![\"finger](\"https://i.guim.co.uk/img/media/6d1d45a9d27e29ed6fe00e6e93201534bc4efcc0/0_160_5309_3186/master/5309.jpg?width=1200&height=1200&quality=85&auto=format&fit=crop&s=9298e5d306e172e41519da4c78a3b3fc\")
","metadata":{"execution":{"iopub.status.busy":"2022-10-03T12:09:50.287051Z","iopub.execute_input":"2022-10-03T12:09:50.287801Z","iopub.status.idle":"2022-10-03T12:09:50.294846Z","shell.execute_reply.started":"2022-10-03T12:09:50.287760Z","shell.execute_reply":"2022-10-03T12:09:50.293156Z"}}},{"cell_type":"markdown","source":"As many horse races have been held in the meantime, betting has been made through past race records. Simply put, the more winning horse riders ride, the higher the chance of winning. But what would we expect if a horse that has never been played, a jockey, played his first game? Or if horses with similar winning careers compete? \nLet's analyze how we can respond to these exceptional situations.","metadata":{}},{"cell_type":"markdown","source":"# 1. : Gold - Curve, Others - First, Last Straight', template=TEMPLATE)\nfig.update_yaxes(title='latitude')\nfig.update_xaxes(title='longitude')\nfig.show()","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:55:18.658211Z","iopub.execute_input":"2022-11-07T04:55:18.658684Z","iopub.status.idle":"2022-11-07T04:55:20.889659Z","shell.execute_reply.started":"2022-11-07T04:55:18.658649Z","shell.execute_reply":"2022-11-07T04:55:20.888476Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"> **NOTE** : Since the separation of the zones was determined after checking them directly, there can be errors. \n> For analysis results that contain zone information, the focus should be on identifying trends rather than accurate figures.","metadata":{}},{"cell_type":"markdown","source":"## 2.2. Angle of rotation \nThe center coordinates are obtained by manually checking \nWhen the center coordinates are selected appropriately, we can see which position leads further by the size of the angle, as shown in the example below. \nIn the examples below, the angle of the yellow lines is greater than the angle of the gray lines because the yellow point is ahead of the gray point. ","metadata":{}},{"cell_type":"code","source":"# temp_aqueduct_ = pd.merge(race_df[race_df['track_id']=='Aqueduct'], track_table, how='left', on=['track_id', 'race_date', 'race_number'])[['latitude', 'longitude']].mean()\n# temp_belmont_ = pd.merge(race_df[race_df['track_id']=='Belmont'], track_table, how='left', on=['track_id', 'race_date', 'race_number'])[['latitude', 'longitude']].mean()\n# temp_saratoga_ = pd.merge(race_df[race_df['track_id']=='Saratoga'], track_table, how='left', on=['track_id', 'race_date', 'race_number'])[['latitude', 'longitude']].mean()\n\nTRACK_CENTER = {\n 'Aqueduct' : {\n 'LONG' : -73.832, #temp_aqueduct_['longitude'],\n 'LATI' : 40.67 #temp_aqueduct_['latitude']\n },\n 'Belmont' : {\n 'LONG' : -73.720, # temp_belmont_['longitude'],\n 'LATI' : 40.714 # temp_belmont_['latitude']\n },\n 'Saratoga' : {\n 'LONG' : -73.772, # temp_saratoga_['longitude'],\n 'LATI' : 43.0705 # temp_saratoga_['latitude']\n }\n}\n\ndef get_degrees(track_id, latitude, longitude):\n x_base, y_base = TRACK_CENTER[track_id]['LONG'], TRACK_CENTER[track_id]['LATI']\n d = math.degrees(math.atan2(latitude-y_base, longitude-x_base))\n if (track_id == 'Belmont') & (d < 0):\n d = 360 + d # counter colockwise\n return d\n\n# visualization\nfig = make_subplots(\n rows=1, cols=3,\n specs=[[{\"type\": \"scatter\"}, {\"type\": \"scatter\"}, {\"type\": \"scatter\"}]],\n subplot_titles=['< Aqueduct >', '< Belmont >', '< Saratoga >']\n)\n\n\ntemp_ = track_table[\n (track_table['track_id'] == \"Aqueduct\") &\n (track_table['race_date'] == \"2019-01-18\") &\n (track_table['race_number'] == 1)\n ].copy()\n# temp_.loc[:, 'section'] = temp_.apply(lambda x : get_section(x['track_id'], x['latitude'], x['longitude']), axis=1)\nfor pn in temp_['program_number'].unique():\n cur_ = temp_[temp_['program_number']==pn]\n \n cur_ = cur_.sort_values(by=['trakus_index'], ascending=True)\n cur_['latitude_lag1'] = cur_['latitude'].shift(1)\n cur_['longitude_lag1'] = cur_['longitude'].shift(1)\n cur_.loc[:, 'section'] = cur_.apply(lambda x : is_cross_curve(x['track_id'], x['longitude'], x['latitude'], x['longitude_lag1'], x['latitude_lag1']), axis=1)\n stt_curve_index = cur_[cur_['section']]['trakus_index'].values[0]\n end_curve_index = cur_[cur_['section']]['trakus_index'].values[1]\n cur_.loc[cur_['trakus_index']
: Red - Finish Line, Yellow - The moment the horse crosses the finish line', template=TEMPLATE)\nfig.update_yaxes(title='latitude')\nfig.update_xaxes(title='longitude')\nfig.show()\n","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:55:23.158945Z","iopub.execute_input":"2022-11-07T04:55:23.159438Z","iopub.status.idle":"2022-11-07T04:55:25.458294Z","shell.execute_reply.started":"2022-11-07T04:55:23.159374Z","shell.execute_reply":"2022-11-07T04:55:25.456780Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# 3. Drive Analysis \nAs a result of the search ([An introduction to track conditions](https://edge.twinspires.com/racing/an-introduction-to-track-conditions-and-all-the-related-lingo/)), I thought that the driving data could be greatly affected by the track condition, so I only targeted the best conditions. \nTherefore, only the Dirt 6 Furlong competitions with fast track status were selected. (293 races) ","metadata":{}},{"cell_type":"code","source":"TRACK_LENGTH = 3960 # feets\n\nall_race_dict = {}\nrace_df = race_condition_table[(race_condition_table['course_type']=='Dirt') &\n (race_condition_table['distance_id']==600) & \n (race_condition_table['track_condition'].isin(['Fast']))\n ].reset_index(drop=True).copy()\n# for i, row in race_condition_table.iterrows():\nfor i, row in race_df.iterrows():\n# print(row)\n \n # filtering\n target_track_id = row['track_id']\n target_course_type = row['course_type']\n target_track_condition = row['track_condition']\n target_distance_id = row['distance_id']\n target_race_number = row['race_number']\n target_race_date = row['race_date']\n \n\n cur_df = start_table[\n (start_table['track_id']==target_track_id) &\n (start_table['course_type']==target_course_type) &\n (start_table['track_condition']==target_track_condition) &\n (start_table['distance_id']==target_distance_id) &\n (start_table['race_number']==target_race_number) &\n (start_table['race_date']==target_race_date)\n ]\n cur_df = cur_df.sort_values(by=['finishing_place'])\n \n# break\n cur_race = pd.DataFrame()\n for ranking in cur_df['finishing_place'].unique():\n temp_ = cur_df[cur_df['finishing_place']==ranking]\n \n cur_track = pd.merge(temp_, track_table, how='left', on=['track_id', 'race_date', 'race_number', 'program_number'])\n cur_track = cur_track.sort_values(by=['trakus_index']).reset_index(drop=True)\n cur_track['latitude_lag1'] = cur_track['latitude'].shift(1)\n cur_track['longitude_lag1'] = cur_track['longitude'].shift(1)\n\n # speed\n cur_track['distance'] = [geopy.distance.geodesic(vs[:2], vs[2:]).feet if sum(np.isnan(vs))==0 else 0 for vs in cur_track[['latitude', 'longitude', 'latitude_lag1', 'longitude_lag1']].values]\n cur_track['speed'] = cur_track['distance'] / 0.25\n cur_track['distance_cum'] = cur_track['distance'].cumsum() # feets : 6 furlongs = 3960 feets\n \n # angle btw two points\n cur_track['latitude_diff'] = cur_track['latitude'].shift(-1) - cur_track['latitude']\n cur_track['longitude_diff'] = cur_track['longitude'].shift(-1) - cur_track['longitude']\n ## get angle with two points\n cur_track['angle'] = cur_track.apply(lambda x : math.degrees(math.atan2(x['latitude_diff'], x['longitude_diff'])), axis=1)\n cur_track['angle'] = (cur_track['angle'] + 360) % 360\n ## get delta of angle\n cur_track['steering_angle'] = cur_track['angle'].diff().shift(-1) # icludes NaN\n \n # angle btw static point and horse point\n cur_track['rotation_angle'] = cur_track.apply(lambda x : get_degrees(target_track_id, x['latitude'], x['longitude']), axis=1)\n \n # section\n cur_track.loc[:, 'section'] = cur_track.apply(lambda x : is_cross_curve(x['track_id'], x['longitude'], x['latitude'], x['longitude_lag1'], x['latitude_lag1']), axis=1)\n if len(cur_track[cur_track['section']]['trakus_index'].values) == 0:\n cur_track.loc[:, 'section'] = 'First Straight'\n elif len(cur_track[cur_track['section']]['trakus_index'].values) == 1:\n stt_curve_index = cur_track[cur_track['section']]['trakus_index'].values[0]\n cur_track.loc[cur_track['trakus_index']
: Aqueduct, race date = {sample_race_date}, race number = {sample_race_number}', template=TEMPLATE, yaxis_range=(0, 1))\nfig.update_yaxes(title='win probability')\nfig.update_xaxes(title='trakus_index')\nfig.show()","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:59:40.128785Z","iopub.execute_input":"2022-11-07T04:59:40.129587Z","iopub.status.idle":"2022-11-07T04:59:42.278812Z","shell.execute_reply.started":"2022-11-07T04:59:40.129540Z","shell.execute_reply":"2022-11-07T04:59:42.277875Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"--- \n### Bad Case \nThe results below is the case that the actual No.1 horse has very low probability of winning during the race. In addition, after the middle of the game, the winning probability of the top horse is close to 0%. The winning probability of the 4th place horse was predicted to be high. ","metadata":{}},{"cell_type":"code","source":"np.random.seed(123)\nsample_num = 0\nsample_race_date = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==test_total_race_nums[sample_num]]['race_date'].unique()[0]\nsample_race_number = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==test_total_race_nums[sample_num]]['race_number'].unique()[0]\n\nsample_df = test_pred_df[(test_pred_df['race_date']==sample_race_date) & (test_pred_df['race_number']==sample_race_number)]\n\nrank_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='cur_rank')\nremain_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='ramain_proj_len')\npred_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='pred')\n\nwin_prob = pred_.copy() #pd.DataFrame()\nsize = 1000\nfor i, row in pred_.iterrows():\n cur_win_prob = pd.DataFrame(index=range(size))\n for fp in range(1, max_rank+1):\n fp_rank_diff = np.random.binomial(remain_.loc[i][fp], row[fp], size)\n pred_rank = rank_.loc[i][fp] - fp_rank_diff\n cur_win_prob[fp] = pred_rank\n cur_win_prob = cur_win_prob.rank(method='min', axis=1)\n for fp in range(1, 6+1):\n win_prob.loc[i, fp] = sum(cur_win_prob[fp]==1) / size\n\n# norm\nwin_prob = win_prob.divide(win_prob.sum(axis=1), axis=0)\n\n# section info for visualization\nsection_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='section')\nsection_[1] = section_[1].diff().fillna(1)\nsection_ = section_[section_[1]!=0][[1]]\n\n# visualization\nshow_df = win_prob.cumsum(axis=1).copy()\ntemp_colors = [DIRT_COLOR, 'Silver', 'rgb(205, 127, 50)', # gold, silver, bronze\n 'rgb(116,169,207)', 'rgb(43,140,190)', 'rgb(37,37,37)'] # skyblue, blue, black\n\nfig = go.Figure()\nfor i, c in enumerate(show_df.columns):\n color_idx = (len(show_df.columns) - i) / len(show_df.columns)\n fig.add_trace(go.Scatter(x=show_df[c].index, y=show_df[c], hoverinfo='x+y', mode='lines', name=c, line=dict(width=0.5, color=temp_colors[i]), fill='tonexty'))\nfig.add_vline(x=section_.index[0], line_width=2, line_color=\"darkgreen\", annotation_text=\"First Straight\", annotation_position=\"bottom right\")\nfig.add_vline(x=section_.index[1], line_width=2, line_color=\"darkgreen\", annotation_text=\"Curve\", annotation_position=\"bottom right\")\nfig.add_vline(x=section_.index[-1], line_width=2, line_color=\"darkgreen\", annotation_text=\"Last Straight\", annotation_position=\"bottom right\")\nfig.update_layout(title_text=f'Win Probability in each trakus index
: Aqueduct, race date = {sample_race_date}, race number = {sample_race_number}', template=TEMPLATE, yaxis_range=(0, 1))\nfig.update_yaxes(title='win probability')\nfig.update_xaxes(title='trakus_index')\nfig.show()","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:59:42.280370Z","iopub.execute_input":"2022-11-07T04:59:42.281032Z","iopub.status.idle":"2022-11-07T04:59:44.437703Z","shell.execute_reply.started":"2022-11-07T04:59:42.280994Z","shell.execute_reply":"2022-11-07T04:59:44.436560Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"--- \n### Dramatic Reversal Case \nThis is a case where the chance of winning rises sharply in the second half. In the middle, the second-place horse prevailed, and in the second half, the third-place horse prevailed, but at the end, the chances of winning the first-place horse rose sharply. ","metadata":{}},{"cell_type":"code","source":"np.random.seed(123)\nsample_num = 5\nsample_race_date = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==test_total_race_nums[sample_num]]['race_date'].unique()[0]\nsample_race_number = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==test_total_race_nums[sample_num]]['race_number'].unique()[0]\n\nsample_df = test_pred_df[(test_pred_df['race_date']==sample_race_date) & (test_pred_df['race_number']==sample_race_number)]\n\nrank_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='cur_rank')\nremain_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='ramain_proj_len')\npred_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='pred')\n\nwin_prob = pred_.copy() #pd.DataFrame()\nsize = 1000\nfor i, row in pred_.iterrows():\n cur_win_prob = pd.DataFrame(index=range(size))\n for fp in range(1, max_rank+1):\n fp_rank_diff = np.random.binomial(remain_.loc[i][fp], row[fp], size)\n pred_rank = rank_.loc[i][fp] - fp_rank_diff\n cur_win_prob[fp] = pred_rank\n cur_win_prob = cur_win_prob.rank(method='min', axis=1)\n for fp in range(1, 6+1):\n win_prob.loc[i, fp] = sum(cur_win_prob[fp]==1) / size\n\n# norm\nwin_prob = win_prob.divide(win_prob.sum(axis=1), axis=0)\n\n# section info for visualization\nsection_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='section')\nsection_[1] = section_[1].diff().fillna(1)\nsection_ = section_[section_[1]!=0][[1]]\n\n# visualization\nshow_df = win_prob.cumsum(axis=1).copy()\ntemp_colors = [DIRT_COLOR, 'Silver', 'rgb(205, 127, 50)', # gold, silver, bronze\n 'rgb(116,169,207)', 'rgb(43,140,190)', 'rgb(37,37,37)'] # skyblue, blue, black\n\nfig = go.Figure()\nfor i, c in enumerate(show_df.columns):\n color_idx = (len(show_df.columns) - i) / len(show_df.columns)\n fig.add_trace(go.Scatter(x=show_df[c].index, y=show_df[c], hoverinfo='x+y', mode='lines', name=c, line=dict(width=0.5, color=temp_colors[i]), fill='tonexty'))\nfig.add_vline(x=section_.index[0], line_width=2, line_color=\"darkgreen\", annotation_text=\"First Straight\", annotation_position=\"bottom right\")\nfig.add_vline(x=section_.index[1], line_width=2, line_color=\"darkgreen\", annotation_text=\"Curve\", annotation_position=\"bottom right\")\nfig.add_vline(x=section_.index[-1], line_width=2, line_color=\"darkgreen\", annotation_text=\"Last Straight\", annotation_position=\"bottom right\")\nfig.update_layout(title_text=f'Win Probability in each trakus index
: Aqueduct, race date = {sample_race_date}, race number = {sample_race_number}', template=TEMPLATE, yaxis_range=(0, 1))\nfig.update_yaxes(title='win probability')\nfig.update_xaxes(title='trakus_index')\nfig.show()","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:59:44.439624Z","iopub.execute_input":"2022-11-07T04:59:44.439967Z","iopub.status.idle":"2022-11-07T04:59:46.607108Z","shell.execute_reply.started":"2022-11-07T04:59:44.439935Z","shell.execute_reply":"2022-11-07T04:59:46.605681Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"--- \n### Ideal Case \nThis is when the odds of winning first, second, and third places are proportional without any significant change during driving. Also, as time goes by, the probability of winning the first place increases, and the probability of winning the rest of the horses gradually decreases. ","metadata":{}},{"cell_type":"code","source":"np.random.seed(123)\nsample_num = 6\nsample_race_date = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==test_total_race_nums[sample_num]]['race_date'].unique()[0]\nsample_race_number = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==test_total_race_nums[sample_num]]['race_number'].unique()[0]\n\nsample_df = test_pred_df[(test_pred_df['race_date']==sample_race_date) & (test_pred_df['race_number']==sample_race_number)]\n\nrank_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='cur_rank')\nremain_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='ramain_proj_len')\npred_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='pred')\n\nwin_prob = pred_.copy() #pd.DataFrame()\nsize = 1000\nfor i, row in pred_.iterrows():\n cur_win_prob = pd.DataFrame(index=range(size))\n for fp in range(1, max_rank+1):\n fp_rank_diff = np.random.binomial(remain_.loc[i][fp], row[fp], size)\n pred_rank = rank_.loc[i][fp] - fp_rank_diff\n cur_win_prob[fp] = pred_rank\n cur_win_prob = cur_win_prob.rank(method='min', axis=1)\n for fp in range(1, 6+1):\n win_prob.loc[i, fp] = sum(cur_win_prob[fp]==1) / size\n\n# norm\nwin_prob = win_prob.divide(win_prob.sum(axis=1), axis=0)\n\n# section info for visualization\nsection_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='section')\nsection_[1] = section_[1].diff().fillna(1)\nsection_ = section_[section_[1]!=0][[1]]\n\n# visualization\nshow_df = win_prob.cumsum(axis=1).copy()\ntemp_colors = [DIRT_COLOR, 'Silver', 'rgb(205, 127, 50)', # gold, silver, bronze\n 'rgb(116,169,207)', 'rgb(43,140,190)', 'rgb(37,37,37)'] # skyblue, blue, black\n\nfig = go.Figure()\nfor i, c in enumerate(show_df.columns):\n color_idx = (len(show_df.columns) - i) / len(show_df.columns)\n fig.add_trace(go.Scatter(x=show_df[c].index, y=show_df[c], hoverinfo='x+y', mode='lines', name=c, line=dict(width=0.5, color=temp_colors[i]), fill='tonexty'))\nfig.add_vline(x=section_.index[0], line_width=2, line_color=\"darkgreen\", annotation_text=\"First Straight\", annotation_position=\"bottom right\")\nfig.add_vline(x=section_.index[1], line_width=2, line_color=\"darkgreen\", annotation_text=\"Curve\", annotation_position=\"bottom right\")\nfig.add_vline(x=section_.index[-1], line_width=2, line_color=\"darkgreen\", annotation_text=\"Last Straight\", annotation_position=\"bottom right\")\nfig.update_layout(title_text=f'Win Probability in each trakus index
: Aqueduct, race date = {sample_race_date}, race number = {sample_race_number}', template=TEMPLATE, yaxis_range=(0, 1))\nfig.update_yaxes(title='win probability')\nfig.update_xaxes(title='trakus_index')\nfig.show()","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:59:46.608887Z","iopub.execute_input":"2022-11-07T04:59:46.609387Z","iopub.status.idle":"2022-11-07T04:59:48.924473Z","shell.execute_reply.started":"2022-11-07T04:59:46.609339Z","shell.execute_reply":"2022-11-07T04:59:48.923174Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"## 4.3. Others \nLet's check the average expected winning probability per game for the first place horse. If all six horses run the same race, the chance of winning is 1/6 (=0.167). When predicting the test data with our model, the average winning probability of the top horse is as follows. \n- The average value here is the average of the expected winning probability at each point in each game and then the average for all games. ","metadata":{}},{"cell_type":"code","source":"np.random.seed(123)\nsample_num = 0\nresults_mean = [] # mean\nresults_last = [] # last 1 second\nfor ttrn in test_total_race_nums:\n sample_race_date = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==ttrn]['race_date'].unique()[0] #'2019-01-18' #'2019-12-22' #'2019-01-18'\n sample_race_number = test_pred_df[test_pred_df['TOTAL_RACE_NUM']==ttrn]['race_number'].unique()[0] # 8 #9 #8\n\n sample_df = test_pred_df[(test_pred_df['race_date']==sample_race_date) & (test_pred_df['race_number']==sample_race_number)]\n\n rank_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='cur_rank')\n remain_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='ramain_proj_len')\n pred_ = pd.pivot_table(sample_df, index='trakus_index', columns='finishing_place', values='pred')\n\n win_prob = pred_.copy() #pd.DataFrame()\n size = 1000\n for i, row in pred_.iterrows():\n cur_win_prob = pd.DataFrame(index=range(size))\n for fp in range(1, max_rank+1):\n fp_rank_diff = np.random.binomial(remain_.loc[i][fp], row[fp], size)\n pred_rank = rank_.loc[i][fp] - fp_rank_diff\n cur_win_prob[fp] = pred_rank\n cur_win_prob = cur_win_prob.rank(method='min', axis=1)\n for fp in range(1, 6+1):\n win_prob.loc[i, fp] = sum(cur_win_prob[fp]==1) / size\n\n # norm\n win_prob = win_prob.divide(win_prob.sum(axis=1), axis=0) \n \n results_mean.append(win_prob[1].mean())\n results_last.append(sum(win_prob[1].tail(4) > 0.5)) # last 1 second\n \nprint(f\"Base winning probability : {1/6 : .4f}\")\nprint(f\"The mean winning probability of 1st horse : {np.mean(results_mean) : .4f}\")\nprint(f\"Ratio : {np.mean(results_mean)/(1/6) : .4f}\")","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T04:59:48.926679Z","iopub.execute_input":"2022-11-07T04:59:48.927580Z","iopub.status.idle":"2022-11-07T05:00:46.242869Z","shell.execute_reply.started":"2022-11-07T04:59:48.927517Z","shell.execute_reply":"2022-11-07T05:00:46.241628Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"With driving data, the winning probability of the No. 1 horse at every moment is approximately **2.3 times** higher than when everyone is driving the same. Similar information already exists as \"odds\". If we check the \"odds\" of the first and non-first-place horses for the same test data, the following is.","metadata":{}},{"cell_type":"code","source":"print(f\"Mean Odds of Non-1st-place: {test_pred_df[test_pred_df['finishing_place']!=1].drop_duplicates(subset=['track_id', 'race_date', 'race_number', 'finishing_place'])['odds'].mean() : .4f}\")\nprint(f\"Mean Odds of 1st-place : {test_pred_df[test_pred_df['finishing_place']==1].drop_duplicates(subset=['track_id', 'race_date', 'race_number', 'finishing_place'])['odds'].mean() : .4f}\")\nratio = test_pred_df[test_pred_df['finishing_place']!=1].drop_duplicates(subset=['track_id', 'race_date', 'race_number', 'finishing_place'])['odds'].mean() /\\\ntest_pred_df[test_pred_df['finishing_place']==1].drop_duplicates(subset=['track_id', 'race_date', 'race_number', 'finishing_place'])['odds'].mean()\nprint(f\"Ratio : {ratio : .4f}\")","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T05:00:46.244465Z","iopub.execute_input":"2022-11-07T05:00:46.244859Z","iopub.status.idle":"2022-11-07T05:00:46.337581Z","shell.execute_reply.started":"2022-11-07T05:00:46.244823Z","shell.execute_reply":"2022-11-07T05:00:46.336317Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"Surprisingly, *the ratio of the winning probability calculated by the model to the existing \"odds\" was very similar.* \"odds\" can be considered to be calculated by collective intelligence for past horse racing results. This analogy is well reflected in the model. \nFinally, in test matches, about 74% had a 50% or more chance of winning the last one second of the actual No. 1 horse. \n- This is the case with the highest winning probability of the first place at the end (last 1 second), as seen in the previous example test results: \"Good Case\", \"Dramatic Reversal\" and \"Ideal Case\". ","metadata":{}},{"cell_type":"code","source":"print(f\"Based on the last second, reasonably predicted rate : {sum([1 for x in results_last if x==4]) / len(results_last) : .4f}\")","metadata":{"_kg_hide-input":true,"execution":{"iopub.status.busy":"2022-11-07T05:00:46.339465Z","iopub.execute_input":"2022-11-07T05:00:46.340153Z","iopub.status.idle":"2022-11-07T05:00:46.347745Z","shell.execute_reply.started":"2022-11-07T05:00:46.340015Z","shell.execute_reply":"2022-11-07T05:00:46.346395Z"},"jupyter":{"source_hidden":true},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# 5. Summary \nSo far, we have created a model that predicts real-time winning probability by analyzing driving data. \nAs the first step, we divided the race section first and checked the relevant statistics for each zone. The driving data checked for each track section are as follows. \n(** sign means a different result than normal.)\n\n1. First straight\n - Acceleration : The time reached to a specific speed has been checked. The first place horse was the best.\n - Average Speed : The average speed in this straight section has been checked. The first place horse was the fastest.\n - Rotation angle : As an alternative to real-time ranking, we checked the angle between the fixed position inside the track and location of the horse. The angle of the No. 1 horse was the largest on average (can be considered ahead) \n \n \n2. Curve\n - Average Speed : We checked the average speed in this curved section, the top horse was the fastest.\n - Travel distance : The distance traveled in the curved section. The shorter the distance, the more it ran inside the corner. The high ranking did not mean that the distance traveled was short. ** \n - Time required : The time it took to pass through the curved section. The first place horse was the fastest.\n - Standard deviation of steering angle : The degree of shaking during cornering. For the top position, the steering angle deviation was small.\n - Moving area : The approximate area between the center of the corner and the curved path. The smaller the area, the more it runs inside the corner. For the top tier, the area was large. ** \n - Difference between the minimum radius point and the half time point: The minimum radius point should normally be the mid-curve point, and the smaller the change in velocity on the curve, the smaller the difference. This value was small for the parent of the Aqueduct. ** \n - Graviy Acceleration : We checked the force applied during cornering. Approximately 0.3 G is applied. \n \n \n3. Last straight\n - Average Speed : We checked the average speed in the last section. The first place horse was the fastest.\n - Comparison of the entry ranking of the straight section and final ranking : When horse first enter the last straight section, the F-score is 0.55 when we compare the actual first place.\n \n \nConsidering the above analysis, I have determined five basic items of driving data. The five factors are position (latitude, hardness), speed, acceleration, steering angle, and rotation angle. We took these factors and considered the ranking at a certain point in time to predict whether we could win the first place for the rest of the distance and time. \nAbout 74% of the test data predicted a 50% chance of winning the first place at the last minute. The ratio of the average expected winning probability to the default winning probability for the first place to the overall interval was similar to that of the first place horse and the non-first place horses. \n \n**Need for improvement** \n1. Track information \n - I analyzed it by referring to the actual map, but it would be nice to have official data for each stadium. \n - For example, by driving course, latitude and longitude data at multiple points \n2. Modeling \n - The previous data results are the results of training and predicting a specific number of horses in a specific stadium. \n - We will be able to extend this to further generalize the model. \n - In addition, a variety of modeling methodologies will be available. \n \n**Further works** \n1. Simulation for first-time horses \n - If we have practice driving data for horses that are competing for the first time, we can predict the winning probability by driving by combining with the existing driving data. \n2. Virtual competition simulation \n - We will be able to combine existing driving data to compete against horses that have not yet competed. \n3. Target specific sections, specific situations \n - Instead of running the entire race, it can also be simulated by replacing it with a first-place probability for a particular section or a chance of injury. \n - In case of injury prediction : If normal is 0 and injury is 1, it seems that target = (state change)/(remaining distance) can be set. \n - For the actual injured horse, the state change is 1, and for the normal horse, the state change is a status change of 0. ","metadata":{}},{"cell_type":"markdown","source":"\n
I send my deepest condolences to the victims of the Itaewon disaster. ![\"finger](\"https://www.pngmart.com/files/9/Black-Ribbon-Transparent-Background.png\")
\n","metadata":{"execution":{"iopub.status.busy":"2022-11-07T06:47:43.538561Z","iopub.execute_input":"2022-11-07T06:47:43.539029Z","iopub.status.idle":"2022-11-07T06:47:43.549827Z","shell.execute_reply.started":"2022-11-07T06:47:43.538993Z","shell.execute_reply":"2022-11-07T06:47:43.547769Z"}}}]}