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How Much Trouble is Early Foul Trouble? -- An interesting mathematical analysis

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Old Jan 9, 2011, 03:11 PM   #1
Mark Seifert
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This link caught my eye on one of the coder twitter feeds I follow. It's based on NBA data, but fun stuff nonetheless:

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Abstract:
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.
And a tidbit from the paper itself:

Quote:
A hypothetical coach who plays on average two starters through foul trouble for the second half of the third quarter rather than playing them without foul trouble for the first half of the fourth quarter in otherwise close games would hurt his probability of winning by about six percent. Thus in expectation over an 82-game regular season of otherwise close games he would lose about five games that he could have won by yanking his foul-troubled starters.
You can grab the full paper here.
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Old Jan 9, 2011, 10:46 PM   #2
AzIlliniFan
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I read (most of) that paper. It made my brain hurt . It is an interesting concept but to determine if it truly holds water I think they need to factor in some/all of the additional factors they noted in closing.
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Old Jan 9, 2011, 11:43 PM   #3
Illest
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Thanks for the link. It's an interesting paper. The big problem is that their methodology doesn't account for endogeneity -- the fact that coaches may select to play starters or not play starters for reasons which are not taken into account in the rest of the regression (like the position that the starters play, injuries to reserves, fatigue to the team which suggest that you "can't afford to take the starter out", etc.)

These sources of endogeneity should produce the result that they found. For instance, if your starters are much better than your bench, then, since starters have played a higher share of team minutes earlier in the game, early leads are effectively smaller for teams which will also prefer to keep their starters in the game with foul trouble, which will appear in their regression as a negative coefficient on the variable FTR, which the authors interpret as meaning that leaving starters in the game with foul trouble is a bad decision.

Or, as most basketball fans would attest, coaches are more likely to leave their starters in the game if they think their team's position is less advantageous, so that, if coaches can judge their team's position by more than just the score, then teams with lower probabilities of winning should be more likely to keep their starters in the game -- leading to a negative coefficient on FTR that, like I say, is interpreted by the authors as evidence for causality in the other direction. Furthermore, if coaches in disadvantageous positions are more likely to leave in their starters, that would explain why they find a correlation between winning percentage and yanking starters.

Short version: Interesting analysis, but they've demonstrated a correlation between losing and leaving starters in the game without demonstrating that leaving starters in actually causes losing.
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Old Jan 10, 2011, 07:11 AM   #4
DaytonIllini
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Quote:
Originally Posted by Illest View Post
Thanks for the link. It's an interesting paper. The big problem is that their methodology doesn't account for endogeneity -- the fact that coaches may select to play starters or not play starters for reasons which are not taken into account in the rest of the regression (like the position that the starters play, injuries to reserves, fatigue to the team which suggest that you "can't afford to take the starter out", etc.)

These sources of endogeneity should produce the result that they found. For instance, if your starters are much better than your bench, then, since starters have played a higher share of team minutes earlier in the game, early leads are effectively smaller for teams which will also prefer to keep their starters in the game with foul trouble, which will appear in their regression as a negative coefficient on the variable FTR, which the authors interpret as meaning that leaving starters in the game with foul trouble is a bad decision.

Or, as most basketball fans would attest, coaches are more likely to leave their starters in the game if they think their team's position is less advantageous, so that, if coaches can judge their team's position by more than just the score, then teams with lower probabilities of winning should be more likely to keep their starters in the game -- leading to a negative coefficient on FTR that, like I say, is interpreted by the authors as evidence for causality in the other direction. Furthermore, if coaches in disadvantageous positions are more likely to leave in their starters, that would explain why they find a correlation between winning percentage and yanking starters.

Short version: Interesting analysis, but they've demonstrated a correlation between losing and leaving starters in the game without demonstrating that leaving starters in actually causes losing.
Not to be argumentative but...
Isn't that a fundamental limitation of all retrospective analysis? That is demonstrating correlation but not necessarily causation? It would be very hard I think to design a study to prove this to be the case.
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Old Jan 10, 2011, 02:35 PM   #5
Illest
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Originally Posted by DaytonIllini View Post
Not to be argumentative but...
Isn't that a fundamental limitation of all retrospective analysis? That is demonstrating correlation but not necessarily causation? It would be very hard I think to design a study to prove this to be the case.
It's a fundamental obstacle to all retrospective analysis. You can get around it in some situations with various tools. In this case, you would probably want to either use instrumental variables or else construct a dynamic optimization problem from micro variables and then solve for parameters based on the data.
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Old Jan 10, 2011, 03:00 PM   #6
DaytonIllini
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That is above my pay grade!
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Old Jan 10, 2011, 03:01 PM   #7
illynifan34
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Nerd alert.
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Old Jan 10, 2011, 03:28 PM   #8
Selfconfour
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Quote:
Originally Posted by illynifan34 View Post
Nerd alert.
It was my understanding there would be no math on this message board.
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Old Jan 10, 2011, 04:51 PM   #9
Mark Seifert
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Originally Posted by Selfconfour View Post
It was my understanding there would be no math on this message board.
HA! Waitaminute, what school did we go to...? There just may be nerds on this board. Maybe. :laugh:
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Old Jan 10, 2011, 06:01 PM   #10
illinicb
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Quote:
Originally Posted by Illest View Post
It's a fundamental obstacle to all retrospective analysis. You can get around it in some situations with various tools. In this case, you would probably want to either use instrumental variables or else construct a dynamic optimization problem from micro variables and then solve for parameters based on the data.
Can I borrow your notes from class?
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Old Jan 11, 2011, 07:00 AM   #11
chriscesco
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My Head Hurts

This thread is not for those of us that spent college "fat, drunk and stupid"....
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Old Jan 11, 2011, 04:18 PM   #12
Botb9
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Correlation is not causation. For me, 6% isn't a significant difference in your chances.
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