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# How Much Trouble is Early Foul Trouble?

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2011 5th MIT Sloan Sports Analytics Conference

2011 5th MIT Sloan Sports Analytics Conference

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• Talk through the coefficients and their meanings, discuss results, pointing out that t-stats are, as explained in previous slide, quite possibly conservative.

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• 1. March 4, 2011
How Much Trouble Is Early Foul Trouble?Presentation to the 2011 MIT Sloan Sports Analytics Conference
Allan MayminPhilip MayminEugene Shen
• 2. 1
The Cost of a Foul…
… is more than just the free throws
• 3. 2
Foul Trouble and “Q+1”
• Not all fouls are created equal. Compare:
• 4. Committing your 5th foul in the first quarter
• 5. Committing your 1st foul in the fourth quarter
• 6. “Q+1” is a simple measure
• 7. You are “in foul trouble” if you have more fouls than the current quarter.
• 8. 2 or more fouls in the first quarter
• 9. 3 or more fouls in the second quarter
• 10. 4 or more fouls in the third quarter
• 11. 5 or more fouls in the fourth quarter
• 3
Threshold Fouls vs. Yanks for the 2006-2007 season
• 12. 4
Table 1: Leaders in Fouls and Threshold Yanks and Non-Yanks for 2006-2007
Frequent Foulers for the 2006-2007 Season
• 13. 5
Foul-Troubled Starters: Yank or Keep?
Is a Starter in Foul Trouble?
2 or more fouls in Q1
3 or more fouls in Q2
4 or more fouls in Q3
5 fouls in Q4
Early in the game?
Deep bench?
NO
YES
YES
KEEP
YANK
YES
NO
NO
• 14. 6
Description of Data
• Tick-by-tick data from 2006-2007, 2007-2008, 2008-2009
• 15. Source: http://basketballgeek.com/data, maintained by Ryan J. Parker
• 16. 3509 games, processed versions of play-by-play data from ESPN.com and NBA.com
• 17. Definitions
• 18. STA is the net number of starters in the game (home minus away)
• 19. FTR is the net number of starters in the game with foul trouble, where foul trouble is defined by the “Q+1” criteria (home minus away)
• 20. When the game begins, each team has 5 starters without foul trouble:
• 21. STA(home) = STA(away) = 5 and FTR(home) = FTR(away) = 0
• 22. The initial net numbers are both zero:
• 23. STA = STA(home) – STA(away) = 0 and FTR = FTR(home) – FTR(away) = 0
• 24. If the home team has a starter in foul trouble, then the coach faces the following choice:
• 25. either keep the starter in the game (hence, increment FTR)
• 26. or yank the starter from the game (hence, decrement STA but leave FTR unchanged).
• 7
“Win Probability Model” Specification
• Estimates the probability of a team winning at any given point in time
• 27. Probability of winning = 𝒩𝐹𝑡/𝜎𝑡
• 28. Stern (1994)
𝐹𝑡=𝓁𝑡+1−𝑡𝜇
𝜎𝑡2=1−𝑡𝜎2
• Our model
𝐹𝑡=𝛼+𝛽𝓁𝓁𝑡+𝛽𝑃𝑃𝑡+1−𝑡𝜇+𝑖=129𝛽𝑖𝐷𝑖𝑡+𝛽𝑆𝑇𝐴𝑆𝑇𝐴𝑡+𝛽𝐹𝑇𝑅𝐹𝑇𝑅𝑡
𝜎𝑡2=1−𝛾𝑡

• 29. 8
“Win Probability Model” Pros and Cons
• 30. Incorporates effects of future consequences of actions, e.g. fouling out
• 31. Dependent variable is winning, which is what matters most
• 32. Easy to add other state information that might affect the probability of winning
• 33. Automatically dampens the effects of early game actions
• 34. Automatically lessens the importance of data points where the game has already been decided
• 36. Maximum likelihood estimation can be slow
• 37. Raw t-statistics overstated because of non-independence and need to be scaled down based on simulation estimates
• 9
“Win Probability” Results
𝐹𝑡=𝛼+𝛽𝓁𝓁𝑡+𝛽𝑃𝑃𝑡+1−𝑡𝜇+𝑖=129𝛽𝑖𝐷𝑖𝑡+𝛽𝑆𝑇𝐴𝑆𝑇𝐴𝑡+𝛽𝐹𝑇𝑅𝐹𝑇𝑅𝑡

• 38. 10
Win Probability Surface
• 39. 11
Playing Foul-Plagued Starters Reduces the Chance of Winning
• 40. 12
Conclusions
What should coaches do?
What should analysts do?
What should owners/GMs do?
𝐹𝑡=𝛼+𝛽𝓁𝓁𝑡
+𝛽𝑃𝑃𝑡
+1−𝑡𝜇
+1−𝑡𝛽𝐹𝑇𝑅𝐹𝑇𝑅𝑡+…
+(𝑌𝑂𝑈𝑅 𝑇𝐸𝑅𝑀 𝐻𝐸𝑅𝐸)
Examples:
Lineup strengths eg WP48
Fatigue factors eg court time
Two-guard, three-guard lineups
Why?To measure strategic impact, not just tactical impact.
Win Probability can complement and incorporate other advanced stats.

Incentive clauses:
Compare stat targets, health
targets, even plus/minus. Not
necessarily optimal or incentive-
compatible.
up all the increases in win prob
relative to replacement player…
decisions together:
Other state variables for home
entertainment.
• 41. 13
Bios: Allan Maymin
Mr. Allan Maymin is currently working on quantitative equity execution algorithms in his role as Quantitative Analyst/Developer at AllianceBernstein.
Prior to starting at AB, Mr. Maymin was an Assistant Trader on the exotic equity derivatives desk at SociétéGénérale.
Prior to SocGen, Allan was a Developer at Platinum Grove Asset Management.
Mr. Maymin has also previously worked on the Huggable, a robotic teddy bear companion built by the Personal Robots Group at the MIT Media Lab, and is a co-author on the associated research and patent application.
Mr. Maymin holds an MS in Financial Engineering from NYU-Polytechnic Institute and a BS in Mathematics from Boston University.
• 42. 14
Bios: Phil Maymin
Dr. Phil Maymin is Assistant Professor of Finance and Risk Engineering at NYU-Polytechnic Institute. He is also the founding managing editor of Algorithmic Finance. He holds a Ph.D. in Finance from the University of Chicago, a Master's in Applied Mathematics from Harvard University, and a Bachelor's in Computer Science from Harvard University. He also holds a J.D. from Northwestern California University School of Law and is an attorney at law admitted to practice in California. He has been a portfolio manager at Long-Term Capital Management, Ellington Management Group, and his own hedge fund, Maymin Capital Management.
As an editor for Basketball News Services, he was credentialed with the New Jersey Nets, and he wrote hundreds of articles on the NBA for hoopsworld.com. He was the Director of Marketing and Promotions for the inaugural issue of Swish Magazine and he holds a Basketball General Manager and Scouting Certificate from Sports Management Worldwide.
He is also an award-winning journalist, a former policy scholar for a free market think tank, a Justice of the Peace, a former Congressional candidate, a columnist for the Fairfield County Weekly and LewRockwell.com, and the author of Yankee Wake Up, Free Your Inner Yankee, Yankee Go Home, and NBA Mysticism: Prophecies Fulfilled and Fortunes Told. He was a finalist for the 2010 Bastiat Prize for Online Journalism.
His popular writings have been published in dozens of media outlets ranging from Forbes to the New York Post to American Banker to regional newspapers, and his research has been profiled in dozens more, including USA Today, Boston Globe, NPR, BBC, Guardian (UK), CNBC, Newsweek Poland, Financial Times Deutschland, and others. His research on behavioral and algorithmic finance has appeared in Quantitative Finance, Journal of Wealth Management, and Risk and Decision Analysis, among others, and his textbook Financial Hacking is due to be released by World Scientific in 2011
• 43. 15
Bios: Eugene Shen
Mr. Eugene Shen is a vice president and derivatives strategist at AllianceBernstein.
Prior to assuming his current role in 2009, Mr. Shen spent seven years at JD Capital Management, where he was a partner and portfolio manager. At JD, Mr. Shen helped manage a multi-strategy equity arbitrage fund and a volatility arbitrage fund.
Previous to JD, Mr. Shen spent three years as a strategist at JWM Partners and Long-Term Capital Management.
Mr. Shen has a MS from MIT's Sloan School of Management and a BA in Applied Mathematics and Economics from Harvard University, and passed general examinations in MIT’s Economics Ph.D. program.
Mr. Shen was born and raised in Houston, Texas, and graduated from Bellaire High School.
• 44. 16
Appendix/Backup Advanced Plus/Minus with Foul Variables
• Methodology
• 45. Replace team dummy variables with player dummy variables
• 46. The dependent variable is the change in score, rather than the probability of winning