FALL 2025

AUTHOR

Anirudh Sengupta, Ardrey Kell High School

ABSTRACT

Intentionally fouling a team during their offensive possession is a strategy that basketball teams have employed for many years. Though popularized in the National Basketball Association (NBA), the technique has also made its way into Collegiate Basketball in recent years. The purpose of intentionally fouling is often to slow down opponent scoring and expose poor free-throw (FT) shooters. Despite previous studies using Markov Chains or analyzing intentional fouling in the NBA, there is a lack of research combining these methods with collegiate men’s basketball rules, particularly the one-and-one bonus.

This paper will examine the optimal times to start intentionally fouling when trailing, using Markov Chains and additional statistical analysis of data from the National Collegiate Athletic Association Division 1 Men’s Basketball (NCAA D1 MBB). Additionally, this study will account for the Bonus and Double Bonus rules specific to NCAA Men’s Basketball. Play-by-play data was compiled from over 4,000 games in the 2024-25 season to calculate statistics that would help identify the probabilities of different plays. Transition matrices were created to determine the expected points in a possession with and without fouls.

By categorizing data based on the time remaining in the game, the expected points for all Division 1 teams in various situations were calculated, enabling the development of a strategy to identify the optimal time for a team to benefit from fouling. The specific examples of the Florida Gators, Alabama Crimson Tide, and App State Mountaineers demonstrate that the optimal time to start fouling changes based on the opposing team. Additionally, the matrices were used to calculate the maximum FT% of a player for which it would be optimal to foul, rather than to give up a possession.

While situations change on a game-by-game basis, the graphs created in this study will provide a general idea of when teams are expected to score fewer points in free throw situations compared to offensive possessions.