[Update 5/17: Thank you for the many interesting comments! Please see my follow-up posted today.]
In a professional basketball game, a player is disqualified (“fouls out”) if he is charged with 6 personal fouls. Observers of the NBA know that the direct effect of fouling out actually has less impact than the indirect effect of “foul trouble.” That is, if a player has a dangerous number of fouls, the coach will voluntarily bench him for part of the game, to lessen the chance of fouling out. Coaches seem to roughly use the rule of thumb that a player with n fouls should sit until n/6 of the game has passed. Allowing a player to play with 3 fouls in the first half is a particular taboo. On rare occasions when this taboo is broken, the announcers will invariably say something like, “They’re taking a big risk here; you really don’t want him to get his 4th.”
Is the rule of thumb reasonable? No! First let’s consider a simple baseline model: Suppose I simply want to maximize the number of minutes my star player is in the game. When should I risk putting him back in the game after his nth foul? It’s a trick question: I shouldn’t bench him at all! Those of you who haven’t been brainwashed by the conventional wisdom on “foul trouble” probably find this obvious. The proof is simple: if he sits, the only thing that has changed when he gets back in is that there is less time left in the game, so his expected minutes have clearly gone down. In fact, the new distribution on minutes is first-order stochastically dominated, being just a truncation of the alternative. This assumes only that his likelihood of getting a foul is time-invariant, which seems reasonable.
OK, while I believe the above argument is very relevant, it oversimplified the objective function, which in practice is not simply to maximize minutes. I’ll discuss caveats now, but please note, there is tremendous value in understanding the baseline case. It teaches that we should pay attention to foul trouble only insofar as our objective is not to maximize minutes. I am very comfortable asserting that coaches don’t understand this!
First caveat: players are more effective when rested. In fact, top stars normally play about 40 of 48 minutes. If it becomes likely that a player will be limited to 30-35 minutes by fouling out, we may be better off loading those minutes further towards the end of the game to maximize his efficiency. Notice, though, that this doesn’t lead to anything resembling the n/6 rule of thumb. It says we should put him back in, at the very latest, when he is fully rested, and this isn’t close to what is done in practice. In fact players often sit so long the rest may have a negative impact, putting them “out of the flow of the game.”
Second caveat: maybe not all minutes are created equal. It may be particularly important to have star players available at the end of the game. On a practical level, the final minute certainly has more possessions than a typical minute, but it also has more fouls, so maybe those effects cancel out. I think the primary issue is more psychological: there is a strong perception that you need to lean more on your superstars at the end of the game. I think this issue is drastically overrated, partly because it’s easy to remember losing in the last minute when a key player has fouled out, but a more silent poison when you lose because you were down going into that minute having rested him too long. By the way, my subjective sense is that the last possession is more similar to any other than conventional wisdom suggests: a wide-open John Paxson or Steve Kerr is a better bet than a double-teamed Michael Jordan any time in the game. On a couple of major occasions, Jordan agreed. This isn’t to underestimate the star’s importance in scoring and getting other players good shots, just to say that this is not necessarily more important in the final minutes. You do often hear that a team will rise to the occasion when a star is injured or suspended, so even conventional wisdom wavers here. Finally, note that the foul-trouble rule of thumb is applied also to players who aren’t the primary scorer, so that this argument wouldn’t seem to apply. I will give coaches a little credit: they do sometimes seem to realize that they shouldn’t worry about foul trouble for bench players who often don’t play at the end anyway.
One more psychological caveat: a player who just picked up a foul he thinks is unfair may be distracted and not have his head in the game immediately afterward. This may warrant a brief rest.
Final note: Conventional wisdom seems to regard foul management as a risk vs. safety decision. You will constantly hear something like, “a big decision here, whether to risk putting Duncan back in with 4 fouls.” This is completely the wrong lens for the problem, since the “risky”* strategy is, with the caveats mentioned, all upside! Coaches dramatically underrate the “risk” of falling behind, or losing a lead, by sitting a star for too long. To make it as stark as possible, observe that the coach is voluntarily imposing the penalty that he is trying to avoid, namely his player being taken out of the game! The most egregious cases are when a player sits even though his team is significantly behind. I almost feel as though the coach prefers the certainty of losing to the “risk” of the player fouling out. There may be a “control fallacy” here: it just feels worse for the coach to have a player disqualified than to voluntarily bench him, even if the result is the same. Also, there is a bit of an agency/perception problem: the coach is trying to maximize keeping his job as well as winning, which makes him lean towards orthodoxy.
There are well-documented cases in the last decade of sports moving towards a more quantitative approach, so maybe there is hope for basketball strategy to change. The foul-trouble orthodoxy is deeply ingrained, and it would be a satisfying blow for rationality to see it overturned.
*Final outcomes are binary, so the classical sense of risk aversion, involving a concave utility function in money, doesn’t apply at all. But there is also a sense of what I call “tactical risk”: a decision may affect the variance of some variable on which your probability of final success depends in a convex (or concave) way. I might write an essay sometime on the different meanings of “risk.” Anyway, here you presumably should be risk-averse in your star’s minutes if ahead, risk-loving if behind. But this is rendered utterly moot by first-order stochastic dominance!
The Leisure of the Theory Class 
49 comments
April 27, 2010 at 11:51 pm
Kevin
We would be letting MEDS down if there wasn’t some discussion here of an agency problem explanation: players desire to maximize minutes, coaches desire to maximize wins. Assume players foul “optimally” at the start of the game (the win-maximizing balance of tenacity and overaggression). When a player has 3 fouls in the first half, he will be ultracareful not to foul again so that he won’t foul out, and therefore play suboptimally from the coach’s perspective. One mechanism available to the coach is to bench that player for a sub more willing to play with win-maximizing defense; even if the sub is “worse” than the star, he may be better than the star conditional on the star attempting to avoid additional fouls.
Of course, the real answer is that sports teams continue to do suboptimal things – witness the punt/go for it problems on 4th down, and in particular the bashing in the media that Bill Belichick took last year on his ill-fated attempt against the Colts (noting that Bill has won 3 rings for the Patriots and is considered by the stats guys to be the coach who goes for it on 4th as close to optimal as any coach in the league). Perhaps the foul result does not show that *coaches* are stupid, but rather than owners or GMs are, and that coaches are maximizing the objective function “keep our job”.
An alternative way to answer the foul question would be to ask someone like Daryl Morey, the stat-heavy MIT engineering and MBA GM of the Rockets.
May 6, 2010 at 7:47 am
Jeff
Hi Kevin,
Actually, Belichick’s call to go for it on 4th down against the Colts was supported by statistics. If you look at the expected values of going for it v. punting, using the odds for each scenario, going for it made sense. The reason it was a “suboptimal” strategy was that it didn’t work, and went against conventional wisdom. That’s why he was bashed by the media.
May 10, 2010 at 10:25 am
DRDR
Kevin agrees. He’s saying that it’s the media, owners, and GMs who are clueless, and the scrutiny of Belichick is one reason why many coaches don’t go for it in that situation.
April 28, 2010 at 12:26 pm
Pnin
There is one more factor at play. If the player is not benched he will try to play more conservatively and avoid fouls so that he will not be fouled out. The coach may bench the player because he want him to stay agressive on defense and not let other tactical considerations interfere with his normal state of mind. In other words, players are not ‘used’ to play with 3 fouls in the first half and it may be hard for them not to make adjustmenst if they are asked to it.
April 28, 2010 at 10:45 pm
Eilon
This argument, about players playing conservatively not to foul out, is not convincing. If the coach believes that Jonathan’s approach is correct, and the player should play straight until they are fouled out, but he is aware that players are not used to it, he will work with the players on changing their attitude, explaining to them why it is better to continue playing.
April 28, 2010 at 3:21 pm
Jonathan Weinstein
Good points. I alluded in passing to the fact that coaches follow orthodoxy because they face heavy criticism if they don’t (even Belichick who should have been above that if anyone was!) It’s also worth noting that players may have trouble playing optimally (Or not want to), especially if unorthodox strategy puts them in an unfamiliar situation.
April 28, 2010 at 4:18 pm
Eran
I don’t know anything about coaches but I believe this is a general phenomena: Agents get more credit and more blame when they deviate from the common wisdom, which leads them to act sub-optimally w.r.t to the objective function they are paid to optimize.
Especially in cases with a high probability for failure, it becomes substantially more profitable for the agent to just go by the book. I guess the technical term for such behavior is CYA.
May 6, 2010 at 7:53 am
Jeff
Jonathan:
You wrote, “…there is a strong perception that you need to lean more on your superstars at the end of the game. I think this issue is drastically overrated…” In some cases, I don’t think it is, particularly here in Cleveland. The Cavaliers do tend to highly rely on LeBron James in the final minutes, and so his 4th quarter minutes are extremely valuable.
May 6, 2010 at 5:11 pm
Dave B
You wrote what I’ve been saying for years: “the coach is voluntarily imposing the penalty that he is trying to avoid.” When a player sits with early foul trouble, he IS fouled out. The coach opts for the certainty of fouling out now rather than the possibility of fouling out later.
You use the NBA as an example, but the practice is more pronounced in college ball (only five fouls) where many teams collapse if they play for long without their star.
The only player with a skill particularly critical at the end of the game is the guard who is the team’s top free throw shooter.
May 7, 2010 at 12:26 am
Jonathan Weinstein
Jeff: Maybe there are occasional exceptions where a team just can’t emotionally handle being without LeBron or whoever in the last minutes. But note, you can also get blown out in the 3rd quarter while he sits. And if it’s a big guy rather than a playmaker, (more commonly in foul trouble) he might be less valuable in the last minute when you start getting fouled.
Eilon: Teaching players hopefully works in the long run, but the coach will need high prestige to convince them he’s not just crazy.
Dave: This idea is simple enough it must have occurred to lots of people! (I first noticed it about 15 years ago.) WordPress auto-generated a link to a sports blog where someone made essentially the same point 4 months ago. But I haven’t seen it anywhere high-profile.
May 9, 2010 at 11:44 pm
Cheap Talk
[…] sport | by jeff Jonathan Weinstein is blogging now at The Leisure of the Theory Class. His first post is a nice one on a common fallacy in basketball strategy. if a player has a dangerous number of […]
May 10, 2010 at 12:24 pm
Jon Biggar
Another factor to consider is whether a superstar has a different productivity curve vs time played than the brench player that would replace him if the coach makes the superstar sit due to foul trouble. Some players might produce better statistics than another player simply because they don’t tire as quickly as another would.
So some players might benefit more from the “rest” of being benched than others.
May 10, 2010 at 12:35 pm
Dan
Overall I agree with the post, but I do think that stars who can create their own shots are especially valuable in the last few minutes. If you give the ball to a star like LeBron with 5 seconds to shoot, he can create a shot that’s almost as good as what the team could get if they had the full 24 seconds to run their offense; a star-less offense that has to rush typically gets a much lower percentage shot. Late in the game is when clock management becomes especially important, so this skill at quickly creating a shot becomes more valuable. If the Cavs are behind, they can rush and give it to LeBron to get quick shots in order to increase the number of possessions that they have to come back. If they’re winning, they can shorten the game by letting 15 seconds run off the clock before starting their offense, knowing that LeBron can still get them a good look before the shot clock expires. These clock management strategies (rushing or waiting) take on more and more weight as the game approaches its finish, which means that playmaking stars become increasingly important (just as conventional wisdom says they do).
May 10, 2010 at 12:41 pm
ChrisD
You state “…there is a strong perception that you need to lean more on your superstars at the end of the game. I think this issue is drastically overrated…”.. but in the NBA, this is not overrated at all. Given the length of the game and the necessity of using some subs, the amount of effort and talent on the floor rises and falls throughout the course of the game. Only at the very end of the game when the outcome is most strongly determined can you guarantee that both teams will do their best to absolutely maximize talent and effort on the floor. That is when you need your LeBron or Tim Duncan. The NBA is notorious for teams trying, but not killing themselves in quarters 1-3. The end of the 4th quarter is when you need your absolute best defenders, best shot creators…etc. because a lot of the rest of the game is about trying to score without working too hard. If you know everyone will be maximizing effort, then you need to max out your talent level to compete in the time frame. If you even casually watch basketball, you know that the hardest stops and scores to get are at the end of the game. While I’m sure there can be improvements made on the conventional wisdom, I think it’s a little presumptuous to call this kind of risk/safety management a “fallacy.”
May 10, 2010 at 12:47 pm
Jared
While I’ve always said that coaches tend to sit players too long when they get in “foul trouble” like you, I think that simply saying you shouldn’t sit them at all ignores two important points (one of which has already been mentioned).
One, the player in foul trouble (FT) does indeed tend to play softer defense when they’re in FT. You can see it especially in center play. Especially when a quicker guard is driving toward them, they’ll back away instead of going for the shot block like they normally would. The important risk-reward relationship here is if when they’re not playing conservatively whether their power to affect the shot (whether by blocking or simply getting in the way) is more advantageous or common than them picking up an additional foul. This depends on a ton of inputs like ref’s allowance for contact, quality of guard play, and help defense. So, in a nutshell, it’s hard to know if this higher level of “conservativeness” is, in fact, a good thing, a bad thing or a wash. This also changes how the player will play on offense in the same way, by the way – although, probably by not as much.
Two, is that it changes how the opposing team plays defense against the star player because they often increase their focus on trying to get the player to pick up an additional foul – typically by way of enducing a player control foul or charge. Again, there are a lot of inputs here that make it ambiguous how this increase in attention will play out. Does it usually result in an additional foul for the player in FT, or is he talented enough on defense to get to the spot and set his feet and thereby force the opposing team into potential FT?
All this begins to remind me of General Equilibrium Analysis where there are no stable solutions because of the complexity of the problem and dynamic nature of games, players, and refs.
May 10, 2010 at 1:51 pm
Jared
I would also note that I don’t recall seeing any study on how ref’s change their manner in calling fouls intra-game. I reffed basketball games in college, and we were actually taught methods like you should try to avoid early “foul-outs”. I know I’ve seen a study that shows that refs tend to actively try to even out foul call numbers between halves even after controlling for other variables. Basically, you could it seems you could come up with scenarios like the following:
Player picks up his 3rd foul with 5 minutes to play in the 1st half (while the refs are still calling it “tight”) and is left in the game. He is then involved in a play in which it is not readily obvious whether or not his 4th foul should be called (block/charge type play would be an obvious candidate). In the first half, this is possibly more likely to be called his 4th than if this same play occurred in the 2nd half.
May 10, 2010 at 12:58 pm
John Wegerzyn
A few more caveats. 1)Opposing teams can target a player with foul trouble by pushing the ball against them, thus increasing their chance to foul out. 2). At the end of the game the opposing team will have their best players on the floor. You can sit out skilled players earlier in the game with a higher likelihood the other team will be playing their less-skilled players than at the end of the game. 3) Most NBA linups are 7-8 deep at best. Teams practice and scheme mostly for linups with skilled players rather than lineups with less skilled/experienced players. At the end of the game you want thse units in.
A lot of the arguments for allowing players to play with foul trouble presume orthodoxy attempts to maximize the last minute or two. Sitting players in the first half and early in the fourth quarter allows the best players and or the coaches chosen lineup to be in the game the last 5 to 7 minutes. (which is sufficient time to make up even doube digit deficits).
May 10, 2010 at 1:07 pm
Mike
What about match-up considerations? Assume that the player in foul trouble is the team’s most effective defender against a particular opponent. When evaluating whether to sit his player, he coach knows that the opposing player will probably not play every minute of the game and that the opposing player will probably be in the game for the final two minutes. So by siting his player until n/6 of the game has passed, the coach is effectively saying that he wishes to deny the opposing team the ability to rely on that one player during the final two minutes of the game.
The cost of this is that the opposing player will be more effective through the course of the game, but this has to be weighted against the fact that this player will not play the entire game and that the opposing team may not rely solely on that player in order to keep other players involved for various reasons. Some of the “risk” referred to by the conventional wisdom may have to do with the risk of providing an opponent with a high probability strategy for scoring points in the final minutes of the game.
May 10, 2010 at 1:55 pm
Steko
(1) While many more fouls are called in the 4th quarter most are intentional. There may be a perception that referees are less likely to call non-tactical fouls in the 4th quarter (esp late in the 4th) where scrutiny of bad calls is more likely.
(2) A key player fouling out becomes a ready made excuse for other players to pin the loss on. There are chemistry impacts going forward that should be avoided instead of exacerbated.
(3) Coaches use the conventional wisdom as an additional tool in the power struggle with players.
(4) There could be a circle the wagons mentality if the blame can be shifted to “bad officiating”. It would be interesting to see a TS% comparison of teams when a star player gets in bad foul trouble. Yao Ming’s career should provide ample data.
(5) While the linear n/6 function might appear to be the conventional wisdom it may in practice have escalating effects. A key starter is rarely benched until the 8th minute if he picks up a foul on the first play. The 2nd and 3rd fouls usually obey n/6. The 4th foul usually means the player is saved for the final 7-8 minutes. A 5th foul often means the last 2-4 depending on circumstances.
May 10, 2010 at 2:03 pm
Alex J
While I agree with the general idea my impression has always been that the coach should stick with his normal rotation to keep players fresh (including one with foul trouble). Maybe only augmenting the rotation to make sure he doesn’t foul out really early thus making his backup play a lot of consecutive minutes at the end of the game.
Another thought I had was maybe he sits his star because the reffs may help keep his team close. This bias that has been shown in papers that fouls tend to be more likely called on the team with less team fouls (which would probably the other team in this case).
Lastly, along with all the other advantages of having a star player at the end of a game mentioned, getting fouls called at the end of a game is hard then normal, when non intentional, so he maybe less likely to foul out late. This is in addition to the advantage of getting the “star” treatment in end or game situations.
May 10, 2010 at 2:39 pm
Jonathan Weinstein
The explanation for the surge of comments in the last 2 hours is that we were linked by Tyler Cowen. Many worthwhile points, here are replies to just a couple:
Re clock management down the final stretch: Agree with that one, some stars really distinguish themselves in that they can reliably get a decent shot off in just a few seconds. This mainly pertains to playmakers I think, less so to the big men who are most often in foul trouble. Also, this seems to apply almost exclusively to having 5 fouls, not fewer.
Re strategic adjustments by either team (foul-ridden player more timid, or other team tries to go at him): These concerns seem to be quashed by the fact the the initial argument says the “payoff matrix” will be worse everywhere for a team who over-rests their star. That is: leaving him in is good if he just ignores his fouls, so if he shows intelligent restraint all the more reason to leave him in. If he is showing too much restraint, yell at him (“I want to trust you and leave you in with 3 fouls, but I have to take you out if you’re just giving up layups.”) For the other team, remember they still have the option to go after him even after you rest him a long time. If they don’t think it’s worth it anymore, presumably you’ve helped them out even more than we thought!
May 13, 2010 at 6:44 pm
Dave C.
Your thesis has so many caveats that it is diluted to uselessness. 1. Players may play better when rested. 2. Maybe all minutes are not equal. 3. Teams will change their strategies in order to put a player in foul trouble in positions where he/she would be more likely to foul. 4. Players who are in foul trouble may benefit from a break to clear their minds. 5. Fouls are less likely to be called during the final minutes (refs want players to just play) than in earlier minutes. 6. Substitutions are made for matchup reasons as well. Etc., etc. You even say that “the “payoff matrix” will be worse everywhere for a team who over-rests their star.” Well, then define what “over-rested” is? Does it mean that if they take him out and win he is “over-rested”? Or does it only apply when they lose?
Bottom line fouls are certainly NOT stochastically determined (thanks Mr. O’Neill). Anyone who has ever watched the game knows this. Certain players get angry, have a bad relationship with a certain ref or many other possibilities.
Finally, do you have ANY data to back up your theory, or is this just your intuition? If you don’t have the data, I don’t see how you are any different that the coaches that pull their player, working off their own prejudices.
May 10, 2010 at 3:19 pm
Colin
While what you say isn’t wrong as far as it goes, you seem to leave out a number of factors that would occur to me.
“a wide-open John Paxson or Steve Kerr is a better bet than a double-teamed Michael Jordan any time in the game.”
Players like that aren’t particularly good at creating their own shots. They need someone to create the shots, either actively or by attracting disproportionate attention. Jordan did both.
Why is Paxson or Kerr open in the first place?
Because Michael Jordan is in the game, and everyone is worried about Michael Jordan taking that shot. And whether rationally or not, make no mistake about it: that fear is MUCH greater with 30 seconds left. A large part of the reason that Kerr, Paxson, Big Shot Bob Horry, etc. are able to even get a shot off is because no one is paying attention to them.
“On a practical level, the final minute certainly has more possessions than a typical minute, but it also has more fouls, so maybe those effects cancel out”
No, they don’t. First, many of those fouls are intentional. And you can influence WHO commits those intentional fouls.
Secondly, good players draw more fouls than average, and thus their mere presence increases the chance that you take more free throws than the opposition. And in the end of a game under clock constraints, that is very important.
Lastly, due to the number of stoppages in play, you’re more likely to enact foul-minimization strategies (in on offense, out on defense). These strategies are rare for star players, but useful for others who have accumulated fouls.
Also, bench players are much more likely to freak out and make dumb mistakes under pressure. Some of the bench players are fresh out of college, ‘cold’ from lack of regular minutes, etc. So it may be best to let the bench players play when there is less pressure on them, and let the starters and stars finish when pressure is greater.
I don’t think you’re wrong per se. Most of the points you raise are very important, and I do think the ‘clutch’ factor of star players is overrated. I just think there are enough counteracting influences that you don’t mention that the optimum is somewhere between you and Doc Rivers.
May 10, 2010 at 3:23 pm
Soly
Enjoyable article. My Dad and I have debated this for years. I stand in the middle ground on issues like this. What the article doesn’t factor in is the effectiveness of a player that has, let’s say, 3 fouls with 6 minutes left in the first half. If that person is Kevin Garnett, and he is guarding Shaq, you can bet that the ball is going into Shaq every single possession, knowing that KG will have to play tentative defense and avoid fouling.
However, I do think coaches over exaggerate the foul trouble issue when they take out perimeter players that are in foul trouble. Post players obviously foul more than perimeter players, as the majority of fouls occur close to the hoop, and post players play near the hoop. A wing guy picking up a 3rd foul isn’t that big of a deal as they rely on their post players to help out on drives near the basket anyway, and they don’t necessarily have to use their fouls as their first line of defense (as wing guys are better free throw shooters anyways).
Nowadays in the NBA, you are seeing teams stock up on defensive centers mainly just to use for fouls. In the Cavs-C’s series alone, there is Shaq, Varajao, Z, Hickson, Garnett, Perkins, Big Baby, and Rasheed Wallace. Therefore, you are more likely to see coaches take the big men out if they get in foul trouble, as it hurts their defensive aggressiveness, and teams typically have players that can replace them and not worry about foul trouble.
May 10, 2010 at 3:23 pm
Estragon
Eran strikes close to the rationale actually employed by coaches: they will be so roundly criticized if they ignore the conventional wisdom and lose they often perceive a value in following the tradition just to avoid the criticism. Now, they will also gain some praise for breaking with the CW when they win, but this will not insulate them from the firestorm the next time they do it and lose.
A practical application of the theory would be to sit the player when he gets the foul putting him at or over n/6 relative to the game clock, but only for the normal rest time. A key play-making star might be held out for the end once he gets 5 fouls.
This method might enable a coach to get most of the benefits of WFTT (Weinstein Foul Trouble Theory) while subjecting himself to somewhat less abuse if he loses.
May 10, 2010 at 3:26 pm
Colin
“Only at the very end of the game when the outcome is most strongly determined can you guarantee that both teams will do their best to absolutely maximize talent and effort on the floor.”
“You can sit out skilled players earlier in the game with a higher likelihood the other team will be playing their less-skilled players than at the end of the game.”
I thought of this argument while writing my comments, but I don’t think it pans out. The ‘effort’ claim might be true in practice, but it’s not theoretically convincing.
Suppose that it is so. The opponent will be playing their best players at minutes 47 and 48, and you lose points by not having a starter in.
Couldn’t you easily gain these points in minutes 23 and 24, when the opponent was resting their stars?
The points count equally. Don’t these two possibilities wash out?
May 10, 2010 at 9:40 pm
ChrisD
You could, but both teams need to rest their stars. Unless all of your stars are more fit than all of the other teams stars, you’re always trading off skill, fitness, and talent. If you leave your stars in for extra minutes, then they could be gassed later…etc.
May 10, 2010 at 4:18 pm
Erik Brynjolfsson
Very interesting analysis, Jonathan.
One other factor I would consider is the option value of flexibility. Different players have different strengths, weaknesses and match-up differently on defense. As a coach, I’d rather have a full toolbox to draw on for as much of the game as possible. For instance, I’d rather have the option of bringing in either or both Ray Allen or Rajan Rondo with 4 fouls, rather than have one fouled out and the other playing with 2-3 fouls. Once a player is out, you lose that flexibility to create a particular play, or a particular match up, or a particular style of offense. For instance, maybe I want to be able to put a small fast team on the floor to counter a particular tactic of the opponent, or maybe I want to be able to run a particular designed play on a critical shot at the end of the quarter, or maybe I want to be able to swap guards if my opponent has found a weakness in one of defensive alignments, etc. Flexibility is also important in case someone gets injured, or just needs a 2 minute breather. A related point is that the more flexibility you have, the harder it is for your opponent to exploit a particular tactic or to know what you might plan to do.
By taking the player with a lot of fouls out of the game early, you preserve the option of having him available for a particular critical situation later.
May 10, 2010 at 4:38 pm
RSaunders
Hi, this is super interesting. I wonder about the role of referrees in this process. If we know that foul calls are a function of, to be generous, context (i.e., who’s calling the game and how, when in the playoff series the game is, who the home team is), then does this change the analysis?
Perhaps it doesn’t matter: if the referree has it in for you/your guy, then you might as well play them as much as you can, but it might make sense to voluntarily sit them until the second half if second half possessions are more valuable (even a big 1st half lead caused by taking out your guy can still be overcome in a half).
May 10, 2010 at 4:59 pm
Phil
There is one way to justify taking players out when they have large numbers of fouls early in the game. You have to believe that players in foul trouble can become targets for the opposing team, i.e. opponents will drive to the basket against these players in an attempt to draw more fouls. You also have to believe that opponents are more likely to do this to a player who has four fouls (or five, etc) early in the game than to a player who has the same number of fouls late in the game. I think this view is at least somewhat plausible considering that we know some teams already target players known for foul trouble issues (Dwight Howard). You could even test this hypothesis by looking at foul rates for a player like Howard as a function of number of fouls and game time.
May 10, 2010 at 11:25 pm
Red Auerbach
Every time Russell made a stupid foul in the 1st Quarter, I took him out, made him throw up again, and put him back in with no less than 2 minutes to go in the quarter. Now if Cousy did it, I let him go because Cous had a better understanding of the game. For those very reasons, I hated to start Heinsohn – what a dumb shit.
I’m glad I never had to coach Iverson.
May 10, 2010 at 11:28 pm
George Karl
Red,
Thank your lucky stars that you didn’t have Iverson and Carmelo on the same team. Jesus….
May 11, 2010 at 2:26 am
Barry O'Neill
Jonathan, if this practice changes they owe you a lot of money.
Some of the postings have tried to refute the idea that voluntarily benching is stochastically dominated, but it’s important to explain why coaches hold their options specifically until the last part of the game. Erik Brynjolfsson’s idea, for example, is good but it doesn’t do that. I’d suggest something on these lines: the “most important” shots are the ones taken at the end of the game. If the team ends up losing by a single point, maybe someone muffed a shot early on, but he isn’t the one to blame for losing the game. The player who’s really responsible (and feels terrible) is the one who missed his shot just before the buzzer sounded. So you want to make sure that your best players are available for the “crucial” last shots.
This decision fallacy is almost never studied. One article is Norm Theory, Comparing Reality to its Alternatives, by Kahneman and Miller in Psychological Review, 1986, but I know of almost no others.
May 11, 2010 at 12:35 pm
Josh Sher
I have always thought that its pretty rediculous how players are pulled out of the game for long periods of time which foul trouble. Now, there are a couple of considerations that you did not mention. First, is that the marginal utility of a player depends on who else is on the floor. As an example, supposse you have only 2 scorers on your team, and your teams offensive efficiency (points per possession) is:
55% with both
53% with just the star
49% with just the 2nd scorer
40% with neither
Further, to simplify, suppose there are 12 minutes left, and the 2nd scorer needs at least 2 different 2 minute rests. Optimal deployment of your resources is not to maximize the time played by the star. Having the star available for certain periods of time is more valuable than others.
The second comment is that, there is actually a third strategy in deploying your resourses. You can have your player in foul trouble adjust his defense (or you can adjust your teams defense) to decrease the probability that the given player commits a foul, at the expense of increasing the opponents offensive efficiency.
Having said all that, yes some times are more important than others for a given player to be available, but often its not nearly as large an effect as it is in my example above and the first order condition of trying to maximixe the amount of (non-tierd) time the player plays is usually the most important thing.
May 11, 2010 at 3:29 pm
Ludwig
Suppose the star player gets in foul trouble v early in the game, picks up 5 fouls in the first 5 mins or so when everyone else just has 1 or 2.
Then the other team would make every attempt to draw that 6th foul from him risking offensive fouls themselves.
However, if he sits out and comes back on for the last 5 minutes of the game he will (most likely) face players who by then also have 4 or 5 fouls and thus wont risk an offensive foul just to get him fouled out.
the point is that a star player who gets in foul trouble early in the game faces more aggressive oponents if he stays on than if he sits out and returns for the last 5 mins of the game (total playing time in this model would be the same assuming that it wouldn’t take him much longer than 5 mins to pick up the next foul if he stays on)
May 12, 2010 at 12:14 am
When should you bench a player in foul trouble? « Beneath The Pitch
[…] should you bench a player in foul trouble? (In basketball, that is.) You shouldn’t, says Jonathan Weinstein at Leisure of the Theory […]
May 12, 2010 at 10:44 pm
Tim VH
uninformed, embarassingly silly article. here’s why:
> foul calls by ref’s come in bunches, such that taking a guy out for some period of time may cool things off (ref’s are human…examples: Rasheed Wallace, Dennis Rodman, Alonzo Mourning);
> it’s all about individual MATCH – UP’s!! Taking out your center after 3 or 4 fouls covering Shaq allows you to put him back in when Shaq is out of the game (as Shaq only plays @ 20 mins p.g. at his age)…..VERY APPLICABLE his post-season with Noah, Perkins, Davis, etc. So, taking a guy out or not depends on whom else individually on the other team your guy is in there against;
> SUBSTITUTIONS — it’s reasonable to sit a guy with foul trouble if the guy substituting for him is roughly as good. But let’s say that the roughly as good substitute has some other problem (he himself has lots of fouls, or injured, or playing poorly, etc.)….it depends;
> Depends predominantly on strategy at the moment: small line-up to run the floor & fast-break?? defensive intensity, not trying to score too much?? Half court set offense to isolate a dominant post-player?? Whether to remove a foul-prone player after the N-th foul is, as much as anything, a function of (a) fit with current strategy, (b) alternative substitutions to fit the current strategy, (c) whether the coach will stick with the current strategy.
I note that you make gleeful exclamations about what coaches don’t understand — that, all else being equal, all minutes are equal.
Perhaps your time is better utilized understanding what you’re trying to analyze.
May 14, 2010 at 7:49 am
Friday Links: Water Walking Edition
[…] Great analysis on foul trouble in basketball games. I love articles such as these, basically saying ‘the conventional wisdom is stupid.’ […]
May 14, 2010 at 8:53 am
Analyzing Foul Trouble (Kellogg School of Mangement) « Bowdoin Daily Sun
[…] […]
May 14, 2010 at 10:59 am
Trent Hamm
You are forgetting about marketing value. What has more value to the NBA: Kobe Bryant taking the last shot or Luke Walton taking the last shot because Kobe has fouled out? It doesn’t matter that Walton might be more likely than Bryant to nail the shot. What matters is the marketing dollars and the television contracts and the people in the seats who paid good money to be entertained and they have been marketed to respond with much more attention and passion to Kobe rather than Luke Walton. The coaches know very well where their bread is buttered and it’s buttered by marketing stars and selling jerseys. The same thing happens at almost every level: the fans know the stars and expect those stars to be on the floor at the peak of the game and the end of the game – the peak-end rule at work.
May 14, 2010 at 10:41 pm
Swirsky's Soldier
the strategic use of fouls should also be considered (ie. prevent a fast break, foul to give with a few secs left on the clock, fouls to stop the clock). These may not be available if a player is in foul trouble.
There are many reasons why a player should play or should sit when in foul trouble. But there is a reason coaches do what they do and have throughout time…. because it works and tends to be more effective than the alternative. (no matter how much we want to believe they are wrong)
May 15, 2010 at 12:07 pm
The 10-man rotation, starring Tony Allen on Antawn Jamison (Yahoo! Sports) | NBA Dunk
[…] SLAM. Antawn Jamison(notes) was bad against the Celtics, especially on this play.PF: LotTC. Lots of words on whether or not teams should pull players in foul trouble.SF: FanHouse. Shoals on […]
May 17, 2010 at 4:37 am
beelpa
It’s important that the players on the court at the end of the game have fouls to “give.” Fouling stops the clock and potentially gives you the ball back. This strategic use of fouls should absolutely be considered in your analysis.
May 21, 2010 at 8:47 am
The Friday Promise…
[…] wrote this yesterday(via The Leisure of the Theory Class) about coaches sitting star players because of theoretical foul trouble. we love smart around here, […]
May 25, 2010 at 7:24 am
me
I agree, players are benched too quickly, especially when they get their second foul.
But…..
Players are less productive when they are in foul trouble, both offensively and defensively.
Driving to the basket, they will worry about getting a foul on a charge.
They won’t rebound as well, as they will worry about an over the back call.
On defense, they will not be as effective guarding a player.
They won’t help out on defense as much, which is where many fould occur.
January 11, 2011 at 5:50 pm
Ben
Some evidence for this found recently:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1736633
June 1, 2010 at 5:35 pm
youdie74
@ Trent Hamm.. I agree with you that there is bussiness industry in sport game like basket ball
April 18, 2011 at 7:22 pm
Why NBA coaches unnecessarily bench players in foul trouble | SNY Why Guys
[…] Here’s an explanation from Northwestern Economist Jonathan Weinstein: Suppose I simply want to maximize the number of minutes my star player is in the game. When should I risk putting him back in the game after his nth foul? It’s a trick question: I shouldn’t bench him at all! Those of you who haven’t been brainwashed by the conventional wisdom on “foul trouble” probably find this obvious. The proof is simple: if he sits, the only thing that has changed when he gets back in is that there is less time left in the game, so his expected minutes have clearly gone down. In fact, the new distribution on minutes is first-order stochastically dominated, being just a truncation of the alternative. This assumes only that his likelihood of getting a foul is time-invariant, which seems reasonable. […]
December 26, 2011 at 5:56 am
Leisure for all
The Planet will be much improved when people took more time for leisure