\n# cols = ['wins', 'top3', 'last', \n# 'time_in_top3', 'time_top1', 'time_last']\n# for col in cols:\n# jok_stat[col] = cum_stat[col] / cum_stat['races']\n# jok_stat['races'] = cum_stat['races']\n\n# for col in cols+['races']:\n# jok_stat[col] = jok_stat.groupby('jockey')[col].shift(1).fillna(0)\n \n# def comparison_participants(df):\n# new_df = pd.DataFrame()\n# for race in df['race_id'].unique():\n# info = df[df['race_id']==race].groupby('race_id').mean() \\\n# .reset_index().drop('jockey', axis=1)\n# info.rename({col: 'avg_'+col for col in info.columns.tolist()[1:]}, \n# axis=1, inplace=True)\n# new_df = pd.concat([new_df, info], axis=0, ignore_index=True)\n# cols = df.columns[-7:]\n# df = df.merge(new_df, on='race_id', how='left')\n# for col in cols:\n# df[f'diff_{col}'] = df[col] - df[f'avg_{col}']\n# df.drop([f'avg_{col}', col], axis=1, inplace=True)\n# return df\n# jok_stat = comparison_participants(jok_stat)\n\n# jok_info = jok_info.merge(jok_stat, on=['jockey', 'race_id'], how='left')\n# jok_info['jockey'] = lej.inverse_transform(jok_info['jockey'])\n\n########################################\n\ndef find_winner_loser(info, joks, race_id, pos, col_name):\n horse = joks[joks['fav_und']==pos]['program_number'].values[0]\n return info[info['program_number']==horse] \\\n .groupby('completed_dist_round')['speed_mph'].mean() \\\n .reset_index().rename({'speed_mph': col_name}, axis=1)\n\ndef ml_preprocessing(df):\n new_df = pd.DataFrame(columns=['race_id', 'program_number', 'avg_sdw', \n 'avg_sdl', 'avg_sda', 'avg_dtl', \n 'l_dtl', 'mode_pos', 'l_pos', \n 'odds', 'j_wt', 'r_dist', 'num_horses'])\n rid, pn, avg_sdw, avg_sdl, avg_sda = [], [], [], [], []\n avg_dtl, l_dtl, mode_pos, l_pos, exp_pos, odds = [], [], [], [], [], []\n j_wt, r_dist, num_horses = [], [], []\n \n jinfo = jok_info[~jok_info['race_id'].isin(list(htd.keys())+[652, 820])]\n # In races 652 and 820 there are participants who didn't reach the finish line\n \n for race in tqdm(jinfo['race_id'].unique()):\n info = df[df['race_id']==race]\n joks = jinfo[jinfo['race_id']==race]\n \n winner_speed = find_winner_loser(info, joks, race, '1st', 'w_speed')\n try: \n loser_speed = find_winner_loser(info, joks, race, 'last', 'l_speed')\n except: # In some races there are several underdogs at once\n loser_speed = find_winner_loser(info, joks, race, 'pre-last', 'l_speed')\n avg_speed = info.groupby('completed_dist_round')['speed_mph'].mean()\\\n .reset_index().rename({'speed_mph': 'avg_speed'}, axis=1)\n \n w_carried = dict(zip(joks['program_number'], joks['weight_carried']))\n odds_stat = dict(zip(joks['program_number'], joks['odds']))\n \n nh = info['num_horses'].values[0]\n num_horses += [nh]*nh\n r_dist += [joks['dist_furlong'].values[0]]*nh\n rid += [joks['race_id'].values[0]]*nh\n \n positions = [[], []] # List with mode of position and last position for min-max scaling\n \n for horse in info['program_number'].unique():\n all_h_info = info[info['program_number']==horse]\n ## --- ##\n h_info = all_h_info.groupby('completed_dist_round') \\\n .agg({'speed_mph': 'mean',\n 'dist_to_lead': 'mean'}).reset_index()\n h_info = h_info.merge(winner_speed, on='completed_dist_round', how='left') \\\n .merge(loser_speed, on='completed_dist_round', how='left') \\\n .merge(avg_speed, on='completed_dist_round', how='left')\n \n cols = ['sdw', 'sdl', 'sda']\n for col1, col2 in zip(h_info.columns[-3:], cols):\n h_info[col2] = round(h_info['speed_mph']/h_info[col1]*100-100, 2)\n \n for list_, col in zip([avg_sdw, avg_sdl, avg_sda],\n ['sdw', 'sdl', 'sda']):\n list_.append(h_info[col].mean())\n ## --- ## \n avg_dtl.append(all_h_info['dist_to_lead'].mean())\n l_dtl.append(all_h_info['dist_to_lead'].values[-1])\n j_wt.append(w_carried[horse])\n odds.append(odds_stat[horse])\n pn.append(horse)\n \n positions[0].append(all_h_info['position'].mode().values[0])\n positions[1].append(all_h_info['position'].values[-1])\n \n for i, list_ in enumerate([mode_pos, l_pos]): # min-max scaling\n pos = positions[i].copy()\n list_ += [(x-min(pos))/(max(pos)-min(pos)) for x in pos]\n \n for list_, col in zip([rid, pn, avg_sdw, avg_sdl, avg_sda, \n avg_dtl, l_dtl, mode_pos, \n l_pos, odds, j_wt, r_dist, num_horses],\n new_df.columns):\n new_df[col] = list_\n return new_df\n\ndf1, df2, df3, df4, df5, df6, df7, df8, df9 = 0,0,0,0,0,0,0,0,0\n\ndef create_ml_df(dist):\n df = full_df[full_df['completed_dist'].between(dist-10, dist)]\n df['completed_dist_round'] = df['completed_dist'].apply(lambda x: math.ceil(x))\n df = df[df['completed_dist_round']>0]\n df = ml_preprocessing(df)\n df = df.merge(jok_info[['race_id', 'program_number', 'final_place']], \n on=['race_id', 'program_number'], how='left')\n arr = df['final_place']\n arr = np.where(arr > 1, 0, 1)\n df['final_place'] = arr\n return df\n\ndf1 = create_ml_df(10)\ndf2 = create_ml_df(20)\ndf3 = create_ml_df(30)\ndf4 = create_ml_df(40)\ndf5 = create_ml_df(50)\ndf6 = create_ml_df(60)\ndf7 = create_ml_df(70)\ndf8 = create_ml_df(80)\ndf9 = create_ml_df(90)\n\ny = df1['final_place']\n\nFOLDS = 5\nseed = 228\n\n############\n# TRAINING #\n############\n\nbest_xgb_params = {\n 'max_depth': 6,\n 'learning_rate': 0.02,\n 'subsample': 0.6,\n 'colsample_bytree': 0.8,\n 'min_child_weight': 44,\n 'gamma': 4,\n 'lambda': 44,\n \n 'seed': seed,\n 'objective': 'binary:logistic',\n 'eval_metric': 'auc'\n } # Found with Optuna\n\nall_predictions, pred_results = [], []\n\ndef ml_train(ml_df, dist):\n global jok_info\n \n X = ml_df.drop(['race_id', 'program_number', 'final_place'], axis=1)\n importances, scores, predictions = [], [], pd.DataFrame()\n \n print(f'Start learning for {dist-10}-{dist}% of race data...')\n k = StratifiedKFold(n_splits=FOLDS, random_state=seed, shuffle=True)\n for fold, (train_idx, val_idx) in enumerate(k.split(X, y)):\n dtrain = xgb.DMatrix(X.iloc[train_idx], label=y.iloc[train_idx])\n dvalid = xgb.DMatrix(X.iloc[val_idx], label=y.iloc[val_idx])\n watchlist = [(dtrain, 'train'), (dvalid, 'eval')]\n \n model = xgb.train(best_xgb_params, dtrain=dtrain, num_boost_round=3000,\n evals=watchlist, early_stopping_rounds=300, \n verbose_eval=False, maximize=True)\n \n imp = model.get_score(importance_type='weight')\n imp_stat = pd.DataFrame({'feature': imp.keys(), \n f'importance_{fold}': imp.values()})\n importances.append(imp_stat)\n \n val_preds = model.predict(dvalid, iteration_range=(0, model.best_ntree_limit))\n results = X.iloc[val_idx]\n results['preds'] = val_preds\n predictions = pd.concat([predictions, results[['preds']]], axis=0)\n val_score = roc_auc_score(y.iloc[val_idx], val_preds)\n scores.append(val_score)\n print(f'--- FOLD {fold+1} AUC score - {round(val_score, 6)} | best iteration - {model.best_ntree_limit} ---')\n \n imp = importances[0].copy()\n for i in range(1, FOLDS): \n imp = imp.merge(importances[i], on='feature', how='left')\n imp['importance'] = imp.iloc[:,1:].mean(axis=1)\n imp = imp.sort_values('importance',ascending=False)\n imp['imp%'] = imp['importance'] / imp['importance'].sum() * 100\n \n predictions = predictions.sort_index().rename({'preds': f'preds{dist}%'}, axis=1)\n ml_df = ml_df.merge(predictions, left_index=True, right_index=True)\n jok_info = jok_info.merge(ml_df[['race_id', 'program_number', f'preds{dist}%']], \n on=['race_id', 'program_number'], how='left')\n \n all_predictions.append(predictions[f'preds{dist}%'].tolist())\n pred_results.append(round(np.mean(scores),3))\n print('*'*45)\n print(f'Final CV AUC score - {np.mean(scores)}\\n')\n \n return imp\n\nimp1 = ml_train(df1, 10)\nimp2 = ml_train(df2, 20)\nimp3 = ml_train(df3, 30)\nimp4 = ml_train(df4, 40)\nimp5 = ml_train(df5, 50)\nimp6 = ml_train(df6, 60)\nimp7 = ml_train(df7, 70)\nimp8 = ml_train(df8, 80)\nimp9 = ml_train(df9, 90)","metadata":{"_kg_hide-input":true,"_kg_hide-output":true,"jupyter":{"source_hidden":true,"outputs_hidden":true},"execution":{"iopub.status.busy":"2022-11-10T13:47:28.467083Z","iopub.execute_input":"2022-11-10T13:47:28.468154Z","iopub.status.idle":"2022-11-10T14:28:35.960431Z","shell.execute_reply.started":"2022-11-10T13:47:28.468090Z","shell.execute_reply":"2022-11-10T14:28:35.959101Z"},"collapsed":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"fig=go.Figure()\ncolors = ['#'+x for x in ['c71c1c', '344d90', '344d90', \n '344d90', '344d90', '344d90', \n '344d90', '344d90', '34675c']]\nfig.add_trace(go.Scatter(x=np.linspace(0,1,11), y=np.linspace(0,1,11), \n name='Random Chance', mode='lines', showlegend=False,\n line=dict(color=\"black\", width=1, dash=\"dot\")))\n \nfor i, dist, res in zip([0,1,2,3,4,5,6,7,8],\n [10,20,30,40,50,60,70,80,90],\n pred_results):\n pred = all_predictions[i]\n fpr, tpr, _ = roc_curve(y, pred)\n roc_auc = auc(fpr, tpr)\n name = (f'{dist-10}-{dist}% | AUC - {res}' if i != 0 else f' {dist-10}-{dist}% | AUC - {res}')\n fig.add_trace(go.Scatter(x=fpr, y=tpr, line=dict(color=colors[i], width=(3 if i in [0,8] else 1)), \n hovertemplate=False,\n visible=(\"legendonly\" if i not in [0,4,8] else True),\n name=name))\n\nfig.update_layout(width=800, height=700, plot_bgcolor='white',\n title=dict(text=\"AUC results of determination of the winner\nThe better the classifier separates two classes (winner and loser) - the larger the AUC (area under curve). It may seem that \"Wow, having data on the start of the race, it is already possible to determine the possible winner with not bad accuracy\". No, it's not. A lot depends on odds. But do the odds determine the expected position all the time of the race? No! After 60% of the distance, odds are no longer the dominant factor. The most important factors in determining the expected position throughout the race are average speed deviation from average speed of participants and distance to the leader. It is also interesting that in the first 40% of the distance, much depends on how much the speed of the participant differs from the speed of the underdog.\n
\n\nBut why XGB? Not LGB or CatBoost? In fact, the difference between the values predicted by them is small (if we talk about expected position, not probability of winning). I also tested LGB using categorical features (track condition, race type), but there were no drastic changes in the results. Why 10%? Not 1% or 5%? To increase the frequency of receipt of the expected results, you can choose any distance interval, but if you choose an interval of 1%, then you will have to train 100 models. Why is this particular approach to model development chosen? This model is just an example, the beginning of what can be improved with an increase in the amount of data.\n
\n\nLet's return to the analysis and take a look at the race we are already familiar with, which I told you about earlier, and see how much the expected position of all participants changes:\n
\n\nWatching this race has become even more interesting. As mentioned earlier, no model could have predicted such an outcome of the race. When Joey R. Martinez reached the finish straight, the probability of his victory was 0.51%! And even with data on 90% of the race and the fact of strong acceleration, his probability of winning was increase up to 10%. The first time I paid attention only to Martinez and Gutierrez, but now I want to pay attention also to Junior Alvarado with the 2nd expected position, who held this position throughout the race and finished 5th! As for the other participants, from the beginning to the end of the race, the probability of their victory was ~4%.\n
\n\nThis race is of sincere interest. But our goal is in the overall evaluate, so let's take a look at the results of all the races at once.\n
","metadata":{}},{"cell_type":"code","source":"def all_expected_position(df):\n res = pd.DataFrame()\n for race_id in df['race_id'].unique():\n race = jok_info[jok_info['race_id']==race_id]\n race = race[['race_id', 'program_number', 'fav_und', \n 'act_pos', 'final_place']+race.columns[-9:].tolist()]\n for col in race.columns[-9:]:\n race[col] = race[col].rank(method='min', ascending=False)\n race[col] = race['final_place'] == race[col]\n res = pd.concat([res, race], ignore_index=True)\n return res\n\nfinal = all_expected_position(jok_info.query('`preds10%` == `preds10%`'))\n\ndef pos_stat(df, position):\n res_df = pd.DataFrame()\n dist, res = [10,20,30,40,50,60,70,80,90], []\n for d in dist:\n res.append(len(df[(df['act_pos']==position)&\n (df[f'preds{d}%']==1)])/df['race_id'].nunique() * 100)\n res_df['dist'], res_df[f'true_pred_{position}'] = dist, res\n return res_df\n\ndef all_pos_stat(df):\n new_df = pd.DataFrame(columns=['dist'])\n new_df['dist'] = [10,20,30,40,50,60,70,80,90]\n for pos in ['1st', '2nd', 'pre-last', 'last']:\n new_df = new_df.merge(pos_stat(df, pos))\n return new_df \n \nraces_true = all_pos_stat(final) \n\nfig = go.Figure()\nfor pos, color in zip(['1st', '2nd', 'pre-last', 'last'],\n ['34675c', '344d90', 'ebc91e', 'c71c1c']):\n fig.add_trace(go.Scatter(x=races_true['dist'], y=races_true[f'true_pred_{pos}'],\n name=pos,\n marker=dict(size=8, color='#'+color, \n line=dict(width=0.5, color='black')),\n line=dict(width=3, color='#'+color),\n hovertemplate='%{y:.2f}%',\n visible=('legendonly' if pos not in ['1st',\n 'last'] else True),\n showlegend=True))\n \nfig.add_hline(y=0, line=dict(width=0.5, color='#b5b5b5'), row=1, col=1)\n\nfig.update_layout(width=800, height=600, plot_bgcolor='white',\n title=dict(text=\"Accuracy of predictions in all races\",\n font=dict(size=22), x=0.104, y=0.95),\n font_family=\"Calibri\", font_color=\"#303030\",\n hoverlabel=dict(font_size=13),\n hovermode='x',\n legend={\"title_text\": \"Finish place\", \"title\": {\"font\": {\"size\": 16}},\n \"bordercolor\": \"#707070\", \"borderwidth\": 0.7, \"bgcolor\": '#f7f7f7', 'y':0.5})\n\nfig.update_xaxes(title_text='Completed distance, %', tickfont_size=13, \n tickvals=[10,20,30,40,50,60,70,80,90], ticks=\"outside\", tickcolor='black', \n ticklen=3, tickson=\"boundaries\")\n\nfig.update_yaxes(title_text='Accuracy, %', showline=False,\n tickfont_size=13, ticks=\"outside\", tickcolor='black', \n ticklen=3, tickson=\"boundaries\")\nfig.show()","metadata":{"_kg_hide-input":true,"jupyter":{"source_hidden":true},"execution":{"iopub.status.busy":"2022-11-10T14:28:46.112558Z","iopub.execute_input":"2022-11-10T14:28:46.112867Z","iopub.status.idle":"2022-11-10T14:29:05.789173Z","shell.execute_reply.started":"2022-11-10T14:28:46.112840Z","shell.execute_reply":"2022-11-10T14:29:05.787575Z"},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"\nEven with data on the completion of 80-90% of the distance, the model is wrong in determining the winner in 22% of races. This indicates a high unpredictability in some races even before the finish line. In 21.6% of the races, the prediction of the winner and in 10.8% of races, the prediction of the loser was correct throughout the race! In 13.2% of the races, the winners became the participants who did not have a dominant probability of winning throughout the race and also there were 23 races, where underdogs with low chances of winning during the race became winners, including the race that was considered in this work.\n
\n\nIn general, the results can not be called impressive and half of the distance, the winner is essentially determined by odds, but don't forget about the availability of only data of the movement of participants. \n
","metadata":{}},{"cell_type":"markdown","source":"#\nWith only physical movement data available, the true causes of deceleration and acceleration can only be based on assumptions. To find the best overall solution for all races, more data is needed. It's not just about quantity, but also about completely new information.\n
\n\nLet's start with the model of determining the expected position before the start of the race. Of course, it is possible to build a model based on the statistics of victories, defeats, taking the top 3, etc., but this does not carry anything innovative. It is important to take into account not only the final race results of each jockey and horse, but also the intermediate results of previous races: time in the leading and last positions, speed depending on the speed of competitors and types of tracks, indicators of the health of the horse, training results, the number of mistakes made by jockeys and the optimality of decisions made, etc. \n
\n\nIf we talk about the model for determining the probability of winning during the race, then the greatest attention should be paid to the horse's health indicators. It is impossible to predict a jockey's mistake, but a sharp deterioration in the state of health or a decline in the strength of the horse is quite possible. I am convinced that the time is coming when there will be added a specialist to the team, who will monitor the horse's health indicators and inform the jockey about the optimality of decisions during the race.\n
\n\nWe had data from 2019 and are already on the eve of 2023. I am sure that in three years there has been collected more data that will allow horse racing to reach a new level!\n
","metadata":{}},{"cell_type":"markdown","source":"#\n