Let me just open this by saying that of all the major sports to which I have devoted strategic thought, my opinions on baseball strategy are probably the most well-formed, with football a distant second and basketball an even more distant third.
With that disclaimer out of the way, I've always thought the behavior of basketball coaches in one particular area of the game somewhat odd: benching players after accumulating a certain number of fouls.
***Disclaimer 2: I have no data supporting the assertions made in this paragraph*** If a player accumulates 2 fouls within the first couple minutes of the game, he is often benched. If at any point during the first half he accumulates 3 fouls, foolish is thought the coach that fails to bench this player for the greater part of the half's remainder. And, like Devan Downey at the mid-point of the second half against Florida, a player that acquires a fourth foul in a close game is sure to see the bench until the game is getting close to its end.
To make sense, this modus operandi would have to assume at least one of the following:
1) Benching the player will ultimately increase the amount of his playing time
2) Having the player available late in the game is more important than having him available at any other time
3) Players are less effective when they have a large number of fouls relative to the time elapsed in the game
I don't really see how you could make an argument that #1 is true, so I will omit analyzing it in detail. It seems to me that the act of benching such a player merely shifts his contribution to the team along a timeline and may inadvertently cut short the potential impact that he may have on the game.
Imagine a world in which athletes do not get fatigued. Player X can play 38 minutes before committing 5 fouls. But when Player X commits his fourth foul, the coach takes him out of the game for five minutes before subbing him back in for the last four minutes of the game. In this scenario, Player X is only on the floor for 35 minutes instead of 38 minutes. After all, neither the coach nor the player can know when he will commit his fifth and final foul.
For the decision to pay off in this scenario, the player's contribution in the final two minutes would need to be at least 1.75 times as valuable as his contribution from the 9 minute mark to the four minute mark*. I'm having difficulty coming up with a possible reason that the final two minutes would be that much more valuable. After all, aren't points scored or prevented in the first minute of the game just as valuable as points scored or prevented in the final minute of the game?
The only real problem that I see with my theory is that players might not perform at their peak level when they are saddled with a large number of fouls for a fear of the consequences of committing subsequent fouls. But I feel that, to some extent, this fear may be exacerbated by the prevailing coaching heuristic in which players with a certain number of fouls at a certain point in the game get sent to the bench.
To summarize: if players are much less effective when they have a large number of fouls and/or it is much more valuable to have a player available at the end of the game than at any other time, then benching players with fouls is a good idea. But those gains would have to be so large (if they exist) that they would outweigh the cost of potentially shortening the amount of time the player is on the floor.
Thoughts? Criticisms?
*Am I thinking about this right? With 9 minutes to go in the game, you could bench the player for 5 minutes (9-5=4) or let the player foul out (9-2=7), giving 7/4=1.75
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5 comments:
I've often wondered the same thing. I would think that the greatest expected value for playing time would be achieved by leaving a player in until he fouls out. In the case of Devan Downey, the number of fouls he had didn't seem to affect his play (or else he would not have continued to foul, especially that cheap reach-in!). Florida's 8-1 run late in the game that proved to be the difference occurred when Downey was on the bench with four fouls.
However, Darrin Horn's defensive scheme requires that players be willing to risk fouling. You can't come away with as many blocks and steals as USC does without also frequently risking foul (especially considering the frustrating frequency of clean plays that are called fouls).
Today, I wish that USC could hit free throws and I am thankful that I also have UConn to cheer for.
You know I was thinking the exact same thing when I was watching the game last night. But I came to a little different conclusion. (Before you read further note that my knowledge of basketball is extremely limited) It would appear that playing at the end of the game is indeed more valuable than playing at any other point in the game. Witness Devan Downey's 11 points in the last minute or so. The last two minutes of a college basketball game seem to last forever. Each play is magnified in importance as each player tends to give his maximum effort. Thus, it would stand to reason that you would, in fact, want your best players in at the end of the game. Now, this theory falls apart if the entire game is played with the same intensity as the last two minutes. However, I think we can safely say that that is the case in few, if any, games.
Not to say that I disagree with your logic (lots of times I wish coaches would leave the players in!), but another way in which the end of the game is more valuable: At the end of the game, teams are more likely to foul in an effort to get the ball back. Having as many players with high FT% in at the end (especially players that will get the ball in their hands) could definitely prove to result in more baskets, provided they get fouled.
To make that free throw case, you would probably have to assume that we would be leading in the final minutes (but not necessarily).
Then, it's not likely that he'll be fouled more than 4 times during that period. Supposing that all of these fouls yield 2 free-throw attempts, that's six points.
Assume that Downey is replaced after fouling out by Brandis Raley-Ross, a 66% free-throw shooter. If he is fouled 4 times in Downey's place, he still gets only 8 attempts, netting 5.33 points, leaving you a difference of .67 points.
Again, real game situations may vary from the one I've created, but I think four fouls in the final minute is A LOT.
I think the lost playing time would probably be worth more than .67 points allowed or prevented by Downey
Whoops. I forgot to include that Downey is a 75% free-throw shooter.
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