By Andrew Puopolo

Earlier on in the NBA Playoffs, I was watching a game in which 5 or 6 possessions in a row ended in a foul. This got me wondering, do playoff games, on average, have more fouls than regular season games? Or was this just a freak occurrence that was specific to that series? In addition, I was curious if this effect was a recent thing, or has been present for a number of years. In 2012, Slate conducted a similar study on the increase in fouls during the playoffs, but I wanted to expand upon it and test this effect for statistical significance. In addition, I wanted to expand upon a 2013 Bleacher Report article and see if there was an extra discrepancy between home and away fouls in the playoffs as compared to the regular season.

To go about this, I scraped the number of fouls for the home and away team for every regular season and playoff game from the 1982-83 season to the 2017-18 season from Basketball Reference, and calculated the total number of fouls in the game and also the difference between the number of fouls for the home team and away team (to see if there’s extra home bias during the playoffs). I then decided to plot these two statistics against each other by year, with confidence intervals around the playoff statistic. First, we take a look at the total number of fouls per game.

From this, we can see that the average number of fouls generally has been decreasing over time in both the regular season and playoffs. In addition, we find that the difference between the regular season average and playoff average has increased over time. In the early years of our study, we find that the difference for each season is not statistically significant at the 5% level. However, for every year since 2000 except 2005, 2007 and 2011, we find that the regular season average lies outside of our 95% confidence interval. This suggests heavy evidence that there are more fouls called in the NBA Playoffs than the NBA regular season.

We also wanted to take a look at the difference between the number of fouls called on the home team and the number of fouls called on the away team.

On this plot, we find that the average difference between away fouls and home fouls is greater in the playoffs than the regular season for most years. However, this difference is infrequently significant at the 5% level, so we cannot conclude with certainty that the difference between home and away fouls is significantly different between the playoffs and regular season.

However, this method of analysis does not take into account specific matchups. For example, when calculating the average number of fouls during the regular season, we are including super low energy matchups between teams that have no chance of making the playoffs and are just “playing out the string” or possibly even tanking for a draft pick. As a result, I decided to rerun the study to take into account playoff matchups. To do this, I decided to run 2500 simulations to create a null distribution as described below:

1.) For each playoff series matchup, calculate the number of games each team played at home. For example in the Eastern Conference Finals between the Celtics and Cavs, this would have meant 4 home games for the Celtics and 3 for the Cavs.

2.) Find all regular season matchups between the two teams for each playoff series.

3.) Randomly sample games (with replacement) between the two teams from the regular season equal to the number of games in step 1. Continuing with the example from step 1, this means that we will have the foul statistics from 4 games (with replacement, so there will be some duplicates) between the Cavs and Celtics at TD Garden and 3 at Quicken Loans Arena.

4.) Repeat this for all playoff series from 1982-present. By doing this, we are creating a null sample of games that is identical to the sample of games from the playoffs. The only difference is that the games in our null sample are from the regular season, while our test statistic is the foul statistics from the 2719 playoff games.

5.) Calculate the average number of fouls in the randomly sampled dataset, and log it.

6.) We repeat steps 3-5 2500 times.

Note: We excluded the 1998-99 Playoffs from this analysis. The reasoning behind this was that there were no regular season matchups between the Spurs and Knicks (due to the lockout shortened season).

By doing the simulation above, we are creating a null distribution for the average number of fouls we would expect for the sequence of games, and see if the empirical result from the playoffs differs from that. After doing this, we get the following histogram for the null distribution, with a vertical red line for our test statistic (the result from the playoff games).

The evidence is overwhelming. None of the simulated trials created an average number of fouls anywhere close to the empirical average of 46.89. This further cements our belief that there are more fouls in playoff games than in regular season games.

We also conducted a similar analysis as described above on the difference between the number of away fouls and home fouls, and got the following results.

Of the 2500 simulations, we find that only 4 yield an average difference between home and away fouls that is greater than the value attained in the playoff games. This yields a p value of .0016. This means we can conclude with significance at the 5% level that the difference between the number of home and away fouls is greater during the playoffs than the regular season.

There were some pretty interesting results from this analysis. The main takeaway is that as the number of fouls called in the NBA has steadily decreased over time, the difference between the number of fouls in the regular season and playoffs has increased. This is despite the fact that the pace of play is 2% slower in the playoffs than it is in the regular season. In addition, we find that the difference between the number of fouls called on the home team vs away team is greater in the playoffs as opposed to the regular season, although the magnitude and significance of this effect is much smaller than the effect on total fouls called.

A possible way of furthering this study would be to adjust for Overtime games (especially in our second method of this analysis) and also control for pace of play. It could be the case that regular season games feature more fastbreak possessions, which are less likely to end in a foul than a regular half court set.

What are the trends that are leading to these effects? It is clear that teams play with more intensity during the playoffs, but why are more fouls being called on the away team as compared to the regular season? Let us know in the comments below.

If you have any questions or comments about this article, please feel free to reach out to Andrew on Twitter @andrew_puopolo or by email at andrewpuopolo@college.harvard.edu.

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