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How Much Trouble is Early Foul Trouble? (ssrn.com)
25 points by cwan on Jan 9, 2011 | hide | past | web | favorite | 15 comments

I just downloaded and took a look at the paper. I've got a problem with it -- it is only looking at data from 2006-2009.

This is an issue, because of the way that benching starters has become conventional wisdom over the last 25 years. In fact, the foul out rate is down over 40% during that period (http://www.pistonpowered.com/2010/12/nba-players-are-fouling...).

So on one hand, yes, playing a starter in foul trouble could cause them to be less aggressive. On the other hand, I suspect there is VERY strong cultural bias that magnifies this.

I would imagine that an NBA team that has either veteran players or a very strong culture of understanding advanced statistics would be able to play as well when in foul trouble. (Think San Antonio, Boston, Dallas and Houston). I would also imagine that the evidence would not be as strong when looking at other time periods.

So it's an interesting observation, but it makes sense that coaches approach this issue on a case-by-case basis. Play Tim Duncan, bench Blake Griffin.

I've been hugely interested in doing some related interest in the sport of Football. I've found that the official stats provider of the NFL, Stats Inc, charges about $40,000 per year for API access to their stats.

Also, the paper reads like academic research, but the layout and citations look rather simple. What gives?

EDIT: Their data source is listed, skimmed over it.

I'd like to add the main author's page:


Looks like he has quite a bit of credentials and a huge interest in basketball. Very impressive.


We use a large dataset of play-by-play NBA data to determine when yanking foul-plagued starters is optimal by applying insights and tools from finance. We find that a team performs significantly worse if a starter with foul trouble is allowed to remain in the game, and that this effect is strongest in the third quarter. We use a novel win-probability technique that is sufficiently general to be useful for other questions simply by appropriately redefining the state variables. Thus, our two contributions are to introduce the new approach and also to demonstrate its usefulness by solving the problem of early foul trouble that had remained unaddressed in the academic literature.

Given the financial stakes at play in professional (and even amateur) athletics, I find it hard to believe that an analysis of optimal "play or sit" strategy wrt player fouls has "remained unaddressed" though a cursory search on Google Scholar didn't turn up much of anything in the way of a counter-example.

It's likely that an analysis has been done, but isn't public. Teams keep lots of advanced stats to themselves as a competitive advantage.

I didn't read this paper, but I never understood why players who get into foul trouble are pulled from games. I guess the only explanation is that players play differently after a few fouls. Otherwise, it doesn't make sense to take someone out so that you don't have to take them out in the future.

Few basketball games are blowouts. The logic of sitting your best player(s) in foul trouble is to hope that your bench can keep the game close so that your best player can win the game in the end.

Why not keep them out there and get a lead sooner, then hope to keep the lead if they do foul out?

I think the idea is that having a lead early versus late gives the opposition a more clear goal with the time to come back.

Basketball games and seasons are very long. Players won't be focused in the entire season or for entire games. Having a deficit to come back from, with the time to do it, gives them a clear objective to focus in on.

Say your star point guard and a center get ejected from the game because they got too many fouls in the middle of the game. This forces the coach to play with a smaller set of players when it matters in the last quarter. The coach wants to be able to put x person on y person on the other team because x matches up with y very well so playing without a full set of players is limiting.

I think the other guy's take is that points are points, regardless of when they occur.

But the other guy also correctly deduces the real issue... foul problems change how you play. You play more timidly. And I think it also results in the other team playing a form of basketball that is generally more desireable, which is to drop the ball into the blocks and try to draw a foul (its generally big men who get in foul trouble quicker than guards).

With that said, I think seeing this result is useful.

weaksauce's point should still be valid too, actually. Choice is power. Assume that by "star player" we're not talking Micheal Jordan but merely somebody who is the best player on the team; having them in reserve in the last quarter means the other team can't simply deploy a strategy that is built on the coach not being able to put that player back out. A bad chess analogy would be facing the choice of retreating your queen back to your home ranks or getting her captured, there is strategic value in just having her back there even if she is not currently in a powerful position. I say it's a bad analogy because basketball players are more complex than chess pieces, with more ways to be weak and strong, but the idea still holds.

Sorry for getting back to this so late. The problem is that your trading choice now (if you dogmatically apply the yank) for choice later. And unlike the queen, MJ on the bench doesn't directly affect the game on the floor. While the queen actually does, even in the backrow.

It's not quite true that having a couple key players on the bench in the middle of the game does not have a direct affect on the game. There are a few key things at play; one, the non key players might thrive during the middle of the game because there is less pressure on them to perform so they might score more than they would at the end of the game. Two, the defense during the middle of the game is not as intense as near the end where the stakes are higher. Three, the clutch players will probably sore more during the last moments of the game where there is more pressure for the win because they have years of experience at the end and generally do not fear the clutch shots.

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