\n \n## 5.2 Producing the Scatter Plot","metadata":{}},{"cell_type":"code","source":"import pickle\nimport matplotlib.pyplot as plt\nimport numpy as np\n\nlist_comparison = []\nlist_counter = []\n\nfor z in range(1, 19):\n times_ball_went_to_the_right = 0\n times_ball_went_to_the_left = 0\n for number in range(18,21):\n f = open('../input/nfldictionaries/NFLlist20' + str(number) + '.pckl', 'rb')\n dictionary = pickle.load(f)\n f.close()\n for name in dictionary:\n\n for date in dictionary[name]:\n # Identifies if the play is a punt play\n try:\n dictionary[name][date][\"football\"][\"puntpositionx\"]\n dictionary[name][date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n # This is a coordinate transformation of all the relevant quantities to the direction of play of the punter\n if float(dictionary[name][date][\"football\"]['x']) - float(dictionary[name][date][name][\"x\"]) > 0:\n football_y = float(dictionary[name][date][\"football\"]['y'])\n punter_y = float(dictionary[name][date][name][\"y\"])\n punter_x = float(dictionary[name][date][name][\"x\"])\n puntresult_y = float(dictionary[name][date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][date][\"football\"]['x']) - float(dictionary[name][date][name][\"x\"]) <= 0:\n football_y = 53.3 - float(dictionary[name][date][\"football\"]['y'])\n punter_y = 53.3 - float(dictionary[name][date][name][\"y\"])\n punter_x = 120 - float(dictionary[name][date][name][\"x\"])\n puntresult_y = 53.3 - float(dictionary[name][date][\"football\"][\"football_landing_position_y\"])\n past_y_offset = 0\n past_y_offset_counter = 0\n\n alpha_amount_of_times_ball_went_right_positive_offset = 0\n alpha_amount_of_times_ball_went_left_positive_offset = 0\n alpha_amount_of_times_ball_went_right_negative_offset = 0\n alpha_amount_of_times_ball_went_left_negative_offset = 0\n\n beta_amount_of_times_ball_went_right_positive_offset = 0\n beta_amount_of_times_ball_went_left_positive_offset = 0\n beta_amount_of_times_ball_went_right_negative_offset = 0\n beta_amount_of_times_ball_went_left_negative_offset = 0\n\n average_punt_length = 0\n average_punt_length_counter = 0\n early_region = 0\n early_region_counter = 0\n mid_region = 0\n mid_region_counter = 0\n late_region = 0\n late_region_counter = 0\n for past_date in dictionary[name]:\n # This goes through all the plays that happened BEFORE the current play's date\n if int(past_date) >= int(date):\n continue\n\n try:\n dictionary[name][past_date][\"football\"][\"puntpositionx\"]\n dictionary[name][past_date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][past_date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][past_date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n if float(dictionary[name][past_date][\"football\"]['x']) - float(dictionary[name][past_date][name][\"x\"]) > 0:\n past_football_y = float(dictionary[name][past_date][\"football\"]['y'])\n past_punter_y = float(dictionary[name][past_date][name][\"y\"])\n past_punter_x = float(dictionary[name][past_date][name][\"x\"])\n past_puntresult_y = float(dictionary[name][past_date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][past_date][\"football\"]['x']) - float(dictionary[name][past_date][name][\"x\"]) <= 0:\n past_football_y = 53.3 - float(dictionary[name][past_date][\"football\"]['y'])\n past_punter_y = 53.3 - float(dictionary[name][past_date][name][\"y\"])\n past_punter_x = 120 - float(dictionary[name][past_date][name][\"x\"])\n past_puntresult_y = 53.3 - float(dictionary[name][past_date][\"football\"][\"football_landing_position_y\"])\n\n past_y_offset_punter = past_football_y-past_punter_y # Gives the y-offset of the punter to the ball, positive value means he's standing to the right, and negative to the left\n\n past_y_offset_puntresult = past_punter_y-past_puntresult_y # Gives the y-offset of the ball when it finally lands relative to the punter's frame 1 position\n\n past_y_offset += past_y_offset_punter # Counts up the y-offset of the punter to the ball for each past play\n\n past_y_offset_counter += 1 # Together with past_y_offset gives us the average y-offset of the punter relative to the ball by division\n\n further_past_average_position = 0\n further_past_average_position_counter = 0\n for further_past_date in dictionary[name]:\n # This goes through all the past game of the past game and calculates the average y-offset relative to the ball up until that point in time\n if int(further_past_date) >= int(past_date):\n continue\n\n try:\n dictionary[name][further_past_date][\"football\"][\"puntpositionx\"]\n dictionary[name][further_past_date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][further_past_date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][further_past_date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n if float(dictionary[name][further_past_date][\"football\"]['x']) - float(dictionary[name][further_past_date][name][\"x\"]) > 0:\n further_past_football_y = float(dictionary[name][further_past_date][\"football\"]['y'])\n further_past_punter_y = float(dictionary[name][further_past_date][name][\"y\"])\n further_past_puntresult_y = float(dictionary[name][further_past_date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][further_past_date][\"football\"]['x']) - float(dictionary[name][further_past_date][name][\"x\"]) <= 0:\n further_past_football_y = 53.3 - float(dictionary[name][further_past_date][\"football\"]['y'])\n further_past_punter_y = 53.3 - float(dictionary[name][further_past_date][name][\"y\"])\n further_past_puntresult_y = 53.3 - float(dictionary[name][further_past_date][\"football\"][\"football_landing_position_y\"])\n\n further_past_average_position += further_past_football_y-further_past_punter_y # Counts up the y-offset of the punter to the ball for each further past play\n further_past_average_position_counter += 1 # Together with further_past_average_position gives us the average y-offset of the punter relative to the ball for the past play by division\n\n # This goes towards calculating alpha\n if past_y_offset_punter > 0:\n if past_y_offset_puntresult > 0:\n alpha_amount_of_times_ball_went_right_positive_offset += 1\n elif past_y_offset_puntresult < 0:\n alpha_amount_of_times_ball_went_left_positive_offset += 1\n elif past_y_offset_punter < 0:\n if past_y_offset_puntresult > 0:\n alpha_amount_of_times_ball_went_right_negative_offset += 1\n if past_y_offset_puntresult < 0:\n alpha_amount_of_times_ball_went_left_negative_offset += 1\n\n # This goes towards calculating beta\n try:\n if further_past_average_position/further_past_average_position_counter > past_y_offset_punter:\n if past_y_offset_puntresult > 0:\n beta_amount_of_times_ball_went_right_positive_offset += 1\n elif past_y_offset_puntresult < 0:\n beta_amount_of_times_ball_went_left_positive_offset += 1\n elif further_past_average_position/further_past_average_position_counter < past_y_offset_punter:\n if past_y_offset_puntresult > 0:\n beta_amount_of_times_ball_went_right_negative_offset += 1\n if past_y_offset_puntresult < 0:\n beta_amount_of_times_ball_went_left_negative_offset += 1\n except ZeroDivisionError:\n pass\n # This goes towards calculating the expected puntlength\n if past_punter_x <= 20:\n early_region += abs(past_punter_y - past_puntresult_y)\n early_region_counter += 1\n elif past_punter_x > 20 and past_punter_x <= 40:\n mid_region += abs(past_punter_y - past_puntresult_y)\n mid_region_counter += 1\n elif past_punter_x > 40:\n late_region += abs(past_punter_y - past_puntresult_y)\n late_region_counter += 1\n average_punt_length += abs(past_punter_y-past_puntresult_y)\n average_punt_length_counter += 1\n\n try:\n punt_length = average_punt_length / average_punt_length_counter # Expected value of the punt length in the y-direction with the punter's initial-frame position as the 0 coordinate\n except ZeroDivisionError:\n continue\n current_y_offset = football_y - punter_y # Current frame 1 y-offset of punter relative to the ball \n past_y_offset = past_y_offset / past_y_offset_counter # Average y-offset up until now\n\n # alpha\n alpha_positive = (alpha_amount_of_times_ball_went_right_positive_offset + 1) / (alpha_amount_of_times_ball_went_left_positive_offset + alpha_amount_of_times_ball_went_right_positive_offset + 2)\n alpha_negative = (alpha_amount_of_times_ball_went_right_negative_offset + 1) / (alpha_amount_of_times_ball_went_left_negative_offset + alpha_amount_of_times_ball_went_right_negative_offset + 2)\n # beta\n beta_positive = (beta_amount_of_times_ball_went_right_positive_offset + 1) / (beta_amount_of_times_ball_went_left_positive_offset + beta_amount_of_times_ball_went_right_positive_offset + 2)\n beta_negative = (beta_amount_of_times_ball_went_right_negative_offset + 1) / (beta_amount_of_times_ball_went_left_negative_offset + beta_amount_of_times_ball_went_right_negative_offset + 2)\n\n # This gives us the Probability of the ball being punted to the right from the punter's inital-frame position\n if current_y_offset > 0:\n try:\n if past_y_offset > current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_positive - 0.5)) * alpha_positive+(1 - abs(2 * (alpha_positive - 0.5))) * beta_positive + abs(2 * (beta_positive - 0.5)) * beta_positive + (1 - abs(2 * (beta_positive - 0.5))) * alpha_positive) / 2\n\n elif past_y_offset < current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_positive - 0.5)) * alpha_positive + (1 - abs(2 * (alpha_positive - 0.5))) * beta_negative + abs(2 * (beta_negative - 0.5)) * beta_negative + (1 - abs(2 * (beta_negative - 0.5))) * alpha_positive) / 2\n except ZeroDivisionError:\n continue\n elif current_y_offset < 0:\n try:\n if past_y_offset > current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_negative - 0.5)) * alpha_negative + (1 - abs(2 * (alpha_negative - 0.5))) * beta_positive + abs(2 * (beta_positive - 0.5)) * beta_positive + (1-abs(2 * (beta_positive - 0.5))) * alpha_negative) / 2\n\n elif past_y_offset < current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_negative - 0.5)) * alpha_negative + (1 - abs(2 * (alpha_negative - 0.5))) * beta_negative + abs(2 * (beta_negative - 0.5)) * beta_negative + (1 - abs(2 * (beta_negative-0.5))) * alpha_negative) / 2\n except ZeroDivisionError:\n continue\n\n if punter_x <= 20 and early_region_counter != 0:\n punt_length = early_region / early_region_counter\n elif punter_x <= 20 and early_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n elif punter_x > 20 and punter_x <= 40 and mid_region_counter != 0:\n punt_length = mid_region / mid_region_counter\n elif punter_x > 20 and punter_x <= 40 and mid_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n elif punter_x > 40 and late_region_counter != 0:\n punt_length = late_region / late_region_counter\n elif punter_x > 40 and late_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n\n # This produces Fig. 1, takes a couple of minutes\n # All the other code cells from now on will mostly be the same up until now (except for variable naming and the loops at the beginning)\n # And only differ by happens below this line\n if prob_ball_goes_right >= z / 20 and prob_ball_goes_right <= z / 20 + 1 / 20:\n if punter_y - puntresult_y > 0:\n times_ball_went_to_the_right += 1\n elif punter_y - puntresult_y < 0:\n times_ball_went_to_the_left += 1\n try:\n list_comparison.append(times_ball_went_to_the_right / (times_ball_went_to_the_right + times_ball_went_to_the_left))\n list_counter.append(times_ball_went_to_the_right + times_ball_went_to_the_left)\n except ZeroDivisionError:\n print(\"WARNING: NO GAMES WITH PROBABILTY BETWEEN \" + str(z / 20) + \" and \" + str(z / 20 + 1 / 20) + \"SO IMAGE IS PROBABLY INVALID\")\n list_counter.append(1)\n\n\n# Takes around ten minutes \nx = []\nfor i in range(2, 20):\n x.append(2 * i * 0.025 - 0.025)\n \ns = np.linspace(0, 1)\nf = s\nplt.ylabel('Percentage of Footballs Punted to the Right')\nplt.xlabel('Probability of Football Punted to the Right')\nplt.plot(s, f)\nplt.scatter(x, list_comparison)\nplt.show()\nfor i in range(len(list_counter)):\n print(str(list_counter[i]) + \" punts with a probability between \" + str(round(i * 0.05 + 0.05, 2)) + \" and \" + str(round(i * 0.05 + 0.1, 2)))","metadata":{"_kg_hide-input":false,"_kg_hide-output":false,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"## 5.3 Producing the Probability Distribution of the Plays","metadata":{}},{"cell_type":"code","source":"import pickle\n#from scipy.optimize import fmin\nimport scipy\nfrom scipy.stats import truncnorm\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom scipy.integrate import quad\n\nf = open('../input/nfldictionaries/NFLlist2018.pckl', 'rb')\ndictionary = pickle.load(f)\nf.close()\n\nname = \"Tress Way\"\ndate = \"201812302329\"\nfor z in range(1, 2):\n # date_sorting_list = []\n # for i in dictionary[name]:\n # date_sorting_list.append(int(i))\n # date_sorting_list = sorted(date_sorting_list) ## undo all of these hashmarks to go over all the year's punt plays of the punter in question in order of date\n # for i in range(len(date_sorting_list)): ## |\n # date_sorting_list[i] = str(date_sorting_list[i]) ## |\n # for date in date_sorting_list: ## v\n for zz in range(1, 2): ## and add a hashtag to this dummy loop\n # Identifies if the play is a punt play\n try:\n dictionary[name][date][\"football\"][\"puntpositionx\"]\n dictionary[name][date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n # This is a coordinate transformation of all the relevant quantities to the direction of play of the punter\n if float(dictionary[name][date][\"football\"]['x']) - float(dictionary[name][date][name][\"x\"]) > 0:\n football_y = float(dictionary[name][date][\"football\"]['y'])\n punter_y = float(dictionary[name][date][name][\"y\"])\n punter_x = float(dictionary[name][date][name][\"x\"])\n puntresult_y = float(dictionary[name][date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][date][\"football\"]['x']) - float(dictionary[name][date][name][\"x\"]) <= 0:\n football_y = 53.3 - float(dictionary[name][date][\"football\"]['y'])\n punter_y = 53.3 - float(dictionary[name][date][name][\"y\"])\n punter_x = 120 - float(dictionary[name][date][name][\"x\"])\n puntresult_y = 53.3 - float(dictionary[name][date][\"football\"][\"football_landing_position_y\"])\n past_y_offset = 0\n past_y_offset_counter = 0\n \n alpha_amount_of_times_ball_went_right_positive_offset = 0\n alpha_amount_of_times_ball_went_left_positive_offset = 0\n alpha_amount_of_times_ball_went_right_negative_offset = 0\n alpha_amount_of_times_ball_went_left_negative_offset = 0\n \n beta_amount_of_times_ball_went_right_positive_offset = 0\n beta_amount_of_times_ball_went_left_positive_offset = 0\n beta_amount_of_times_ball_went_right_negative_offset = 0\n beta_amount_of_times_ball_went_left_negative_offset = 0\n \n average_punt_length = 0\n average_punt_length_counter = 0\n early_region = 0\n early_region_counter = 0\n mid_region = 0\n mid_region_counter = 0\n late_region = 0\n late_region_counter = 0\n for past_date in dictionary[name]:\n # This goes through all the plays that happened BEFORE the current play's date\n if int(past_date) >= int(date):\n continue\n\n try:\n dictionary[name][past_date][\"football\"][\"puntpositionx\"]\n dictionary[name][past_date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][past_date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][past_date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n if float(dictionary[name][past_date][\"football\"]['x']) - float(dictionary[name][past_date][name][\"x\"]) > 0:\n past_football_y = float(dictionary[name][past_date][\"football\"]['y'])\n past_punter_y = float(dictionary[name][past_date][name][\"y\"])\n past_punter_x = float(dictionary[name][past_date][name][\"x\"])\n past_puntresult_y = float(dictionary[name][past_date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][past_date][\"football\"]['x']) - float(dictionary[name][past_date][name][\"x\"]) <= 0:\n past_football_y = 53.3 - float(dictionary[name][past_date][\"football\"]['y'])\n past_punter_y = 53.3 - float(dictionary[name][past_date][name][\"y\"])\n past_punter_x = 120 - float(dictionary[name][past_date][name][\"x\"])\n past_puntresult_y = 53.3 - float(dictionary[name][past_date][\"football\"][\"football_landing_position_y\"])\n \n past_y_offset_punter = past_football_y-past_punter_y # Gives the y-offset of the punter to the ball, positive value means he's standing to the right, and negative to the left\n \n past_y_offset_puntresult = past_punter_y-past_puntresult_y # Gives the y-offset of the ball when it finally lands relative to the punter's frame 1 position\n \n past_y_offset += past_y_offset_punter # Counts up the y-offset of the punter to the ball for each past play\n \n past_y_offset_counter += 1 # Together with past_y_offset gives us the average y-offset of the punter relative to the ball by division\n \n further_past_average_position = 0\n further_past_average_position_counter = 0\n for further_past_date in dictionary[name]:\n # This goes through all the past game of the past game and calculates the average y-offset relative to the ball up until that point in time\n if int(further_past_date) >= int(past_date):\n continue\n\n try:\n dictionary[name][further_past_date][\"football\"][\"puntpositionx\"]\n dictionary[name][further_past_date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][further_past_date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][further_past_date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n if float(dictionary[name][further_past_date][\"football\"]['x']) - float(dictionary[name][further_past_date][name][\"x\"]) > 0:\n further_past_football_y = float(dictionary[name][further_past_date][\"football\"]['y'])\n further_past_punter_y = float(dictionary[name][further_past_date][name][\"y\"])\n further_past_puntresult_y = float(dictionary[name][further_past_date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][further_past_date][\"football\"]['x']) - float(dictionary[name][further_past_date][name][\"x\"]) <= 0:\n further_past_football_y = 53.3 - float(dictionary[name][further_past_date][\"football\"]['y'])\n further_past_punter_y = 53.3 - float(dictionary[name][further_past_date][name][\"y\"])\n further_past_puntresult_y = 53.3 - float(dictionary[name][further_past_date][\"football\"][\"football_landing_position_y\"])\n \n further_past_average_position += further_past_football_y-further_past_punter_y # Counts up the y-offset of the punter to the ball for each further past play\n further_past_average_position_counter += 1 # Together with further_past_average_position gives us the average y-offset of the punter relative to the ball for the past play by division\n\n # This goes towards calculating alpha\n if past_y_offset_punter > 0:\n if past_y_offset_puntresult > 0:\n alpha_amount_of_times_ball_went_right_positive_offset += 1\n elif past_y_offset_puntresult < 0:\n alpha_amount_of_times_ball_went_left_positive_offset += 1\n elif past_y_offset_punter < 0:\n if past_y_offset_puntresult > 0:\n alpha_amount_of_times_ball_went_right_negative_offset += 1\n if past_y_offset_puntresult < 0:\n alpha_amount_of_times_ball_went_left_negative_offset += 1\n \n # This goes towards calculating beta\n try:\n if further_past_average_position/further_past_average_position_counter > past_y_offset_punter:\n if past_y_offset_puntresult > 0:\n beta_amount_of_times_ball_went_right_positive_offset += 1\n elif past_y_offset_puntresult < 0:\n beta_amount_of_times_ball_went_left_positive_offset += 1\n elif further_past_average_position/further_past_average_position_counter < past_y_offset_punter:\n if past_y_offset_puntresult > 0:\n beta_amount_of_times_ball_went_right_negative_offset += 1\n if past_y_offset_puntresult < 0:\n beta_amount_of_times_ball_went_left_negative_offset += 1\n except ZeroDivisionError:\n pass\n # This goes towards calculating the expected puntlength\n if past_punter_x <= 20:\n early_region += abs(past_punter_y - past_puntresult_y)\n early_region_counter += 1\n elif past_punter_x > 20 and past_punter_x <= 40:\n mid_region += abs(past_punter_y - past_puntresult_y)\n mid_region_counter += 1\n elif past_punter_x > 40:\n late_region += abs(past_punter_y - past_puntresult_y)\n late_region_counter += 1\n average_punt_length += abs(past_punter_y-past_puntresult_y)\n average_punt_length_counter += 1\n\n try:\n punt_length = average_punt_length / average_punt_length_counter # Expected value of the punt length in the y-direction with the punter's initial-frame position as the 0 coordinate\n except ZeroDivisionError:\n continue\n current_y_offset = football_y - punter_y # Current frame 1 y-offset of punter relative to the ball \n past_y_offset = past_y_offset / past_y_offset_counter # Average y-offset up until now\n \n # alpha\n alpha_positive = (alpha_amount_of_times_ball_went_right_positive_offset + 1) / (alpha_amount_of_times_ball_went_left_positive_offset + alpha_amount_of_times_ball_went_right_positive_offset + 2)\n alpha_negative = (alpha_amount_of_times_ball_went_right_negative_offset + 1) / (alpha_amount_of_times_ball_went_left_negative_offset + alpha_amount_of_times_ball_went_right_negative_offset + 2)\n # beta\n beta_positive = (beta_amount_of_times_ball_went_right_positive_offset + 1) / (beta_amount_of_times_ball_went_left_positive_offset + beta_amount_of_times_ball_went_right_positive_offset + 2)\n beta_negative = (beta_amount_of_times_ball_went_right_negative_offset + 1) / (beta_amount_of_times_ball_went_left_negative_offset + beta_amount_of_times_ball_went_right_negative_offset + 2)\n\n # This gives us the Probability of the ball being punted to the right from the punter's inital-frame position\n if current_y_offset > 0:\n try:\n if past_y_offset > current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_positive - 0.5)) * alpha_positive+(1 - abs(2 * (alpha_positive - 0.5))) * beta_positive + abs(2 * (beta_positive - 0.5)) * beta_positive+(1 - abs(2 * (beta_positive - 0.5))) * alpha_positive) / 2\n\n elif past_y_offset < current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_positive - 0.5)) * alpha_positive + (1 - abs(2 * (alpha_positive - 0.5))) * beta_negative + abs(2 * (beta_negative - 0.5)) * beta_negative + (1 - abs(2 * (beta_negative - 0.5))) * alpha_positive) / 2\n except ZeroDivisionError:\n continue\n elif current_y_offset < 0:\n try:\n if past_y_offset > current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_negative - 0.5)) * alpha_negative + (1 - abs(2 * (alpha_negative - 0.5))) * beta_positive + abs(2 * (beta_positive - 0.5)) * beta_positive + (1-abs(2 * (beta_positive - 0.5))) * alpha_negative) / 2\n\n elif past_y_offset < current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_negative - 0.5)) * alpha_negative + (1 - abs(2 * (alpha_negative - 0.5))) * beta_negative + abs(2 * (beta_negative - 0.5)) * beta_negative + (1 - abs(2 * (beta_negative-0.5))) * alpha_negative) / 2\n except ZeroDivisionError:\n continue\n # calculates the expected punt length\n if punter_x <= 20 and early_region_counter != 0:\n punt_length = early_region / early_region_counter\n elif punter_x <= 20 and early_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n elif punter_x > 20 and punter_x <= 40 and mid_region_counter != 0:\n punt_length = mid_region / mid_region_counter\n elif punter_x > 20 and punter_x <= 40 and mid_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n elif punter_x > 40 and late_region_counter != 0:\n punt_length = late_region / late_region_counter\n elif punter_x > 40 and late_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n\n # This gives us the probability distribution in the standard coordinate frame (still in the direction of the punting team) where y goes from 0 (right) to 53.3 (left)\n # (not necessarily in the order of low date -> high date)\n myclip_a = 0\n myclip_b = 53.3\n if punt_length <= 6 and average_punt_length_counter == 1 or punt_length >= 24 and average_punt_length_counter == 1: # This provides more realistic results when there is only one punt to go off of\n my_std = 8\n my_mean = punter_y - 12\n else:\n my_mean = punter_y - punt_length\n my_std = punt_length * 2 / 3\n myclip_a2 = 0\n myclip_b2 = 53.3\n if punt_length <= 6 and average_punt_length_counter == 1 or punt_length >= 24 and average_punt_length_counter == 1: # This provides more realistic results when there is only one punt to go off of\n my_std2 = 8\n my_mean2 = punter_y + 12\n else:\n my_mean2 = punter_y + punt_length\n my_std2 = punt_length * 2 / 3\n a = (myclip_a - my_mean) / my_std\n b = (myclip_b - my_mean) / my_std\n a2 = (myclip_a2 - my_mean2) / my_std2\n b2 = (myclip_b2 - my_mean2) / my_std2\n x_range = np.linspace(0, 53.3, 54)\n x_range2 = np.linspace(0, 53.3, 54)\n # finds the maximum of our probability distribution to make the graphs include all of the y-values from 0 up\n def our_function(x):\n return prob_ball_goes_right * (truncnorm.pdf(x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(x, a2, b2, loc = my_mean2, scale = my_std2))\n def our_function_mirrored(x):\n return prob_ball_goes_right * (truncnorm.pdf((53.3-x), a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf((53.3-x), a2, b2, loc = my_mean2, scale = my_std2))\n max_x = scipy.optimize.fmin(lambda x: -our_function(x), 0, disp = False)\n max_x_mirrored = 53.3 - scipy.optimize.fmin(lambda x: -our_function_mirrored(x), 0, disp = False)\n if prob_ball_goes_right * (truncnorm.pdf(max_x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(max_x, a2, b2, loc = my_mean2, scale = my_std2)) >= prob_ball_goes_right * (truncnorm.pdf(max_x_mirrored, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(max_x_mirrored, a2, b2, loc = my_mean2, scale = my_std2)):\n plt.ylim(0,prob_ball_goes_right * (truncnorm.pdf(max_x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(max_x, a2, b2, loc = my_mean2, scale = my_std2)))\n elif prob_ball_goes_right * (truncnorm.pdf(max_x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(max_x, a2, b2, loc = my_mean2, scale = my_std2)) < prob_ball_goes_right * (truncnorm.pdf(max_x_mirrored, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(max_x_mirrored, a2, b2, loc = my_mean2, scale = my_std2)):\n plt.ylim(0,prob_ball_goes_right * (truncnorm.pdf(max_x_mirrored, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(max_x_mirrored, a2, b2, loc = my_mean2, scale = my_std2)))\n \n plt.ylabel('Probability')\n plt.xlabel('Y-Direction')\n plt.plot(x_range, prob_ball_goes_right * (truncnorm.pdf(x_range, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(x_range2, a2, b2, loc = my_mean2, scale = my_std2)))\n # We can integrate the probabilty distribution over a desired area to give us the probability of the ball landing within that area\n # For example we can split the field into thirds\n right = quad(lambda x: prob_ball_goes_right * (truncnorm.pdf(x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(x, a2, b2, loc = my_mean2, scale = my_std2)), 0, 53.3 / 3)\n center = quad(lambda x: prob_ball_goes_right * (truncnorm.pdf(x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(x, a2, b2, loc = my_mean2, scale = my_std2)), 53.3 / 3, 53.3 / 3 * 2)\n left = quad(lambda x: prob_ball_goes_right * (truncnorm.pdf(x, a, b, loc = my_mean, scale = my_std)) + (1 - prob_ball_goes_right) * (truncnorm.pdf(x, a2, b2, loc = my_mean2, scale = my_std2)), 53.3 / 3 * 2, 53.3)\n print(\"\")\n print(\"\")\n print(name)\n print(\"date \" + date)\n print(\"gameid \" + dictionary[name][date][name][\"gameid\"])\n print(\"playid \" + dictionary[name][date][name][\"playid\"])\n print(\"right: \" + str(right[0]))\n print(\"center: \" + str(center[0]))\n print(\"left: \" + str(left[0]))\n print(\"actual landing spot of punt: \" + str(round(puntresult_y, 2)))\n plt.show()\n\n\n","metadata":{"_kg_hide-input":false,"_kg_hide-output":false,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"## 5.4 Measures for Comparing the Accuracy of Competing Models
\n\n### 5.4.1 Measure for the Accuracy of the Direction of a Punt\n\nI don't have any state-of-the-art model to compare this to, so I can't say how accurate this model is. After all, while my model does match the probability curve extremely well, which gives me great confidence that it is at least very good, there may always be a more accurate model possible, which, while my model may predict some punts to have a $60\\%$ chance of going to the right, might really be able further distinguish between half of them being $80\\%$ and the other half $40\\%$, while still giving an overall average of $60\\%$.
And, ultimately, an all-knowing future-seeing model would be able to call the direction correctly $100\\%$ of the time.\n\nI do *lot* of esports and sports modelling, which I post on [reddit](https://www.reddit.com/user/LowEntertainment2621). Any sports modelling I post should be taken with a grain of salt though since I just don't have the level of information on who's playing and who's injured as is reflected in the average bookmakers' market prices and these things make up at least a third of the calculation for sports.\n\nSo the following method of comparing different models is inspired by that.\n\nWe will ask the two models to be compared to give us a probability of the football going to the right from the punter's initial-frame-position and then give fair odds to each of their predictions that the opposing model can use to bet on.
And we just look at which model wins out. It is of course absolutely ***crucial*** that both models only ever use information from the past.\n\nNote that one model profiting against another model doesn't necessarily mean that the other model doesn't profit against the first model, especially when given fair odds, so what we need to do in the general case is really ask which model profits *more* than the other and also consider how much the expected profit deviates from the actual profit.\n\nLet's, as an example, compare my model to a model which says it's $50/50$ each time.\n\n","metadata":{}},{"cell_type":"code","source":"import pickle\n\n\ntotal_profit = 0\ntotal_profit_second_model = 0\ntotal_bets_placed = 0\ntotal_bets_placed_second_model = 0\nexpected_profit = 0\nexpected_profit_second_model = 0\nfor z in range(1, 2):\n for number in range(18,21):\n f = open('../input/nfldictionaries/NFLlist20' + str(number) + '.pckl', 'rb')\n dictionary = pickle.load(f)\n f.close()\n for name in dictionary:\n\n for date in dictionary[name]:\n # Identifies if the play is a punt play\n try:\n dictionary[name][date][\"football\"][\"puntpositionx\"]\n dictionary[name][date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n # This is a coordinate transformation of all the relevant quantities to the direction of play of the punter\n if float(dictionary[name][date][\"football\"]['x']) - float(dictionary[name][date][name][\"x\"]) > 0:\n football_y = float(dictionary[name][date][\"football\"]['y'])\n punter_y = float(dictionary[name][date][name][\"y\"])\n punter_x = float(dictionary[name][date][name][\"x\"])\n puntresult_y = float(dictionary[name][date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][date][\"football\"]['x']) - float(dictionary[name][date][name][\"x\"]) <= 0:\n football_y = 53.3 - float(dictionary[name][date][\"football\"]['y'])\n punter_y = 53.3 - float(dictionary[name][date][name][\"y\"])\n punter_x = 120 - float(dictionary[name][date][name][\"x\"])\n puntresult_y = 53.3 - float(dictionary[name][date][\"football\"][\"football_landing_position_y\"])\n past_y_offset = 0\n past_y_offset_counter = 0\n\n alpha_amount_of_times_ball_went_right_positive_offset = 0\n alpha_amount_of_times_ball_went_left_positive_offset = 0\n alpha_amount_of_times_ball_went_right_negative_offset = 0\n alpha_amount_of_times_ball_went_left_negative_offset = 0\n\n beta_amount_of_times_ball_went_right_positive_offset = 0\n beta_amount_of_times_ball_went_left_positive_offset = 0\n beta_amount_of_times_ball_went_right_negative_offset = 0\n beta_amount_of_times_ball_went_left_negative_offset = 0\n\n average_punt_length = 0\n average_punt_length_counter = 0\n early_region = 0\n early_region_counter = 0\n mid_region = 0\n mid_region_counter = 0\n late_region = 0\n late_region_counter = 0\n for past_date in dictionary[name]:\n # This goes through all the plays that happened BEFORE the current play's date\n if int(past_date) >= int(date):\n continue\n\n try:\n dictionary[name][past_date][\"football\"][\"puntpositionx\"]\n dictionary[name][past_date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][past_date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][past_date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n if float(dictionary[name][past_date][\"football\"]['x']) - float(dictionary[name][past_date][name][\"x\"]) > 0:\n past_football_y = float(dictionary[name][past_date][\"football\"]['y'])\n past_punter_y = float(dictionary[name][past_date][name][\"y\"])\n past_punter_x = float(dictionary[name][past_date][name][\"x\"])\n past_puntresult_y = float(dictionary[name][past_date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][past_date][\"football\"]['x']) - float(dictionary[name][past_date][name][\"x\"]) <= 0:\n past_football_y = 53.3 - float(dictionary[name][past_date][\"football\"]['y'])\n past_punter_y = 53.3 - float(dictionary[name][past_date][name][\"y\"])\n past_punter_x = 120 - float(dictionary[name][past_date][name][\"x\"])\n past_puntresult_y = 53.3 - float(dictionary[name][past_date][\"football\"][\"football_landing_position_y\"])\n\n past_y_offset_punter = past_football_y-past_punter_y # Gives the y-offset of the punter to the ball, positive value means he's standing to the right, and negative to the left\n\n past_y_offset_puntresult = past_punter_y-past_puntresult_y # Gives the y-offset of the ball when it finally lands relative to the punter's frame 1 position\n\n past_y_offset += past_y_offset_punter # Counts up the y-offset of the punter to the ball for each past play\n\n past_y_offset_counter += 1 # Together with past_y_offset gives us the average y-offset of the punter relative to the ball by division\n\n further_past_average_position = 0\n further_past_average_position_counter = 0\n for further_past_date in dictionary[name]:\n # This goes through all the past game of the past game and calculates the average y-offset relative to the ball up until that point in time\n if int(further_past_date) >= int(past_date):\n continue\n\n try:\n dictionary[name][further_past_date][\"football\"][\"puntpositionx\"]\n dictionary[name][further_past_date][\"football\"][\"ball_snappositionx\"]\n except KeyError:\n continue\n try:\n dictionary[name][further_past_date][\"football\"][\"punt_blockedpositionx\"]\n continue\n except KeyError:\n pass\n try:\n dictionary[name][further_past_date][\"football\"]['football_landing_position_y']\n except KeyError:\n continue\n if float(dictionary[name][further_past_date][\"football\"]['x']) - float(dictionary[name][further_past_date][name][\"x\"]) > 0:\n further_past_football_y = float(dictionary[name][further_past_date][\"football\"]['y'])\n further_past_punter_y = float(dictionary[name][further_past_date][name][\"y\"])\n further_past_puntresult_y = float(dictionary[name][further_past_date][\"football\"][\"football_landing_position_y\"])\n elif float(dictionary[name][further_past_date][\"football\"]['x']) - float(dictionary[name][further_past_date][name][\"x\"]) <= 0:\n further_past_football_y = 53.3 - float(dictionary[name][further_past_date][\"football\"]['y'])\n further_past_punter_y = 53.3 - float(dictionary[name][further_past_date][name][\"y\"])\n further_past_puntresult_y = 53.3 - float(dictionary[name][further_past_date][\"football\"][\"football_landing_position_y\"])\n\n further_past_average_position += further_past_football_y-further_past_punter_y # Counts up the y-offset of the punter to the ball for each further past play\n further_past_average_position_counter += 1 # Together with further_past_average_position gives us the average y-offset of the punter relative to the ball for the past play by division\n\n # This goes towards calculating alpha\n if past_y_offset_punter > 0:\n if past_y_offset_puntresult > 0:\n alpha_amount_of_times_ball_went_right_positive_offset += 1\n elif past_y_offset_puntresult < 0:\n alpha_amount_of_times_ball_went_left_positive_offset += 1\n elif past_y_offset_punter < 0:\n if past_y_offset_puntresult > 0:\n alpha_amount_of_times_ball_went_right_negative_offset += 1\n if past_y_offset_puntresult < 0:\n alpha_amount_of_times_ball_went_left_negative_offset += 1\n\n # This goes towards calculating beta\n try:\n if further_past_average_position/further_past_average_position_counter > past_y_offset_punter:\n if past_y_offset_puntresult > 0:\n beta_amount_of_times_ball_went_right_positive_offset += 1\n elif past_y_offset_puntresult < 0:\n beta_amount_of_times_ball_went_left_positive_offset += 1\n elif further_past_average_position/further_past_average_position_counter < past_y_offset_punter:\n if past_y_offset_puntresult > 0:\n beta_amount_of_times_ball_went_right_negative_offset += 1\n if past_y_offset_puntresult < 0:\n beta_amount_of_times_ball_went_left_negative_offset += 1\n except ZeroDivisionError:\n pass\n # This goes towards calculating the expected puntlength\n if past_punter_x <= 20:\n early_region += abs(past_punter_y - past_puntresult_y)\n early_region_counter += 1\n elif past_punter_x > 20 and past_punter_x <= 40:\n mid_region += abs(past_punter_y - past_puntresult_y)\n mid_region_counter += 1\n elif past_punter_x > 40:\n late_region += abs(past_punter_y - past_puntresult_y)\n late_region_counter += 1\n average_punt_length += abs(past_punter_y - past_puntresult_y)\n average_punt_length_counter += 1\n\n try:\n punt_length = average_punt_length / average_punt_length_counter # Expected value of the punt length in the y-direction with the punter's initial-frame position as the 0 coordinate\n except ZeroDivisionError:\n continue\n current_y_offset = football_y - punter_y # Current frame 1 y-offset of punter relative to the ball \n past_y_offset = past_y_offset / past_y_offset_counter # Average y-offset up until now\n\n # alpha\n alpha_positive = (alpha_amount_of_times_ball_went_right_positive_offset + 1) / (alpha_amount_of_times_ball_went_left_positive_offset + alpha_amount_of_times_ball_went_right_positive_offset + 2)\n alpha_negative = (alpha_amount_of_times_ball_went_right_negative_offset + 1) / (alpha_amount_of_times_ball_went_left_negative_offset + alpha_amount_of_times_ball_went_right_negative_offset + 2)\n # beta\n beta_positive = (beta_amount_of_times_ball_went_right_positive_offset + 1) / (beta_amount_of_times_ball_went_left_positive_offset + beta_amount_of_times_ball_went_right_positive_offset + 2)\n beta_negative = (beta_amount_of_times_ball_went_right_negative_offset + 1) / (beta_amount_of_times_ball_went_left_negative_offset + beta_amount_of_times_ball_went_right_negative_offset + 2)\n\n # This gives us the Probability of the ball being punted to the right from the punter's inital-frame position\n if current_y_offset > 0:\n try:\n if past_y_offset > current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_positive - 0.5)) * alpha_positive+(1 - abs(2 * (alpha_positive - 0.5))) * beta_positive + abs(2 * (beta_positive - 0.5)) * beta_positive+(1 - abs(2 * (beta_positive - 0.5))) * alpha_positive) / 2\n\n elif past_y_offset < current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_positive - 0.5)) * alpha_positive + (1 - abs(2 * (alpha_positive - 0.5))) * beta_negative + abs(2 * (beta_negative - 0.5)) * beta_negative + (1 - abs(2 * (beta_negative - 0.5))) * alpha_positive) / 2\n except ZeroDivisionError:\n continue\n elif current_y_offset < 0:\n try:\n if past_y_offset > current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_negative - 0.5)) * alpha_negative + (1 - abs(2 * (alpha_negative - 0.5))) * beta_positive + abs(2 * (beta_positive - 0.5)) * beta_positive + (1-abs(2 * (beta_positive - 0.5))) * alpha_negative) / 2\n\n elif past_y_offset < current_y_offset:\n prob_ball_goes_right = (abs(2 * (alpha_negative - 0.5)) * alpha_negative + (1 - abs(2 * (alpha_negative - 0.5))) * beta_negative + abs(2 * (beta_negative - 0.5)) * beta_negative + (1 - abs(2 * (beta_negative-0.5))) * alpha_negative) / 2\n except ZeroDivisionError:\n continue\n\n if punter_x <= 20 and early_region_counter != 0:\n punt_length = early_region / early_region_counter\n elif punter_x <= 20 and early_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n elif punter_x > 20 and punter_x <= 40 and mid_region_counter != 0:\n punt_length = mid_region / mid_region_counter\n elif punter_x > 20 and punter_x <= 40 and mid_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n elif punter_x > 40 and late_region_counter != 0:\n punt_length = late_region / late_region_counter\n elif punter_x > 40 and late_region_counter == 0:\n punt_length = average_punt_length / average_punt_length_counter\n\n # This compares the accuracy of different models when it comes to calling the direction correctly\n first_model_odds = (1 - prob_ball_goes_right) / prob_ball_goes_right\n second_model_odds = (1 - 0.5) / 0.5\n if first_model_odds < second_model_odds:\n if punter_y - puntresult_y > 0:\n total_profit += second_model_odds\n total_bets_placed += 1\n expected_profit += 1 / (1 + first_model_odds) * second_model_odds - (1 - 1 / (1 + first_model_odds))\n elif punter_y - puntresult_y < 0:\n total_profit -= 1\n total_bets_placed += 1\n expected_profit += 1 / (1 + first_model_odds) * second_model_odds - (1 - 1 / (1 + first_model_odds))\n elif first_model_odds > second_model_odds:\n if punter_y - puntresult_y < 0:\n total_profit += 1 / second_model_odds\n total_bets_placed += 1\n expected_profit += 1 / (1 + 1 / first_model_odds) * 1 / second_model_odds - (1 - 1 / (1 + 1 / first_model_odds))\n elif punter_y - puntresult_y > 0:\n total_profit -= 1\n total_bets_placed += 1\n expected_profit += 1 / (1 + 1 / first_model_odds) * 1 / second_model_odds - (1 - 1 / (1 + 1 / first_model_odds))\n\n if second_model_odds < first_model_odds:\n if punter_y - puntresult_y > 0:\n total_profit_second_model += first_model_odds\n total_bets_placed_second_model += 1\n expected_profit_second_model += 1 / (1 + second_model_odds) * first_model_odds - (1 - 1 / (1 + second_model_odds))\n elif punter_y - puntresult_y < 0:\n total_profit_second_model -= 1\n total_bets_placed_second_model += 1\n expected_profit_second_model += 1 / (1 + second_model_odds) * first_model_odds - (1 - 1 / (1 + second_model_odds))\n elif second_model_odds > first_model_odds:\n if punter_y - puntresult_y < 0:\n total_profit_second_model += 1 / first_model_odds\n total_bets_placed_second_model += 1\n expected_profit_second_model += 1 / (1 + 1 / second_model_odds) * 1 / first_model_odds - (1 - 1 / (1 + 1 / second_model_odds))\n elif punter_y - puntresult_y > 0:\n total_profit_second_model -= 1\n total_bets_placed_second_model += 1\n expected_profit_second_model += 1 / (1 + 1 / second_model_odds) * 1 / first_model_odds - (1 - 1 / (1 + 1 / second_model_odds))\n \nprint(\"my model profit: \" + str(total_profit) + \" over \" + str(total_bets_placed) + \" bets (\" + str(expected_profit) + \" expected)\" )\nprint(\"50/50 model profit: \" + str(total_profit_second_model) + \" over \" + str(total_bets_placed_second_model) + \" bets (\" + str(expected_profit_second_model) + \" expected)\" )\n ","metadata":{"_kg_hide-input":false,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"So my model beats the $50/50$ model.","metadata":{}},{"cell_type":"markdown","source":"