NBA Home Court Advantage¶
Part 4: Which Box Score Statistics Contribute to Home Court Advantage?¶
If the home team has a higher win probability, that advantage should be evident in at least some of the box score statistics. Home court advantage could result from better offense, better defense, or a mix of the two.
In this notebook, we'll examine how basic box score statistics vary between home and away games.
We'll continue to use the games from the 1996-97 through 2016-17 NBA regular seasons as our data set.
import numpy as np
import pandas as pd
pd.options.display.max_rows = 999
pd.options.display.max_columns = 999
pd.options.display.float_format = '{:.3f}'.format
%matplotlib inline
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.colors import rgb2hex
import seaborn as sns
sns.set()
sns.set_context('notebook')
plt.style.use('ggplot')
from scipy import stats
from pathlib import Path
PROJECT_DIR = Path.cwd().parent / 'basketball' / 'nba'
DATA_DIR = PROJECT_DIR / 'data' / 'prepared'
DATA_DIR.mkdir(exist_ok=True, parents=True)
def load_nba_historical_matchups(input_dir):
"""Load pickle file of NBA matchups prepared for analytics."""
PKLFILENAME = 'stats_nba_com-matchups-1996_97-2016_17.pkl'
pklfile = input_dir.joinpath(PKLFILENAME)
return pd.read_pickle(pklfile)
matchups = load_nba_historical_matchups(DATA_DIR)
matchups.shape
(26787, 41)
seasons = sorted(list(matchups['season'].unique()))
len(seasons)
21
def prepare_regular_season(matchups):
df = matchups.copy()
df = df[df['season_type'] == 'regular']
return df
reg = prepare_regular_season(matchups)
reg.shape
(24797, 41)
teams = sorted(list(reg['team_curr_h'].unique()))
len(teams)
30
Aggregating the Data¶
We are going to try to identify which team box score statistics improve at home compared to on the road. In order to do this properly, we need to isolate the impact of location (home versus away) from the match up itself. Otherwise, the variation created by differences in opponent quality will swamp the impact of home court.
To do this, we are going to group box score statistics by season, team, and opponent. Grouping in this way will allow us to control for the variation in team quality in different seasons. It will also allow us to control for the different quanlity of various opponents.
Within this grouping, we will separate the home games from the away games, and get the average box score statistics for each. Then, we can subtract the average away game statistics from the average home game statistics. The difference between the grouped home and away statistics will be our measure of how team performance improves just by virtue of playing at home.
The below Python code uses pandas to implement this idea. Also, note that we are going to scale the statistics for a standard 48-minute game. We will also compute shooting percentages for field goals, three-pointers, and free throws.
HOME = 'H'
AWAY = 'A'
def aggregation(group, home_away):
suffix = '_h' if home_away == HOME else '_a'
# Get the home or away columns and strip off the suffix
stat_cols = [col[:-2] for col in group.columns if suffix in col and 'team' not in col]
# Scale the stats for a 48-minute game and get the group average
result = {}
for col in stat_cols:
result[col] = (group[col+suffix] / group['min'] * 48.0).mean()
# Compute shooting percentages for the group
pct_cols = ['fg', 'fg3', 'ft']
for col in pct_cols:
result[col+'_pct'] = (100.0 * group[col+'m'+suffix] / group[col+'a'+suffix]).mean()
return pd.Series(result, index=list(result.keys()))
The above function computes the average statistics for each season, team and opponent grouping, scaled to a standard 48-minute game. It will also compute the shooting percentages. Notice that this function doesn't do the home versus away subtraction. That will come later.
The function below does the actual grouping, and calls the above function for each group. It also keeps track of how many games are in each group.
def aggregate_stats(data, home_away):
suffix = '_h' if home_away == HOME else '_a'
other_suffix = '_a' if home_away == HOME else '_h'
team = 'team_curr' + suffix
opponent = 'team_curr' + other_suffix
# Apply the aggregation by season, team and opponent
df = data.groupby(['season', team, opponent]).apply(aggregation, home_away)
# Add a count of the number of games in this group
df['games'] = data.groupby(['season', team, opponent]).size()
df = df.reset_index().rename(columns={team: 'team', opponent: 'opponent'})
df = df.set_index(['season', 'team', 'opponent'])
# Drop NA rows (i.e., team vs itself, team vs CHA prior to expansion)
cols = [col for col in df.columns if col != 'games']
return df.dropna()[['games']+cols]
Let's do the grouping and aggregation for the home games first.
home_df = aggregate_stats(reg, HOME)
home_df.shape
(17290, 18)
There are 17,290 distinct groups of home games by season, team and opponent.
home_df.head()
| games | pts | fgm | fga | fg3m | fg3a | ftm | fta | oreb | dreb | ast | tov | stl | blk | pf | fg_pct | fg3_pct | ft_pct | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| season | team | opponent | ||||||||||||||||||
| 1996-97 | ATL | BKN | 2.000 | 109.000 | 37.000 | 76.000 | 12.000 | 26.500 | 23.000 | 28.000 | 10.500 | 30.500 | 22.000 | 16.000 | 9.000 | 5.000 | 19.000 | 48.710 | 45.214 | 82.143 |
| BOS | 2.000 | 100.000 | 38.500 | 84.000 | 8.000 | 25.000 | 15.000 | 19.000 | 17.500 | 30.000 | 22.500 | 17.000 | 10.000 | 7.500 | 19.000 | 45.828 | 34.225 | 78.333 | ||
| CHI | 2.000 | 98.000 | 34.500 | 81.000 | 7.500 | 24.500 | 21.500 | 24.500 | 15.500 | 28.500 | 13.500 | 13.000 | 7.500 | 4.500 | 19.500 | 42.593 | 30.303 | 85.646 | ||
| CLE | 2.000 | 90.000 | 31.000 | 66.500 | 7.000 | 21.000 | 21.000 | 24.000 | 8.000 | 25.000 | 19.500 | 15.000 | 6.500 | 5.000 | 19.000 | 47.368 | 33.409 | 86.933 | ||
| DAL | 1.000 | 93.000 | 37.000 | 72.000 | 11.000 | 24.000 | 8.000 | 15.000 | 9.000 | 29.000 | 22.000 | 13.000 | 9.000 | 3.000 | 13.000 | 51.389 | 45.833 | 53.333 |
Let's check to make sure didn't drop any games from our data set during the aggregation.
home_df['games'].sum()
24797.0
The correct number of games got picked up in the aggregation. Since the aggregation takes a while, let's save the results in a CSV file in case we want to pick up this analysis on a different occasion.
csvfile = DATA_DIR.joinpath('stats_nba_com-agg_matchup_box_scores-home-1996_97-2016_17.csv')
home_df.to_csv(csvfile, index=True, float_format='%g')
Now we can perform the same steps for the away games.
away_df = aggregate_stats(reg, AWAY)
away_df.shape
(17290, 18)
away_df.head()
| games | pts | fgm | fga | fg3m | fg3a | ftm | fta | oreb | dreb | ast | tov | stl | blk | pf | fg_pct | fg3_pct | ft_pct | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| season | team | opponent | ||||||||||||||||||
| 1996-97 | ATL | BKN | 2.000 | 93.500 | 35.500 | 88.000 | 8.000 | 30.500 | 14.500 | 17.500 | 17.000 | 28.000 | 18.000 | 12.500 | 8.500 | 5.000 | 15.000 | 40.413 | 26.407 | 81.250 |
| BOS | 2.000 | 99.500 | 38.000 | 81.000 | 10.000 | 26.000 | 13.500 | 24.500 | 12.500 | 33.000 | 28.000 | 24.000 | 11.500 | 6.500 | 19.500 | 46.558 | 38.370 | 55.051 | ||
| CHI | 2.000 | 74.000 | 27.000 | 79.500 | 5.500 | 18.500 | 14.500 | 19.000 | 14.500 | 25.500 | 12.000 | 16.000 | 9.000 | 4.000 | 16.000 | 33.972 | 28.205 | 77.451 | ||
| CLE | 2.000 | 78.000 | 28.500 | 66.500 | 7.000 | 21.500 | 14.000 | 18.000 | 9.000 | 28.500 | 18.500 | 13.500 | 7.000 | 5.000 | 17.500 | 43.617 | 32.717 | 76.190 | ||
| DAL | 1.000 | 109.000 | 40.000 | 74.000 | 19.000 | 27.000 | 10.000 | 22.000 | 12.000 | 37.000 | 26.000 | 15.000 | 6.000 | 9.000 | 14.000 | 54.054 | 70.370 | 45.455 |
away_df['games'].sum()
24797.0
csvfile = DATA_DIR.joinpath('stats_nba_com-agg_matchup_box_scores-away-1996_97-2016_17.csv')
away_df.to_csv(csvfile, index=True, float_format='%g')
Combining the Home and Away Data¶
Now that we have aggregated the home games and the away games, we need to combine the information. Remember, our goal is to subtract each team's home game performance from the same team's away game performance, grouped by season and opposing team.
We can use the pandas join() method to accomplish this. We will add a suffix to each of the data columns to keep trach of which statistics came from the home games, and which came from the away games.
df = home_df.join(away_df, how='outer', lsuffix='_h', rsuffix='_a')
df.shape
(17554, 36)
Checking the Number of Rows¶
Notice that the number of rows in the combined DataFrame is larger than the number of rows in each of the home and away DataFrame objects. That means we need to look more closely at whether the join() method created any rows with missing or null data. We will do that shortly. First, let's take a look at the combined data.
df.head()
| games_h | pts_h | fgm_h | fga_h | fg3m_h | fg3a_h | ftm_h | fta_h | oreb_h | dreb_h | ast_h | tov_h | stl_h | blk_h | pf_h | fg_pct_h | fg3_pct_h | ft_pct_h | games_a | pts_a | fgm_a | fga_a | fg3m_a | fg3a_a | ftm_a | fta_a | oreb_a | dreb_a | ast_a | tov_a | stl_a | blk_a | pf_a | fg_pct_a | fg3_pct_a | ft_pct_a | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| season | team | opponent | ||||||||||||||||||||||||||||||||||||
| 1996-97 | ATL | BKN | 2.000 | 109.000 | 37.000 | 76.000 | 12.000 | 26.500 | 23.000 | 28.000 | 10.500 | 30.500 | 22.000 | 16.000 | 9.000 | 5.000 | 19.000 | 48.710 | 45.214 | 82.143 | 2.000 | 93.500 | 35.500 | 88.000 | 8.000 | 30.500 | 14.500 | 17.500 | 17.000 | 28.000 | 18.000 | 12.500 | 8.500 | 5.000 | 15.000 | 40.413 | 26.407 | 81.250 |
| BOS | 2.000 | 100.000 | 38.500 | 84.000 | 8.000 | 25.000 | 15.000 | 19.000 | 17.500 | 30.000 | 22.500 | 17.000 | 10.000 | 7.500 | 19.000 | 45.828 | 34.225 | 78.333 | 2.000 | 99.500 | 38.000 | 81.000 | 10.000 | 26.000 | 13.500 | 24.500 | 12.500 | 33.000 | 28.000 | 24.000 | 11.500 | 6.500 | 19.500 | 46.558 | 38.370 | 55.051 | ||
| CHI | 2.000 | 98.000 | 34.500 | 81.000 | 7.500 | 24.500 | 21.500 | 24.500 | 15.500 | 28.500 | 13.500 | 13.000 | 7.500 | 4.500 | 19.500 | 42.593 | 30.303 | 85.646 | 2.000 | 74.000 | 27.000 | 79.500 | 5.500 | 18.500 | 14.500 | 19.000 | 14.500 | 25.500 | 12.000 | 16.000 | 9.000 | 4.000 | 16.000 | 33.972 | 28.205 | 77.451 | ||
| CLE | 2.000 | 90.000 | 31.000 | 66.500 | 7.000 | 21.000 | 21.000 | 24.000 | 8.000 | 25.000 | 19.500 | 15.000 | 6.500 | 5.000 | 19.000 | 47.368 | 33.409 | 86.933 | 2.000 | 78.000 | 28.500 | 66.500 | 7.000 | 21.500 | 14.000 | 18.000 | 9.000 | 28.500 | 18.500 | 13.500 | 7.000 | 5.000 | 17.500 | 43.617 | 32.717 | 76.190 | ||
| DAL | 1.000 | 93.000 | 37.000 | 72.000 | 11.000 | 24.000 | 8.000 | 15.000 | 9.000 | 29.000 | 22.000 | 13.000 | 9.000 | 3.000 | 13.000 | 51.389 | 45.833 | 53.333 | 1.000 | 109.000 | 40.000 | 74.000 | 19.000 | 27.000 | 10.000 | 22.000 | 12.000 | 37.000 | 26.000 | 15.000 | 6.000 | 9.000 | 14.000 | 54.054 | 70.370 | 45.455 |
Notice that this DataFrame uses a pandas MultiIndex structure for the 3 index columns. Here is an example of how to access a particular match up for a particular season.
df.loc['2016-17', ['WAS', 'UTA'], ['WAS', 'UTA']]
| games_h | pts_h | fgm_h | fga_h | fg3m_h | fg3a_h | ftm_h | fta_h | oreb_h | dreb_h | ast_h | tov_h | stl_h | blk_h | pf_h | fg_pct_h | fg3_pct_h | ft_pct_h | games_a | pts_a | fgm_a | fga_a | fg3m_a | fg3a_a | ftm_a | fta_a | oreb_a | dreb_a | ast_a | tov_a | stl_a | blk_a | pf_a | fg_pct_a | fg3_pct_a | ft_pct_a | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| season | team | opponent | ||||||||||||||||||||||||||||||||||||
| 2016-17 | UTA | WAS | 1.000 | 95.000 | 33.000 | 72.000 | 10.000 | 25.000 | 19.000 | 31.000 | 7.000 | 35.000 | 20.000 | 12.000 | 9.000 | 7.000 | 18.000 | 45.833 | 40.000 | 61.290 | 1.000 | 102.000 | 34.000 | 72.000 | 11.000 | 24.000 | 23.000 | 32.000 | 9.000 | 41.000 | 18.000 | 25.000 | 10.000 | 11.000 | 19.000 | 47.222 | 45.833 | 71.875 |
| WAS | UTA | 1.000 | 92.000 | 37.000 | 87.000 | 8.000 | 22.000 | 10.000 | 13.000 | 6.000 | 22.000 | 21.000 | 16.000 | 16.000 | 1.000 | 27.000 | 42.529 | 36.364 | 76.923 | 1.000 | 88.000 | 35.000 | 87.000 | 5.000 | 17.000 | 13.000 | 16.000 | 14.000 | 31.000 | 12.000 | 15.000 | 8.000 | 1.000 | 23.000 | 40.230 | 29.412 | 81.250 |
The first row in the above example are Utah's statistics, when they played Washington during the 2016-17 regular season. The columns ending in _h are Utah's home statistics, and the columns ending in _a are their away statistics. We can see from the games columns that the Jazz and the Wizards played 1 game in Salt Lake City and 1 game in Washington, D.C. during that season.
The second row is the same match up, but with Washington's statistics.
Let's just double-check that we still have all the relevant regular season games captured in this DataFrame.
df['games_h'].sum()
24797.0
df['games_a'].sum()
24797.0
Understanding the Number of Rows¶
All the games are there. But, as we noticed above, extra rows were created in this DataFrame when we merged the home and away game data. Let's check to see how many rows have at least one null or missing value.
len(df[df.isnull().any(axis=1)])
528
Bingo. The joined DataFrame had 264 extra rows compared to the original home and away DataFrame objects (264 = 17,554 - 17,290).
And, 528 is double 264. This means that there are some match ups in particular seasons that didn't have both home and away games. The reason the 264 is doubled is that for one match up row in the table, the home game columns are null, and in the other row, the away game columsn are null.
Let's take a look at the rows that have missing values.
df[df.isnull().any(axis=1)].head()
| games_h | pts_h | fgm_h | fga_h | fg3m_h | fg3a_h | ftm_h | fta_h | oreb_h | dreb_h | ast_h | tov_h | stl_h | blk_h | pf_h | fg_pct_h | fg3_pct_h | ft_pct_h | games_a | pts_a | fgm_a | fga_a | fg3m_a | fg3a_a | ftm_a | fta_a | oreb_a | dreb_a | ast_a | tov_a | stl_a | blk_a | pf_a | fg_pct_a | fg3_pct_a | ft_pct_a | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| season | team | opponent | ||||||||||||||||||||||||||||||||||||
| 1998-99 | ATL | DAL | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | 1.000 | 85.000 | 32.000 | 86.000 | 4.000 | 16.000 | 17.000 | 26.000 | 18.000 | 31.000 | 18.000 | 12.000 | 5.000 | 9.000 | 17.000 | 37.209 | 25.000 | 65.385 |
| HOU | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | 1.000 | 93.000 | 38.000 | 92.000 | 4.000 | 10.000 | 13.000 | 17.000 | 15.000 | 26.000 | 18.000 | 4.000 | 10.000 | 8.000 | 18.000 | 41.304 | 40.000 | 76.471 | ||
| LAC | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | 1.000 | 103.000 | 40.000 | 74.000 | 2.000 | 7.000 | 21.000 | 24.000 | 9.000 | 32.000 | 23.000 | 8.000 | 7.000 | 5.000 | 19.000 | 54.054 | 28.571 | 87.500 | ||
| MEM | 1.000 | 84.000 | 30.000 | 78.000 | 2.000 | 9.000 | 22.000 | 26.000 | 18.000 | 27.000 | 11.000 | 15.000 | 10.000 | 6.000 | 26.000 | 38.462 | 22.222 | 84.615 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | ||
| PHX | 1.000 | 93.000 | 31.000 | 74.000 | 9.000 | 24.000 | 22.000 | 24.000 | 15.000 | 37.000 | 18.000 | 19.000 | 7.000 | 6.000 | 21.000 | 41.892 | 37.500 | 91.667 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
Let's see which seasons don't have balanced match ups between home and away games.
df[df.isnull().any(axis=1)].groupby(['season']).size()
season 1998-99 168 2011-12 360 dtype: int64
This makes sense. These are the seasons that experienced lockouts and therefore didn't have a normal schedule.
In our analysis, we need to subtract the away game aggregate statistics from the home game aggregate statistics. So, we'll have to drop these rows that have null values.
Home versus Away Difference¶
Now we are ready to do the subtract to create the home court advantage analysis.
def matchup_home_edge(df):
stat_cols = [col[:-2] for col in df.columns if '_h' in col and 'games' not in col]
df = df.copy().dropna()
for col in stat_cols:
df[col] = df[col+'_h'] - df[col+'_a']
df['games'] = df['games_h'] + df['games_a']
df['games'] = df['games'].astype(int)
return df[['games']+stat_cols]
hca = matchup_home_edge(df)
hca.head()
| games | pts | fgm | fga | fg3m | fg3a | ftm | fta | oreb | dreb | ast | tov | stl | blk | pf | fg_pct | fg3_pct | ft_pct | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| season | team | opponent | ||||||||||||||||||
| 1996-97 | ATL | BKN | 4 | 15.500 | 1.500 | -12.000 | 4.000 | -4.000 | 8.500 | 10.500 | -6.500 | 2.500 | 4.000 | 3.500 | 0.500 | 0.000 | 4.000 | 8.297 | 18.807 | 0.893 |
| BOS | 4 | 0.500 | 0.500 | 3.000 | -2.000 | -1.000 | 1.500 | -5.500 | 5.000 | -3.000 | -5.500 | -7.000 | -1.500 | 1.000 | -0.500 | -0.730 | -4.146 | 23.283 | ||
| CHI | 4 | 24.000 | 7.500 | 1.500 | 2.000 | 6.000 | 7.000 | 5.500 | 1.000 | 3.000 | 1.500 | -3.000 | -1.500 | 0.500 | 3.500 | 8.621 | 2.098 | 8.195 | ||
| CLE | 4 | 12.000 | 2.500 | 0.000 | 0.000 | -0.500 | 7.000 | 6.000 | -1.000 | -3.500 | 1.000 | 1.500 | -0.500 | 0.000 | 1.500 | 3.752 | 0.692 | 10.742 | ||
| DAL | 2 | -16.000 | -3.000 | -2.000 | -8.000 | -3.000 | -2.000 | -7.000 | -3.000 | -8.000 | -4.000 | -2.000 | 3.000 | -6.000 | -1.000 | -2.665 | -24.537 | 7.879 |
Notice how we differenced the home and away statistics and returned a simpler DataFrame. The original home and away DataFrame objects are unchanged, of course.
Home Court Impact on Box Score Statistics¶
Now let's take a look at the impact of home court on box score statistics.
We'll separate out the statistics by type, either scoring or other.
stats_cols = [col for col in hca.columns if col not in ['games']]
scoring_cols = [col for col in stats_cols if any(s in col for s in ['pts', 'fg', 'ft'])]
other_cols = [col for col in stats_cols if col not in scoring_cols]
First, let's see how many games typically occurred between a particular pair of teams in each season.
hca['games'].describe()
count 17026.000 mean 2.882 std 0.927 min 2.000 25% 2.000 50% 3.000 75% 4.000 max 5.000 Name: games, dtype: float64
We see that each match up in our data set occurred between 2 and 5 times per season, with a typical value of 3 games. We know from the rules of the NBA season that teams in the same Division play more games, so this distribution makes sense.
Now, let's look at the scoring and other statistics.
hca[scoring_cols].describe()
| pts | fgm | fga | fg3m | fg3a | ftm | fta | fg_pct | fg3_pct | ft_pct | |
|---|---|---|---|---|---|---|---|---|---|---|
| count | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 |
| mean | 3.099 | 1.071 | 0.166 | 0.154 | 0.001 | 0.803 | 0.985 | 1.225 | 0.883 | 0.279 |
| std | 12.508 | 5.483 | 7.373 | 3.235 | 5.374 | 7.151 | 8.752 | 6.618 | 15.459 | 12.067 |
| min | -50.000 | -21.000 | -33.000 | -18.000 | -26.000 | -33.000 | -41.000 | -28.482 | -80.000 | -56.618 |
| 25% | -5.000 | -2.500 | -4.696 | -2.000 | -3.500 | -4.000 | -4.788 | -3.092 | -8.772 | -7.585 |
| 50% | 3.000 | 1.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 1.189 | 0.739 | 0.274 |
| 75% | 11.000 | 4.500 | 5.000 | 2.000 | 3.500 | 5.500 | 6.500 | 5.467 | 10.464 | 8.036 |
| max | 55.000 | 23.000 | 32.000 | 16.000 | 24.000 | 29.000 | 44.000 | 29.252 | 72.143 | 52.941 |
hca[other_cols].describe()
| oreb | dreb | ast | tov | stl | blk | pf | |
|---|---|---|---|---|---|---|---|
| count | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 | 17026.000 |
| mean | 0.374 | 1.057 | 1.666 | -0.373 | 0.119 | 0.639 | -0.532 |
| std | 4.653 | 5.825 | 5.680 | 4.501 | 3.418 | 3.025 | 4.920 |
| min | -23.000 | -26.000 | -20.000 | -22.000 | -14.500 | -12.085 | -20.500 |
| 25% | -2.613 | -2.802 | -2.000 | -3.083 | -2.000 | -1.000 | -4.000 |
| 50% | 0.500 | 1.000 | 1.513 | -0.415 | 0.000 | 0.500 | -0.500 |
| 75% | 3.293 | 5.000 | 5.308 | 2.500 | 2.130 | 2.500 | 2.826 |
| max | 29.000 | 26.000 | 31.000 | 18.000 | 16.000 | 16.000 | 20.943 |
Scoring¶
If you look at the pts column, you will see that the same 3.1 point home court advantage emerges from our aggregated data.
Looking at that same column, you will also see that there is a lot of variation around that average. Remember, the data we're looking at are match ups within a particular season. The point differentials between the same two teams is not very consistent, even within the same season.
Let's plot the point differential.
def get_bins(s):
mins = s.min()
maxs = s.max()
return np.arange(2*(round(mins/2)-1), 2*(round(maxs/2)+2), 2)
fig, ax = plt.subplots(figsize=(10, 5))
# Plot points distribution
data = hca['pts']
ax = sns.distplot(data, bins=get_bins(data), kde=False, fit=stats.norm, ax=ax)
ax.set_xlabel('Avg. Home Points - Avg. Away Points, by Matchup and Season')
ax.set_ylabel('Frequency')
ax.set_title('Home Court Impact on Points Scored')
ax.text(x=35, y=0.008, s='Bins are 2 points wide')
ax.axvline(x=data.mean(), linestyle='--', alpha=0.5, color='black')
plt.show()
The plot shows that a normal distribution fits the aggregated data relatively well. Nothing really stands out from the plot. Even so, the average impact of 3.1 points looks relatively small compared to the noisiness of the data.
Better Shooting Isn't the Whole Story¶
It's hard to pinpoint exactly how home court advantage translates into superior scoring. Field goal percentage goes up by about 1.2% on average, and three-point shooting percentage goes up by about 0.9% on average.
These modest improvements in scoring percentage are pointing in the right direction, but aren't sufficient to clearly explain the magnitude of NBA home court advantage.
Other Statistics¶
If you look at the other statistics, you will see that rebounding improves, and assists improve, and turnovers improve, and steals improve, and blocks improve, and personal fouls called against the team improve. Of course, you wouldn't expect statistics like blocks and personal fouls to directly benefit scoring.
The overall message is: teams really do play better at home, and the benefit shows up in a lot of statistics. We will have to dig deeper in future analysis to try to understand better what is going on.
Box Score Variation by Team¶
To conclude, let's look at how these same statistics vary by team, aggregated over the course of the 21 complete regular seasons.
cols = ['pts', 'fg_pct', 'fg3_pct', 'ft_pct',] + other_cols
hca.groupby('team')[cols].mean().sort_values(by='pts', ascending=False)
| pts | fg_pct | fg3_pct | ft_pct | oreb | dreb | ast | tov | stl | blk | pf | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| team | |||||||||||
| DEN | 4.579 | 0.992 | 1.410 | -0.086 | 0.199 | 1.757 | 3.591 | -0.775 | -0.114 | 1.839 | 0.169 |
| ATL | 4.186 | 1.738 | 0.709 | -0.024 | 0.502 | 0.786 | 1.946 | -0.573 | -0.066 | -0.248 | -0.134 |
| WAS | 4.140 | 1.681 | 1.037 | 1.774 | 0.296 | 0.498 | 1.411 | -0.436 | 0.376 | 0.363 | -0.669 |
| SAC | 4.138 | 1.372 | 1.734 | -0.042 | 0.532 | 1.070 | 0.226 | -0.245 | -0.182 | 0.312 | -0.269 |
| GSW | 4.066 | 1.959 | 0.966 | -0.138 | 0.787 | 1.279 | 3.084 | -0.202 | 0.143 | 0.441 | -0.482 |
| POR | 4.039 | 1.505 | 0.987 | 0.097 | 0.590 | 0.708 | 2.206 | -0.418 | 0.218 | -0.290 | -0.770 |
| DAL | 3.724 | 1.120 | 1.302 | 0.179 | 0.986 | 1.367 | 0.669 | -0.125 | 0.341 | 0.641 | -0.291 |
| MIA | 3.723 | 1.732 | 0.311 | 0.657 | -0.218 | 0.195 | -0.720 | -0.673 | 0.439 | 0.285 | -0.801 |
| UTA | 3.516 | 1.658 | 2.340 | 0.138 | -0.404 | 1.859 | 0.364 | -0.846 | 0.101 | 1.130 | -0.605 |
| CLE | 3.513 | 1.337 | 2.518 | 1.683 | 0.396 | 1.378 | 3.727 | -0.307 | -0.149 | 1.323 | -1.041 |
| ORL | 3.487 | 1.425 | -0.033 | 0.107 | 0.679 | 0.842 | 0.436 | 0.113 | 0.208 | 0.323 | -0.610 |
| LAL | 3.430 | 1.059 | -0.213 | -0.470 | 0.713 | 1.477 | 2.883 | 0.190 | 0.109 | 0.846 | 0.002 |
| SAS | 3.416 | 1.814 | 1.427 | -0.810 | 0.016 | 1.271 | 1.815 | 0.093 | 0.374 | 1.114 | -0.613 |
| IND | 3.357 | 1.083 | 1.584 | 0.687 | 0.839 | 1.648 | 1.062 | -1.061 | 0.049 | 1.018 | -1.107 |
| CHA | 3.268 | 0.681 | 1.074 | 0.196 | 0.436 | 1.000 | 1.697 | -0.850 | -0.130 | 1.604 | -0.014 |
| PHX | 3.255 | 1.215 | 1.239 | 0.999 | 0.231 | 1.074 | 0.345 | -0.475 | -0.072 | 0.701 | -0.614 |
| MIL | 3.194 | 1.451 | 1.261 | 0.547 | 0.465 | 0.350 | 2.293 | -0.406 | 0.140 | 0.078 | -0.826 |
| NOP | 3.111 | 1.630 | 0.815 | -0.402 | 0.348 | 0.650 | 3.207 | -0.436 | 0.501 | 0.856 | -0.669 |
| DET | 3.065 | 1.138 | 0.561 | 0.814 | 0.211 | 1.131 | 1.867 | 0.076 | 0.011 | 0.766 | -0.262 |
| NYK | 2.928 | 1.218 | -0.045 | 0.583 | 0.467 | 0.426 | -0.047 | -0.329 | 0.153 | -0.324 | -0.606 |
| MEM | 2.863 | 1.240 | 1.068 | 0.470 | 0.367 | 1.322 | 0.604 | -0.261 | -0.051 | 1.133 | -0.514 |
| BKN | 2.755 | 0.861 | 1.134 | 0.969 | 0.977 | 1.077 | 1.522 | 0.247 | 0.005 | 0.469 | -0.163 |
| OKC | 2.625 | 1.389 | 1.332 | 0.717 | -0.230 | 0.571 | 1.424 | -0.221 | 0.666 | 0.620 | -0.363 |
| TOR | 2.367 | 0.999 | 1.353 | 1.009 | 0.388 | 0.781 | 1.962 | -0.496 | -0.030 | 1.062 | -0.826 |
| LAC | 2.071 | 1.307 | -0.532 | 0.261 | -0.235 | 0.840 | 1.886 | -0.010 | 0.171 | 1.016 | -0.265 |
| PHI | 1.938 | 0.956 | 0.707 | 0.630 | 0.088 | 0.995 | 2.240 | -0.226 | 0.156 | -0.069 | -0.241 |
| HOU | 1.853 | 0.607 | -0.689 | -1.130 | 0.615 | 1.486 | 1.536 | -0.660 | -0.017 | 0.628 | -1.100 |
| MIN | 1.556 | 0.700 | -0.289 | -1.344 | -0.257 | 1.430 | 2.112 | -0.997 | -0.173 | 0.525 | -0.498 |
| CHI | 1.545 | -0.094 | 0.647 | 0.194 | 0.983 | 1.456 | 2.462 | -0.909 | 0.227 | 0.991 | -0.392 |
| BOS | 1.314 | 0.789 | 0.855 | 0.059 | 0.463 | 0.964 | 2.168 | -0.157 | 0.084 | 0.367 | -1.194 |
In this table, we are sorting by average point differential (home versus away), grouped by season and matchup. In this ordering, Denver is still on top, but teams such as Utah and Cleveland are further down the list than in our prior analysis.
This table also makes clear that the impact of home court on particular statistics appears to vary significantly by team. For example, the Nuggets, the Jazz and the Pacers show a relatively large drop in turnovers, while the Warriors and the Spurs show a relatively large increase in shooting efficiency.