In order to have a mature discussion about foul trouble, we need to know what foul trouble is. I could define it myself, but there are really only two groups of people who should be making this determination: coaches and players. These two entities are not completely independent. If a coach treats a player like he is in foul trouble, he’ll probably play like he’s in foul trouble. Nonetheless, as a first step it’s easy to identify what coaches think, so let’s take a look at the data.

What I’ve done here is look at how coaches treat starters. If a starter has X fouls, how likely is he in the game with Y minutes left? Here’s the resulting graph using games since the 2009-2010 season. 

I should mention a few notes on the data. While the NCAA provides play-by-play data in a standardized (if unwieldy) format, there are some limitations to it. Substitution data is not always correct. In a study where we need information about whether a player is on floor, this is a problem and forces some of the data to be discarded.

The other issue is that the play-by-play does not distinguish between technical fouls and regular fouls. I have ways to correct for this, but there are definitely a few cases that slipped through the cracks. However, most of the data included here should be correct.

Now let’s use the chart to look at how fouls have an impact on playing time.

One foul: Think of the player with zero fouls as the control group early in the game. Players picking up an early foul see a slight impact on playing time. For instance, with 17 minutes left in the first half, a starter with no fouls will be on the bench just 4% of the time, while a starter with one foul will be benched 12% of the time. By the time we get to the 11-minute mark of the first half, the player with one foul is treated the same as the player with no fouls.

Two fouls: The player with two fouls has his minutes severely restricted for the entirety of the first half. There is some leniency given with 4-6 minutes until halftime, but there is very little opportunity for the player with two fouls to see the floor in the first half. There is odd unanimity among coaches that a player with two fouls should be protected with 20:01 remaining and should not be protected with 20:00 left in the game. If you are of the mindset that coaches are too aggressive benching guys with two fouls, this is a good piece of evidence that a herd mentality exists.

Three fouls: There aren’t many cases of guys getting three fouls in the first half, but when they do, they sit. And some of them don’t even start the second half. The ones that do tend to head to the bench before the normal time for a starter. By roughly the nine-minute mark, the player with three fouls is back to playing the same amount of time as other starters. But even in the worst case, a coach does not consider three fouls as big of a deal in the second half as a player getting two in the first half.

Four fouls: The player with four fouls doesn’t get to the 50% mark in playing time until there are five minutes left in the game. And he doesn’t get out of foul trouble in all coaches’ minds until there are two minutes left. An interesting data artifact is that in the very last minute, the likelihood of a starter being on the floor is inverse to the number of fouls he has. If a player has made it to the final minute with no fouls, chances are he hasn’t played as much as others in the starting lineup and is less likely to be on the floor in closing time.

If there’s one thing to be learned from this exercise it’s that coaches really value starting the same lineup in the first and second half. “It’s not about who starts the game, but who finishes it,” the saying goes. But coaches have a lot more flexibility about who finishes the game than who starts the second half. (Some of the playing time dip at the end of the game for starters is the result of lopsided finishes.)

Coaches universally consider the end of the first half the end of foul trouble for a player with two fouls. There is no such agreement on the player with three or four fouls, for whom coaches dole out playing time with more judgment.

For that reason, I’ll be focusing on the two-foul decision initially. There’s a lot less context involved in the first half while decision-making in the second half is more influenced by time and score. Which coaches are most and least likely to put a player on the floor with two fouls in the first half? We’ll find that out in the next installment.