Preprint / Version 1

College Basketball: An In-depth Study of the “Foul Up 3” Dilemma


  • Julian Zapata-Hall The Ohio State University



Basketball, college, Decision Making, sport coaching, strategy, strategic fouling, up 3


To foul or not to foul? Within college basketball, the decision to foul or not with a 3-point lead (the foul up 3 dilemma) significantly affects teams. For example, a single fouling decision can directly determine the outcome of a game or even an entire season. Within this study, I take a novel look at the foul up 3 dilemma, which was previously studied within a single interval of time remaining on the game. As opposed to adjusting in such a way, I study the foul up 3 dilemma across time. Moreover, in this study, I consider time as a two-dimensional variable (time remaining on the game clock, time remaining on the shot clock) because of the relevance of both clocks in college basketball. My research focuses on generating a coachable strategy that outlines the superior fouling decision for many different time combinations.

To achieve coachability, I sent a survey to more than 3,100 men's college basketball coaches across the country, which helped me understand the different fouling strategies and the restrictions coaches face when fouling. Based on the fouling strategies received, I divide the final 21 seconds remaining on the game clock and shot clock into 34 cells for analysis. Play-by-play (PBP) data from the 2010 to 2022 seasons of NCAA Division 1 Men's Basketball (MBB) are collected from the NCAA website to inform the study.

I calculate overtime-adjusted win percentages regarding two possible fouling decisions: foul and no foul, for each cell. The decision associated with the highest calculated overtime-adjusted win percentage is the recommended fouling decision for that cell. Additionally, I discuss the viability of a third possible fouling decision: the lane violation method. All code, data and detailed instructions are available at to facilitate reproducibility.

The strategy I define here is coachable by any coaching staff in college basketball and is highly beneficial for the purpose of increasing winning in up 3 situations. The average gain associated with using the recommended strategy across all cells is 1.63 overtime-adjusted win percentage points.

Acknowledgements - This study would not be the same without the help of these great people:

Bob Walsh, Chris Murphy, Ken Pomeroy, Kevin Weckworth, Laurie Shaw, Roger Hoerl, Sebastian Kurtek,  Sudarshan Gopaladesikan and Wayne Winston


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Ezekowitz, J. (2010, August 24). Up Three, Time Running out, Do We Foul? The First Comprehensive CBB Analysis. The Harvard Sports Analysis Collective.

NCAA Publications. (2023a). 2023-24 Men’s Rules Book. NCAA Publications., 36-39. ISSN: 1042-3877.

NCAA Publications. (2023b). 2023-24 Men’s Rules Book. NCAA Publications., 48. ISSN: 1042-3877.

NCAA Publications. (2023c). 2023-24 Men’s Rules Book. NCAA Publications., 84-85. ISSN: 1042-3877.

NCAA Publications. (2023d). 2023-24 Men’s Rules Book. NCAA Publications., 95-96. ISSN: 1042-3877.

NCAA Publications. (2023d). 2023-24 Men’s Rules Book. NCAA Publications., 97-102. ISSN: 1042-3877.

Pomeroy, K. (2013, February 12). Yet Another Study about Fouling When Up 3. The Blog.

Pomeroy, K., & Safir, J. (2020, July 21). The guide to fouling when leading (or tied). The Blog.

Winston, W. L. (2012). Mathletics: How gamblers, managers, and sports enthusiasts use mathematics in baseball, basketball, and football. Princeton, NJ: Princeton University Press, 631-636. DOI: 9781400842070.