Rating Player Defensive Fouls Drawn and Committed

I have no idea how important defensive fouls are. This bothers me, as fouls are an important part of the game. Clearly you’d prefer to draw more fouls than you commit, but how important is it relative to the other things players do? How might a player and team increase (decrease) the number of fouls they draw (commit)?

By presenting basic ratings of player’s defensive fouls drawn and committed, this post will be my first step it trying to answer these questions.

Modeling Defensive Fouls

When rating player defensive fouls drawn and committed, there were a few basic questions I also wanted to answer (and control for):

1. Does knowing which player shot the ball provide any useful information?
2. What role does offensive rebounding play?
3. What information do steals provide us?

Because of these needs, I’ve chosen to use a varying intercept model to rate the players and answer these questions.

The Data Set

The data set used to fit these models comes from the play-by-play data for the 2008-2009 regular season. After naively assigning each player’s position for every lineup (using the method described in the post on player offensive rebounding rates), I’ve grouped the data based on the following criteria for each player and position pair:

• Offensive lineup location: home versus away
• How the play started
• Which position shot the ball to end the play
• Which position rebounded the ball to start the play
• Which position stole the ball to start the play

The Fits: Offense (Fouls Drawn)

The fits below allow us to estimate the probability a player at the given position draws a foul on a given play:

• PG: logit^-1(-2.84 -6.26(was FG2 shooter) -5.37(was FG3 shooter) -0.34(live oreb) +0.28(live oreb x the rebounder) +6.22(was FG2 shooter x the FG2 shooter) +2.70(was FG3 shooter x the FG3 shooter) +0.76(steal x the stealer))
• SG: logit^-1(-3.00 -5.31(was FG2 shooter) -4.94(was FG3 shooter) -0.24(live oreb) +0.16(live oreb x the rebounder) +5.47(was FG2 shooter x the FG2 shooter) +2.45(was FG3 shooter x the FG3 shooter) +0.79(steal x the stealer))
• SF: logit^-1(-3.20 -4.82(was FG2 shooter) -4.02(was FG3 shooter) -0.28(live oreb) +0.30(live oreb x the rebounder) +5.23(was FG2 shooter x the FG2 shooter) +1.54(was FG3 shooter x the FG3 shooter) +0.64(steal x the stealer))
• PF: logit^-1(-3.18 -3.47(was FG2 shooter) -3.16(was FG3 shooter) -0.26(live oreb) +0.31(live oreb x the rebounder) +3.92(was FG2 shooter x the FG2 shooter) +0.70(was FG3 shooter x the FG3 shooter) +0.72(steal x the stealer))
• C: logit^-1(-3.11 -3.00(was FG2 shooter) -2.49(was FG3 shooter) -0.20(live oreb) +0.22(live oreb x the rebounder) +3.53(was FG2 shooter x the FG2 shooter) -1.60(was FG3 shooter x the FG3 shooter) +0.31(steal x the stealer))

The coefficients are all statistically significant except for the coefficient for the center’s “was FG3 shooter x the FG3 shooter” with a p-value of 0.11. Also, higher order interactions between these predictors were examined, but the data does not suggest they are beneficial and were thus removed from the models.

Interpreting these fits can be tricky, so here are the major points:

• For all positions except point guards, we expect a player that attempts a 2pt shot to be fouled more often than when the player does not attempt a 2pt shot.
• We expect the player that attempts a 3pt shot to be fouled less often than when the player does not attempt a 3pt shot.
• When guards obtain offensive rebounds our expectation of the rate at which these players draw fouls decreases. Our expectation increases slightly when all other positions obtain an offensive rebound.
• Plays that start with the player stealing the ball increases our expectation of that player being fouled.

These are the sort of general statements we can make with these model fits. They don’t allow us to fully understand how a player or team can increase (decrease) the number of fouls they draw (commit), but they give us some insight.

One issue is that there are likely other unobserved covariates that are correlated with these predictors that are likely to tell the real story (such as 2pt shot attempts from drives in the paint). The league doesn’t count this stuff, so we have to use common sense when trying to figure out what this model is telling us.

For example, I’m fairly certain that having a big spot up for a mid-range jumper isn’t going to increase that player’s number of fouls drawn when he’s able to attempt that shot. That just doesn’t make sense… does it?

All that said, there are likely other things we might be able to take into account (such as a player’s role in the offense) that may give us more insight. For now, though, these role specific details are wrapped up into the player ratings themselves.

The Fits: Defense (Fouls Committed)

The fits below are for estimating the probability a defensive player commits a foul on a given play. I didn’t want to get too fancy with this initial look, so I simply looked at counterpart position data to see what information that provides us. The fits are:

• PG: logit^-1(-2.85 -1.98(was FG2 shooter) -3.63(was FG3 shooter) -0.19(live oreb) +0.42(steal) +1.03(counterpart was FG2 shooter) +0.20(counterpart was stealer))
• SG: logit^-1(-2.89 -1.66(was FG2 shooter) -3.36(was FG3 shooter) -0.17(live oreb) +0.35(steal) +0.53(counterpart was FG2 shooter) +0.22(counterpart was stealer))
• SF: logit^-1(-2.98 -1.47(was FG2 shooter) -3.27(was FG3 shooter) -0.15(live oreb) +0.17(steal) +0.67(counterpart was FG2 shooter))
• PF: logit^-1(-2.95 -1.13(was FG2 shooter) -2.95(was FG3 shooter) -0.10(live oreb) +0.04(steal) +0.45(counterpart was FG2 shooter))
• C: logit^-1(-2.90 -0.95(was FG2 shooter) -2.84(was FG3 shooter) -0.07(live oreb) -0.25(steal) +0.66(counterpart was FG2 shooter))

Here’s how we’d interpret these fits:

• Knowing the counterpart player attempts a 2pt shot increases our expectation for the player committing a foul compared to knowing someone other than the counterpart player attempted a 2pt shot.
• When the opponent attempts a 3pt shot our expectations on the odds the defense commits a foul are very low.
• Opponent offensive rebounds decrease our expectation of a foul for each position.
• We expect centers to foul at a lower rate on plays that start with an opponent steal, but we expect all other positions to foul at a higher rate on these plays. Knowing counterpart information is informative for guards, and it increases our expectation further for these players.

The 08-09 Defensive Foul Ratings

The spreadsheets below list the ratings for each player along with 95% confidence intervals for these ratings:

08-09 Ratings: Defensive Fouls Drawn

08-09 Ratings: Defensive Fouls Committed

The defensive fouls drawn ratings are sorted such that the higher the rating the more defensive fouls we expect this player to draw. The defensive fouls committed ratings are sorted such that the lower the rating the fewer defensive fouls we expect this player to commit.

The 95% confidence intervals are provided to show the uncertainty in the actual player’s rating. We can consider players that have an interval that does not cross zero to be above or below average (depending on the sign of the rating).

Summary

The model and associated ratings presented in this post is merely a first look at trying to understand defensive fouls.

As you might imagine, there are plenty of areas to continue to analyze. One is taking the entire lineup into account at once to rate the fouls drawn and committed at the same time. Another is (gasp!) looking at what impact refs have.

Ultimately fouls are just a single factor that defines a player. So there is also work left to do to understand how fouls compare to shooting percentages, turnover and rebounding rates, etc.