Home Court Advantage: An exploratory and Bayesian analysis of performance in the 2020–21 NBA Season
Hypothesis
Due to the COVID-19 pandemic and resulting restrictions on large-scale gatherings from March 2020 up until the present, NBA attendance in the 2020–21 regular season was limited to anywhere from zero in some arenas (such as in Portland, where empty late-regular season games prompted a frustrated Damian Lillard tweet) to partial capacity in others. The daily leaguewide average attendance numbers speak for themselves (Plot 1).
This drastic change in attendance, while necessary for public health and safety, negatively impacts one of the main advantages of a team playing on its home court: the fans. In the most dramatic example of this problem, the Toronto Raptors played exactly zero games in Toronto, playing instead in Tampa Bay — more than 1300 miles from home — essentially negating any advantage in those 36 “home” games.
Research Question
Did NBA teams this season perform worse at home than they have historically? In this analysis, I will examine two measures of performance that are clearly relevant to team performance (point differential, the average difference between a team’s points and opponent’s points per game played, and win percentage, the number of wins per game played) and compare measures from this season (2021) to historical numbers (2016–2020) to see if there is a tangible difference between home team performance this year and in years past.
Analysis: Point Differential
Plot 2 is simply a histogram of point differential in each game broken down by year. Different colors highlight the winner of each game, green when the away team won and purple when the home team won. If you’re looking for it, you can see hints of a more even home-away distribution in recent years (2020 and 2021) than in previous years, where purple dominates.
This relationship is even more obvious when we break down the games by competitiveness and look at the game-by-game matchups between teams with a closer win percentage. Plot 3 shows how we break up those matchups:
For each matchup between 2016 and 2021, we subtract the away team’s final regular season win percentage from the home team’s final regular season win percentage. If one team has a win percentage at least 0.146 higher than the other team, then they are favored (I will also refer to this category as heavily favored). If the win percentages are within 0.146, then whichever team’s win percentage is higher is slightly favored (also referred to as “competitive”), and if win percentages are equal, the home team is given this distinction.
The 0.146 figure is based on equal division of the dataset, and in a perfect world, this would create four categories with an exactly equal number of matchups. In this (rather imperfect) world, Figure 1 shows that the categories are not exactly equal, and this is largely because there are 208 instances where the teams in a particular game finished the season with exactly the same win percentage, but they were added to the Home Slightly Favored category for reasons based on the very same home court advantage that I am trying to provide statistical evidence against. Funny how life works.
Plot 4 is a little bit more complicated (and a little bit more difficult to read size-wise) but works essentially the same way as Plot 2. The main difference is that it provides evidence that the year-to-year change is occurring in matchups that are a little more competitively balanced.
In the first and last columns, which signal matchups with heavy favorites, point differential distributions look about the same from row to row (year to year). But in the middle columns, there’s evidence of change; in 2016 games where the away team was slightly favored, performance is relatively equal, but in 2020, those same matchup types saw away teams start to pull away. In the third column, where home teams are slightly favored, a distinct home advantage in 2016 and 2017 became a little bit more even in 2020–21.
These trends are visualized more simply in Plot 5 below.
This line plot encapsulates the same information as the histograms above with fewer dimensions; rather than looking at point differential distribution, we are looking at one number for each category — average point differential. A higher value on the y-axis indicates a more dominant home point differential, while a lower value indicates a more dominant away point differential. The black dots in the middle are a weighted leaguewide average.
In the same vein, Plot 5 indicates that leaguewide average point differential is trending towards away teams and away from home teams, and the main contributors to the trend are the more competitive matchups.
Analysis: Win Percentage
I wanted to finish this analysis by examining the wins and losses for home teams in each category. Plot 6 illustrates the underlying theme of deterioration of home court advantage, where the trend is mostly driven by, once again, the more competitive matchup categories.
Let’s take a more in-depth look at the win percentage distributions for the competitive categories in particular. To try to get a sense of how much different this season has been than years past, I’ll utilize Bayesian techniques to update prior information about the win percentage distribution and find tangible differences between 2016–2020 data and 2021 data.
Competitive Matchups
AWAY TEAM SLIGHTLY FAVORED
Plot 7 shows probability distributions for the prior information (historical data), data information (2021 season), and posterior (all years combined) for matchups with away teams slightly favored. Plot 8 shows results from 200,000 simulations based on updated 2021 data.
With updated information from the 2021 NBA season, there is reasonable evidence (probability 0.772) that win percentage for home teams is decreasing in games where the away team is slightly favored, and the estimate for the true win percentage is around 0.504.
HOME TEAM SLIGHTLY FAVORED
Plots 9 and 10 show almost the exact same trend, and they very closely resemble results from the previous section. Again, updated information provided by 2021 data indicates a downturn in home team win percentage (with probability 0.765) that indicates a significant difference in home team performance this year than in years past. The estimated win percentage for home teams in these matchup types is 0.663.
Conclusion
There is an obvious downward trend in home team win percentage this year that could be based on huge drops attendance, but there are also other factors that could explain this trend. Three-point shooting increases have spiked the volatility of wins and losses, and as more three-pointers go up every season, the effects of other factors might matter less and less.
In another analysis, attendance could be directly examined and grouped so that the relationship between lower attendance and win percentage could be measured, rather than simply season-by-season differences. For the purposes of this article, the findings indicate we have found at least some evidence of a decreasing effect of home court advantage, linked closely with exceptionally low attendance this past season.
References
Sports Reference LLC. Basketball-Reference.com — Basketball Statistics and History. https://www.basketball-reference.com/. (May 2021)
Zatzman, L. (2021, January 5). The Raptors are struggling on and off the court in Tampa Bay. Raptors Republic. https://www.raptorsrepublic.com/2021/01/05/the-raptors-are-struggling-on-and-off-the-court-in-tampa-bay/
