We’ve looked at how coaches define foul trouble and got an idea of how each active coach deviates from the norm. Now it’s time to find out how players define trouble.

I’m going forward under the assumption that a player’s effectiveness is more impacted on the defensive end when he has foul trouble. With that as justification, we can look at foul rates to get a hint at when a player feels like he has to play less aggressively on defense. Just like we did when assessing how coaches define foul trouble, I’ll group foul rates by players that have X fouls.

To begin with, let’s look at foul rate given a starter’s foul count in the first half only, adjusted for playing time…

Foul rates since 2010 for starters with a given number of personal fouls, first half only1

PF  PF/40 
 0  2.66
 1  2.34
 2  1.71

It’s pretty clear that the starters with two fouls are less willing to commit fouls than their peers who have zero or one fouls. You can get conclusive proof that these players are acting abnormally by comparing the foul rates in the second half.

Foul rates since 2010 for starters with a given number of personal fouls, second half only2

PF  PF/40
 0  2.94
 1  3.19
 2  3.28

After halftime, starters with two fouls commit fouls more frequently than their teammates with zero or one fouls. This makes sense: Players that have accumulated more fouls figure to be a bit more foul prone in general. You’d expect them to have higher foul rates going forward, other circumstances being equal.

It also illustrates that the restraint shown by the two-foul players in the first half is even greater than the raw numbers indicate. The two-foul starters should have a higher foul rate than the zero- and one-foul players if they were acting normally, but instead their foul rate is 27% less than the one-foul player and 36% less than the starter with zero fouls.

One of the criticisms of benching a player in foul trouble is that that player is unlikely to eventually foul out, so why not play them more? But that’s not exactly the problem to be considered. Players have a self-preservation mentality and Davis Rozitis excepted, they’ll find ways to avoid disqualification for as long as possible. And these methods aren’t usually consistent with playing winning basketball in the moment.

But to really see how players define foul trouble we need to see how foul rates (PF per 40 minutes played) evolve minute-by-minute for starters with X fouls. Here you go…

Foul rate by PF

Generally speaking, the behavior of players with X fouls mimics the tendency of coaches to restrict their playing time, whose graph I’ll reproduce here…

Playing time by foul rate

The biggest exception that I can see is with starters with one foul in the first half. Coaches don’t pay them much mind, reducing their playing time only slightly early in the half, but treating them the same as if they had zero fouls later in the half. However, throughout the first half starters with one foul actually foul at a noticeably smaller rate than starters with zero fouls.

The two-foul starters are even more cautious in the first half. More strikingly, they respect the seemingly-irrational halftime discontinuity established by their coaches. The foul rate of the two-foul starter rapidly increases after halftime – just as their playing time does.

Three-foul starters play it tentatively for roughly the first 10-12 minutes of the second half, but not as cautiously as two-foul starters are in the first half. Likewise, their playing time is limited for about the first 10-12 minutes of the second half, but not as much as for two-fouls in the first half.

Starters with four fouls are in full-on preservation mode almost until the very end of the game3 and coaches don’t completely trust them until there are 2-3 minutes remaining.

In summary, there isn’t much difference in how coaches and players define foul trouble. Players are acting the way coaches think they should act. Or maybe players are acting the way they think their coaches expect them to act. It can’t be a total coincidence the two groups’ behavior agree so well.

Coaches would prefer to have an aggressive reserve in the game over a tentative starter and it’s possible they have an understanding of when the starter will be tentative. Or maybe players react to how their coach treats them and in the cases where they do see the court with foul trouble, they’re more determined to validate their coach’s trust.

If it’s the latter, it’s interesting that a player’s self-preservation instinct kicks in AFTER he gets into what his coach considers foul trouble. The main exception is the one-foul player in the first half who appears to work a little harder to avoid the bench time that comes with picking up number two.

The main argument against sitting players in foul trouble is that players rarely foul out and sitting them is just depriving the best players of playing time. However, you could reframe the debate. Instead of maximizing minutes for his best players, a coach’s job is also to minimize bad minutes. There’s a self-preservation instinct in most players and in situations where that instinct is the strongest, there figures to be a negative impact on the player’s defense.

Hey, maybe the best coach would train his players to play the same way regardless of their foul count.4 If that was accomplished, then we could focus on the goal of maximizing minutes. But it seems that players will never be able to ignore the reality that once they get a fifth foul, their playing time is permanently reduced to zero for what could be the most exciting parts of the game.

That’s a big incentive to reduce one’s foul rate after getting into foul trouble and become a defensive liability. While I wouldn’t side with the most extreme coaches that refuse to play guys in foul trouble, there’s plenty of evidence to suggest that ignoring foul trouble isn’t a viable approach, either.

^1 Foul rates computed by averaging foul rate at each minute remaining of the first half, excluding the first two minutes when foul rates are extremely low.
^2 Same method used as in the first half table, but ignoring the last two minutes of the second half when foul rates spike.
^3 I’ve omitted the last minute of play from the players’ plot as the rates for all players skyrocket as possession time decreases and strategic fouls come into play.
^4 It’s possible Lorenzo Romar has already done this.