On ESPN if you watch the gamecast of a game they give an updated win percentage as the game progresses. We are going to produce a similar prediction, calculating win percentage for a home team given point differential, quarter, and time left in the game.

We are calculating:
p(home_win|[time_left, point_diff]=[t,p])

We’ll do the simplest frequentist prediction by counting up the number of games where [t,p] occurs and then counting up the number of games where that [t,p] occurs and the home team won. This project is mostly to practice working with data both in python, but also later in SQL because I will perform this same analysis with an NCAA BigQuery database.

# This Python 3 environment comes with many helpful analytics libraries installed
# It is defined by the kaggle/python docker image: https://github.com/kaggle/docker-python
# For example, here's several helpful packages to load in

import numpy as np # linear algebra
import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)
from matplotlib import pyplot as plt
%matplotlib inline

# Input data files are available in the "../input/" directory.
# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory

import os
for dirname, _, filenames in os.walk('/kaggle/input'):
    for filename in filenames:
        print(os.path.join(dirname, filename))

# Any results you write to the current directory are saved as output.

/kaggle/input/nba-playbyplay-data-20182019/NBA-PBP-2018-2019.csv

df = pd.read_csv('/kaggle/input/nba-playbyplay-data-20182019/NBA-PBP-2018-2019.csv')
df.head()
URL GameType Location Date Time WinningTeam Quarter SecLeft AwayTeam AwayPlay ... FreeThrowNum EnterGame LeaveGame TurnoverPlayer TurnoverType TurnoverCause TurnoverCauser JumpballAwayPlayer JumpballHomePlayer JumpballPoss
0 /boxscores/201810160BOS.html regular TD Garden Boston Massachusetts October 16 2018 8:00 PM BOS 1 720 PHI Jump ball: J. Embiid vs. A. Horford (B. Simmon... ... NaN NaN NaN NaN NaN NaN NaN J. Embiid - PHI A. Horford - BOS B. Simmons
1 /boxscores/201810160BOS.html regular TD Garden Boston Massachusetts October 16 2018 8:00 PM BOS 1 700 PHI R. Covington misses 3-pt jump shot from 27 ft ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2 /boxscores/201810160BOS.html regular TD Garden Boston Massachusetts October 16 2018 8:00 PM BOS 1 700 PHI NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
3 /boxscores/201810160BOS.html regular TD Garden Boston Massachusetts October 16 2018 8:00 PM BOS 1 675 PHI NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
4 /boxscores/201810160BOS.html regular TD Garden Boston Massachusetts October 16 2018 8:00 PM BOS 1 673 PHI Defensive rebound by D. Saric ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 40 columns

df.columns

Index(['URL', 'GameType', 'Location', 'Date', 'Time', 'WinningTeam', 'Quarter',
       'SecLeft', 'AwayTeam', 'AwayPlay', 'AwayScore', 'HomeTeam', 'HomePlay',
       'HomeScore', 'Shooter', 'ShotType', 'ShotOutcome', 'ShotDist',
       'Assister', 'Blocker', 'FoulType', 'Fouler', 'Fouled', 'Rebounder',
       'ReboundType', 'ViolationPlayer', 'ViolationType', 'TimeoutTeam',
       'FreeThrowShooter', 'FreeThrowOutcome', 'FreeThrowNum', 'EnterGame',
       'LeaveGame', 'TurnoverPlayer', 'TurnoverType', 'TurnoverCause',
       'TurnoverCauser', 'JumpballAwayPlayer', 'JumpballHomePlayer',
       'JumpballPoss'],
      dtype='object')

df['home_pt_diff'] = df.HomeScore - df.AwayScore
df.tail()
URL GameType Location Date Time WinningTeam Quarter SecLeft AwayTeam AwayPlay ... EnterGame LeaveGame TurnoverPlayer TurnoverType TurnoverCause TurnoverCauser JumpballAwayPlayer JumpballHomePlayer JumpballPoss home_pt_diff
613666 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR K. Leonard makes free throw 1 of 2 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN -3
613667 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR K. Leonard makes free throw 2 of 2 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN -4
613668 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN -4
613669 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN -4
613670 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 5 0 TOR End of Game ... NaN NaN NaN NaN NaN NaN NaN NaN NaN -4

5 rows × 41 columns

df['time_left'] = (4-df.Quarter)*720+df.SecLeft
df.tail()
URL GameType Location Date Time WinningTeam Quarter SecLeft AwayTeam AwayPlay ... LeaveGame TurnoverPlayer TurnoverType TurnoverCause TurnoverCauser JumpballAwayPlayer JumpballHomePlayer JumpballPoss home_pt_diff time_left
613666 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR K. Leonard makes free throw 1 of 2 ... NaN NaN NaN NaN NaN NaN NaN NaN -3 0
613667 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR K. Leonard makes free throw 2 of 2 ... NaN NaN NaN NaN NaN NaN NaN NaN -4 0
613668 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR NaN ... NaN NaN NaN NaN NaN NaN NaN NaN -4 0
613669 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 4 0 TOR NaN ... NaN NaN NaN NaN NaN NaN NaN NaN -4 0
613670 /boxscores/201906130GSW.html playoff Oracle Arena Oakland California June 13 2019 9:00 PM TOR 5 0 TOR End of Game ... NaN NaN NaN NaN NaN NaN NaN NaN -4 -720

5 rows × 42 columns

# Only need a few of these columns to perform
df.drop(['URL', 'GameType', 'Location','AwayPlay', 'HomePlay',
       'Shooter', 'ShotType', 'ShotOutcome', 'ShotDist',
       'Assister', 'Blocker', 'FoulType', 'Fouler', 'Fouled', 'Rebounder',
       'ReboundType', 'ViolationPlayer', 'ViolationType', 'TimeoutTeam',
       'FreeThrowShooter', 'FreeThrowOutcome', 'FreeThrowNum', 'EnterGame',
       'LeaveGame', 'TurnoverPlayer', 'TurnoverType', 'TurnoverCause',
       'TurnoverCauser', 'JumpballAwayPlayer', 'JumpballHomePlayer',
       'JumpballPoss', 'AwayScore', 'HomeScore','Quarter','SecLeft'], axis=1, inplace=True)

games_groupby = df.groupby(['Date', 'Time', 'HomeTeam', 'WinningTeam'])
games_groupby.count()
AwayTeam home_pt_diff time_left
Date Time HomeTeam WinningTeam
April 1 2019 10:00 PM PHO PHO 453 453 453
7:00 PM IND IND 433 433 433
7:30 PM BOS BOS 455 455 455
BRK MIL 541 541 541
NYK NYK 433 433 433
... ... ... ... ... ... ...
October 31 2018 10:30 PM PHO SAS 451 451 451
7:30 PM BRK BRK 571 571 571
8:00 PM CHI DEN 488 488 488
MIN MIN 494 494 494
NYK IND 433 433 433

1312 rows × 3 columns

games = [x[0] for x in games_groupby ]

home_wins = [int(game[2]==game[3]) for game in games]
home_wins[:10]

[1, 1, 1, 0, 1, 1, 0, 1, 1, 1]

prior_home_win = sum(home_wins)/len(home_wins)
print(prior_home_win)

0.5907012195121951

games_groupby_zip = games_groupby.apply(lambda x: list(zip([t for t in x['time_left']], [p for p in x['home_pt_diff']])))

t_p_win = list(zip(games_groupby_zip, home_wins))

t_p_win[0]

([(2880, 0),
  (2861, 0),
  (2855, 0),
  (2852, 0),
  (2838, 0),
  (2835, 0),
  (2818, 0),
  (2816, 0),
  (2803, 2),
  (2776, 2),
  (2774, 2),
  (2768, 2),
  (2767, 2),
  (2760, 2),
  (2752, 2),
  (2749, 4),
  (2734, 4),
  (2731, 4),
  (2730, 2),
  (2727, 2),
  (2727, 2),
  (2710, 0),
  (2694, 3),
  (2682, 3),
  (2680, 3),
  (2665, 3),
  (2665, 3),
  (2657, 3),
  (2657, 3),
  (2644, 3),
  (2641, 3),
  (2623, 3),
  (2621, 3),
  (2612, 3),
  (2597, 1),
  (2579, 4),
  (2559, 4),
  (2556, 4),
  (2550, 4),
  (2548, 4),
  (2541, 4),
  (2541, 4),
  (2541, 4),
  (2532, 4),
  (2532, 4),
  (2517, 7),
  (2517, 7),
  (2517, 8),
  (2495, 6),
  (2472, 8),
  (2472, 8),
  (2472, 8),
  (2472, 8),
  (2472, 9),
  (2458, 9),
  (2455, 9),
  (2455, 7),
  (2455, 7),
  (2455, 7),
  (2455, 7),
  (2448, 7),
  (2432, 7),
  (2430, 7),
  (2414, 5),
  (2396, 8),
  (2374, 8),
  (2372, 8),
  (2368, 8),
  (2368, 8),
  (2368, 8),
  (2355, 6),
  (2343, 6),
  (2322, 4),
  (2305, 4),
  (2303, 4),
  (2296, 4),
  (2296, 4),
  (2296, 4),
  (2296, 3),
  (2296, 2),
  (2296, 2),
  (2280, 2),
  (2272, 2),
  (2272, 2),
  (2272, 2),
  (2272, 2),
  (2270, 2),
  (2258, 2),
  (2256, 2),
  (2254, 2),
  (2250, 2),
  (2244, 2),
  (2243, 2),
  (2241, 0),
  (2234, 0),
  (2234, 0),
  (2223, -2),
  (2223, -2),
  (2223, -3),
  (2211, -3),
  (2210, -3),
  (2205, 0),
  (2197, 0),
  (2195, 0),
  (2192, 2),
  (2173, 2),
  (2172, 2),
  (2172, 2),
  (2172, 3),
  (2172, 3),
  (2172, 3),
  (2172, 4),
  (2165, 4),
  (2165, 4),
  (2165, 4),
  (2160, 7),
  (2160, 7),
  (2160, 8),
  (2160, 8),
  (2148, 10),
  (2133, 10),
  (2131, 10),
  (2118, 12),
  (2103, 10),
  (2078, 10),
  (2075, 10),
  (2068, 10),
  (2065, 10),
  (2060, 10),
  (2059, 10),
  (2048, 10),
  (2046, 10),
  (2040, 12),
  (2018, 12),
  (2017, 12),
  (2014, 14),
  (2014, 14),
  (2014, 14),
  (2012, 14),
  (2004, 14),
  (2003, 14),
  (1997, 14),
  (1994, 14),
  (1985, 14),
  (1985, 15),
  (1985, 15),
  (1985, 16),
  (1973, 16),
  (1963, 13),
  (1945, 13),
  (1935, 13),
  (1934, 13),
  (1926, 13),
  (1923, 13),
  (1916, 13),
  (1916, 13),
  (1916, 13),
  (1916, 14),
  (1906, 11),
  (1888, 14),
  (1878, 14),
  (1878, 14),
  (1878, 14),
  (1878, 14),
  (1866, 17),
  (1864, 17),
  (1864, 17),
  (1847, 15),
  (1830, 17),
  (1808, 17),
  (1808, 17),
  (1799, 15),
  (1787, 17),
  (1763, 17),
  (1763, 16),
  (1763, 16),
  (1763, 15),
  (1748, 15),
  (1745, 15),
  (1745, 15),
  (1737, 15),
  (1733, 15),
  (1728, 18),
  (1728, 18),
  (1728, 19),
  (1706, 17),
  (1684, 17),
  (1682, 17),
  (1672, 15),
  (1672, 15),
  (1672, 14),
  (1672, 14),
  (1672, 14),
  (1672, 14),
  (1665, 14),
  (1665, 15),
  (1665, 16),
  (1653, 14),
  (1653, 14),
  (1653, 14),
  (1651, 14),
  (1635, 16),
  (1617, 14),
  (1598, 17),
  (1583, 17),
  (1582, 17),
  (1581, 17),
  (1581, 16),
  (1581, 15),
  (1566, 17),
  (1545, 15),
  (1531, 15),
  (1529, 15),
  (1518, 15),
  (1516, 15),
  (1511, 17),
  (1498, 17),
  (1495, 17),
  (1488, 17),
  (1487, 17),
  (1482, 17),
  (1482, 18),
  (1482, 18),
  (1482, 18),
  (1482, 18),
  (1482, 19),
  (1463, 17),
  (1441, 19),
  (1441, 19),
  (1441, 19),
  (1440, 19),
  (1426, 19),
  (1417, 21),
  (1396, 21),
  (1395, 21),
  (1395, 21),
  (1395, 22),
  (1380, 22),
  (1362, 22),
  (1356, 22),
  (1344, 22),
  (1341, 22),
  (1333, 20),
  (1320, 20),
  (1317, 20),
  (1307, 18),
  (1297, 18),
  (1284, 18),
  (1282, 18),
  (1280, 18),
  (1280, 18),
  (1280, 18),
  (1280, 18),
  (1280, 17),
  (1262, 17),
  (1260, 17),
  (1260, 17),
  (1260, 17),
  (1246, 14),
  (1244, 14),
  (1244, 14),
  (1233, 16),
  (1214, 14),
  (1214, 14),
  (1214, 14),
  (1212, 14),
  (1195, 16),
  (1180, 16),
  (1178, 16),
  (1172, 19),
  (1161, 16),
  (1148, 16),
  (1146, 16),
  (1132, 16),
  (1131, 16),
  (1124, 16),
  (1119, 16),
  (1116, 16),
  (1113, 18),
  (1112, 18),
  (1112, 18),
  (1094, 16),
  (1068, 16),
  (1067, 16),
  (1066, 16),
  (1054, 16),
  (1049, 18),
  (1032, 16),
  (1014, 16),
  (1012, 16),
  (1007, 16),
  (1007, 16),
  (999, 14),
  (988, 16),
  (975, 14),
  (970, 14),
  (970, 14),
  (966, 14),
  (965, 14),
  (952, 14),
  (951, 14),
  (948, 14),
  (948, 14),
  (948, 14),
  (948, 14),
  (948, 14),
  (948, 13),
  (934, 13),
  (930, 13),
  (930, 13),
  (928, 13),
  (925, 13),
  (923, 13),
  (922, 11),
  (922, 11),
  (915, 11),
  (912, 11),
  (903, 11),
  (900, 11),
  (895, 11),
  (887, 11),
  (884, 11),
  (875, 9),
  (857, 11),
  (837, 11),
  (837, 10),
  (837, 9),
  (830, 9),
  (817, 9),
  (814, 9),
  (806, 9),
  (803, 9),
  (803, 7),
  (797, 7),
  (795, 7),
  (792, 7),
  (791, 7),
  (790, 7),
  (773, 7),
  (771, 7),
  (766, 7),
  (764, 7),
  (759, 9),
  (746, 7),
  (727, 7),
  (722, 7),
  (722, 7),
  (720, 7),
  (703, 5),
  (683, 5),
  (682, 5),
  (682, 5),
  (673, 7),
  (646, 7),
  (643, 7),
  (631, 9),
  (631, 9),
  (631, 9),
  (631, 9),
  (629, 9),
  (621, 9),
  (619, 9),
  (612, 11),
  (612, 11),
  (612, 11),
  (612, 11),
  (612, 12),
  (592, 12),
  (591, 12),
  (587, 15),
  (570, 15),
  (555, 15),
  (551, 15),
  (541, 15),
  (541, 14),
  (541, 13),
  (524, 15),
  (513, 15),
  (511, 15),
  (507, 17),
  (507, 17),
  (496, 14),
  (478, 14),
  (477, 14),
  (474, 16),
  (445, 16),
  (445, 16),
  (433, 16),
  (433, 16),
  (433, 16),
  (433, 16),
  (433, 16),
  (427, 16),
  (407, 16),
  (395, 16),
  (393, 16),
  (386, 16),
  (384, 16),
  (373, 16),
  (372, 16),
  (370, 14),
  (351, 14),
  (349, 14),
  (342, 11),
  (340, 11),
  (340, 11),
  (340, 11),
  (324, 13),
  (310, 13),
  (309, 13),
  (308, 11),
  (291, 11),
  (288, 11),
  (273, 11),
  (272, 11),
  (271, 9),
  (248, 9),
  (246, 9),
  (226, 9),
  (224, 9),
  (219, 9),
  (216, 9),
  (212, 6),
  (196, 8),
  (174, 8),
  (170, 8),
  (168, 8),
  (168, 9),
  (168, 10),
  (158, 10),
  (145, 12),
  (145, 12),
  (145, 12),
  (122, 12),
  (120, 12),
  (117, 12),
  (116, 12),
  (114, 9),
  (98, 11),
  (85, 9),
  (85, 9),
  (85, 8),
  (67, 10),
  (58, 10),
  (56, 10),
  (36, 13),
  (36, 13),
  (31, 13),
  (28, 13),
  (28, 11),
  (21, 11),
  (21, 9),
  (0, 9)],
 1)

def probability(t,p, t_p_win):
    total_games = 0
    home_wins = 0
    games = []
    for pbp, home_win in t_p_win:
        previous_play = (2880,0)
        occurred=0
        for play in pbp:
            if (p==previous_play[1] or p==play[1]) and (t<=previous_play[0] and t>=play[0]):
                occurred = 1
                games.append((pbp, home_win))
            previous_play = play
        if occurred == 1:
            total_games+=1
            home_wins+=home_win
    return (home_wins, total_games, games, home_wins/total_games*100)

w,t,games,p = probability(0, -2, t_p_win)
print(w,t,p)

40 44 90.9090909090909

Interestingly even with zero seconds left and a lead for the home team there is a possibility for a loss. This is because the zero seconds left is not precise, there could be 0.3 seconds left for example. The below game is an example.

print(games[0])

([(2880, 0), (2860, -2), (2849, -2), (2845, -2), (2833, -5), (2820, -3), (2802, -3), (2799, -3), (2796, -3), (2792, -3), (2782, -3), (2779, -3), (2770, -3), (2763, -3), (2758, -6), (2746, -6), (2738, -4), (2727, -4), (2723, -4), (2716, -4), (2713, -4), (2698, -6), (2685, -3), (2675, -3), (2675, -4), (2675, -5), (2670, -5), (2661, -2), (2648, -2), (2645, -2), (2634, -2), (2630, -2), (2627, 0), (2608, 0), (2605, 0), (2601, 0), (2598, 0), (2587, 0), (2583, 0), (2575, 0), (2572, 0), (2570, -2), (2548, 1), (2530, -1), (2521, -1), (2521, -1), (2521, -1), (2521, -1), (2511, -1), (2507, -1), (2507, -1), (2507, -1), (2507, -1), (2507, -1), (2507, -1), (2507, 0), (2507, 1), (2496, -1), (2483, -1), (2480, -1), (2478, 2), (2465, 2), (2462, 2), (2452, 2), (2448, 2), (2438, -1), (2424, -1), (2424, 0), (2424, 0), (2424, 0), (2424, 0), (2424, 0), (2420, 0), (2404, 0), (2404, -1), (2404, -1), (2404, -1), (2404, -1), (2404, -2), (2391, -2), (2391, -2), (2385, -2), (2382, -2), (2381, -2), (2379, -4), (2370, -4), (2367, -4), (2367, -4), (2367, -3), (2367, -3), (2367, -2), (2356, -2), (2351, -4), (2331, -4), (2328, -4), (2309, -4), (2306, -4), (2306, -4), (2306, -4), (2306, -4), (2306, -4), (2306, -5), (2306, -6), (2294, -6), (2294, -5), (2290, -5), (2287, -5), (2275, -5), (2273, -5), (2272, -7), (2265, -7), (2265, -7), (2265, -7), (2265, -7), (2265, -8), (2251, -8), (2250, -8), (2247, -6), (2230, -8), (2215, -8), (2215, -7), (2215, -7), (2215, -6), (2190, -6), (2186, -6), (2167, -6), (2163, -6), (2161, -6), (2161, -6), (2161, -6), (2161, -7), (2160, -7), (2160, -7), (2160, -7), (2147, -7), (2143, -9), (2130, -9), (2130, -8), (2130, -7), (2124, -7), (2117, -7), (2114, -7), (2106, -5), (2092, -5), (2081, -5), (2076, -5), (2076, -7), (2072, -5), (2057, -8), (2039, -8), (2037, -8), (2035, -6), (2027, -8), (2014, -8), (2011, -8), (2007, -8), (2003, -8), (2001, -8), (2001, -7), (2001, -7), (2001, -7), (2001, -6), (1994, -6), (1994, -7), (1994, -7), (1994, -8), (1986, -8), (1976, -8), (1972, -8), (1972, -6), (1960, -9), (1937, -7), (1926, -7), (1922, -7), (1920, -7), (1914, -10), (1895, -10), (1895, -10), (1895, -10), (1895, -10), (1888, -8), (1888, -8), (1888, -7), (1877, -7), (1869, -7), (1867, -7), (1859, -7), (1856, -7), (1855, -7), (1854, -7), (1853, -7), (1851, -7), (1850, -7), (1849, -7), (1845, -9), (1845, -9), (1845, -9), (1845, -10), (1835, -10), (1835, -10), (1835, -10), (1835, -10), (1835, -10), (1835, -9), (1822, -9), (1820, -9), (1812, -7), (1800, -9), (1800, -9), (1800, -10), (1792, -7), (1779, -7), (1779, -7), (1779, -7), (1779, -7), (1779, -6), (1779, -5), (1770, -5), (1765, -5), (1757, -2), (1736, -2), (1736, -2), (1730, -2), (1727, -2), (1718, 0), (1718, 0), (1718, 1), (1701, 1), (1701, 1), (1686, 1), (1684, 1), (1679, -1), (1665, 1), (1658, 1), (1658, 0), (1658, -1), (1643, -1), (1643, -1), (1623, -1), (1614, 1), (1603, 1), (1603, 1), (1603, 1), (1603, 1), (1603, 1), (1591, -2), (1572, -2), (1569, -2), (1556, -2), (1554, -2), (1545, -2), (1539, -2), (1539, -2), (1538, -2), (1537, -2), (1533, -2), (1526, -2), (1521, -2), (1521, -2), (1507, -2), (1505, -2), (1505, -2), (1505, -3), (1505, -4), (1491, -4), (1489, -4), (1489, -2), (1473, -4), (1469, -1), (1467, -1), (1467, -2), (1467, -3), (1451, -3), (1451, -3), (1451, -3), (1451, -2), (1443, -2), (1443, -3), (1443, -4), (1440, -4), (1440, -4), (1440, -4), (1427, -1), (1415, -1), (1412, -1), (1405, -1), (1402, -1), (1395, -1), (1393, -1), (1390, -1), (1386, -1), (1369, -1), (1366, -1), (1360, -1), (1356, -1), (1354, -1), (1353, -3), (1353, -3), (1353, -3), (1353, -3), (1350, -3), (1328, -3), (1327, -5), (1327, -5), (1312, -5), (1310, -5), (1310, -6), (1310, -6), (1308, -6), (1308, -6), (1308, -7), (1308, -8), (1297, -8), (1297, -7), (1297, -7), (1294, -7), (1282, -7), (1281, -7), (1280, -9), (1268, -9), (1268, -8), (1268, -7), (1253, -9), (1237, -6), (1219, -6), (1217, -6), (1212, -6), (1208, -6), (1205, -6), (1201, -6), (1198, -6), (1189, -6), (1189, -6), (1180, -6), (1174, -3), (1173, -3), (1173, -3), (1162, -5), (1162, -5), (1146, -3), (1121, -6), (1106, -6), (1098, -8), (1098, -8), (1098, -8), (1096, -8), (1089, -8), (1088, -8), (1088, -8), (1075, -6), (1058, -6), (1056, -6), (1051, -6), (1051, -5), (1051, -5), (1051, -5), (1051, -5), (1051, -4), (1033, -7), (1017, -7), (1017, -6), (1017, -6), (1017, -6), (1017, -5), (1003, -5), (1001, -5), (1000, -5), (999, -5), (998, -5), (998, -6), (998, -7), (998, -7), (991, -7), (991, -7), (991, -7), (991, -6), (991, -6), (988, -6), (968, -6), (964, -6), (960, -4), (953, -4), (952, -4), (952, -4), (952, -4), (952, -4), (944, -4), (941, -4), (935, -4), (935, -5), (935, -5), (935, -6), (920, -3), (898, -3), (894, -5), (894, -5), (885, -5), (882, -5), (873, -8), (849, -6), (833, -6), (833, -6), (833, -6), (833, -7), (815, -7), (810, -7), (810, -7), (809, -7), (805, -7), (802, -7), (798, -7), (797, -7), (797, -7), (797, -7), (797, -7), (797, -7), (797, -6), (788, -9), (776, -9), (773, -9), (759, -9), (753, -9), (752, -9), (748, -9), (747, -7), (730, -9), (722, -6), (720, -6), (702, -8), (683, -8), (682, -10), (682, -10), (672, -10), (670, -10), (670, -10), (654, -10), (650, -10), (646, -7), (620, -7), (620, -8), (620, -9), (606, -9), (594, -11), (593, -11), (593, -11), (578, -11), (578, -11), (578, -11), (578, -10), (578, -10), (575, -10), (564, -10), (560, -10), (554, -10), (552, -10), (544, -12), (538, -10), (523, -10), (519, -10), (507, -10), (503, -10), (501, -10), (493, -10), (493, -10), (493, -10), (493, -10), (479, -8), (456, -10), (438, -7), (424, -7), (421, -7), (415, -5), (414, -5), (414, -5), (414, -5), (414, -5), (405, -5), (401, -5), (390, -5), (379, -5), (374, -5), (374, -5), (374, -5), (371, -5), (368, -5), (354, -5), (351, -5), (341, -2), (338, -2), (338, -2), (338, -2), (329, -2), (324, -2), (323, -2), (321, -2), (318, -5), (304, -5), (298, -5), (291, -5), (287, -5), (283, -5), (283, -4), (283, -3), (267, -3), (264, -3), (255, -3), (253, -3), (251, -1), (251, -1), (251, -1), (251, 0), (239, -2), (226, 1), (203, 1), (200, 1), (200, 1), (200, 1), (188, 1), (185, 1), (180, 1), (180, 1), (175, 1), (167, -1), (145, -1), (143, -1), (128, -1), (124, -1), (113, -1), (110, -1), (99, -1), (96, -1), (81, -1), (75, -1), (69, 1), (69, 1), (61, -1), (48, 1), (36, -1), (29, -1), (29, -1), (29, -1), (29, -1), (29, -1), (7, -1), (3, -1), (3, -1), (3, -1), (3, -1), (3, -1), (2, 2), (1, 2), (1, 2), (1, 2), (0, 2), (0, 1), (0, 0), (0, 0), (0, 0), (0, -1), (0, -1)], 0)

# How important is a 2 point lead for the home team
time = reversed(range(0,2881,15))
prob = [probability(t,2,t_p_win)[3] for t in time]
prob

[60.46511627906976,
 60.55776892430279,
 62.94277929155313,
 65.43909348441926,
 62.71186440677966,
 61.59695817490495,
 63.75545851528385,
 64.39024390243902,
 64.03940886699507,
 63.63636363636363,
 62.5,
 59.47712418300654,
 57.85714285714286,
 59.541984732824424,
 65.54054054054053,
 68.48484848484848,
 63.1578947368421,
 65.06849315068493,
 58.108108108108105,
 56.9620253164557,
 52.41379310344828,
 52.41935483870967,
 49.166666666666664,
 55.00000000000001,
 60.0,
 60.447761194029844,
 60.97560975609756,
 63.565891472868216,
 62.30769230769231,
 59.154929577464785,
 60.15625,
 63.2,
 62.39316239316239,
 67.0,
 63.30275229357798,
 63.06306306306306,
 62.264150943396224,
 50.505050505050505,
 50.526315789473685,
 56.52173913043478,
 58.82352941176471,
 58.76288659793815,
 64.48598130841121,
 66.30434782608695,
 56.470588235294116,
 58.0246913580247,
 65.4320987654321,
 60.0,
 55.55555555555556,
 57.30337078651685,
 62.5,
 61.111111111111114,
 58.88888888888889,
 59.49367088607595,
 62.33766233766234,
 64.63414634146342,
 59.45945945945946,
 59.42028985507246,
 57.14285714285714,
 64.58333333333334,
 62.88659793814433,
 58.139534883720934,
 57.14285714285714,
 60.97560975609756,
 61.627906976744185,
 58.46153846153847,
 68.18181818181817,
 67.03296703296702,
 63.1578947368421,
 64.61538461538461,
 60.810810810810814,
 64.0,
 63.1578947368421,
 65.33333333333333,
 68.65671641791045,
 68.75,
 64.17910447761194,
 66.66666666666666,
 59.67741935483871,
 66.10169491525424,
 63.63636363636363,
 56.25,
 57.14285714285714,
 62.19512195121951,
 64.28571428571429,
 67.12328767123287,
 68.11594202898551,
 60.0,
 56.52173913043478,
 60.3448275862069,
 57.8125,
 58.666666666666664,
 55.55555555555556,
 60.810810810810814,
 60.273972602739725,
 57.534246575342465,
 56.75675675675676,
 57.971014492753625,
 65.0,
 63.23529411764706,
 67.16417910447761,
 68.85245901639344,
 66.66666666666666,
 71.01449275362319,
 67.1875,
 65.15151515151516,
 67.16417910447761,
 66.66666666666666,
 64.0625,
 64.70588235294117,
 75.38461538461539,
 71.875,
 70.0,
 63.1578947368421,
 63.63636363636363,
 62.96296296296296,
 62.5,
 59.67741935483871,
 69.81132075471697,
 68.75,
 62.903225806451616,
 64.17910447761194,
 60.0,
 64.28571428571429,
 63.49206349206349,
 64.7887323943662,
 65.15151515151516,
 68.25396825396825,
 69.23076923076923,
 72.3076923076923,
 72.3076923076923,
 73.33333333333333,
 70.6896551724138,
 66.07142857142857,
 66.15384615384615,
 68.33333333333333,
 73.21428571428571,
 76.0,
 72.54901960784314,
 66.66666666666666,
 68.08510638297872,
 65.9090909090909,
 64.44444444444444,
 67.3913043478261,
 63.76811594202898,
 70.17543859649122,
 73.58490566037736,
 78.18181818181819,
 75.92592592592592,
 66.0377358490566,
 68.42105263157895,
 69.23076923076923,
 73.58490566037736,
 71.42857142857143,
 67.24137931034483,
 63.934426229508205,
 64.58333333333334,
 73.68421052631578,
 66.66666666666666,
 61.702127659574465,
 58.620689655172406,
 60.0,
 67.27272727272727,
 76.47058823529412,
 75.51020408163265,
 75.51020408163265,
 65.95744680851064,
 67.24137931034483,
 62.06896551724138,
 64.91228070175438,
 70.17543859649122,
 62.903225806451616,
 65.0,
 69.81132075471697,
 66.66666666666666,
 70.83333333333334,
 74.50980392156863,
 76.92307692307693,
 71.1864406779661,
 63.793103448275865,
 59.67741935483871,
 65.57377049180327,
 62.96296296296296,
 64.0,
 71.11111111111111,
 72.3404255319149,
 62.5,
 68.29268292682927,
 66.66666666666666,
 68.18181818181817,
 85.41666666666666,
 92.0,
 90.9090909090909]

time = range(0,2881,15)
plt.plot([t for t in time], prob)

[<matplotlib.lines.Line2D at 0x7f22371edd30>]

png

Above graph of win percentages is not very smooth, would be interesting to consider ways to smooth this graph out. Applying other ML algorithms to this could help with this since ML algorithms assume a smooth underlying probability function.