The REAL Trouble With Foul Trouble

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https://content.linkedin.com/content/dam/business/talent-solutions/global/en_us/blog/2019/04/How-NBA-hires-top-coaches.jpg

Summary

Introduction

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https://www.basketball-reference.com/boxscores/pbp/201910220TOR.html

Establishing Some Ground Rules

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This bar chart shows the percentage of time a player gets immediately taken out after a foul. Blue represents players who either became or were in foul trouble on the foul, red represents players who fouled but did not become in foul trouble

How often does a player foul out?

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The image above shows the percentage of players who ended up fouling out of the game based on the quarter of the game as well as the number of fouls they had. The percentages are all low, showing a player fouling out is not a common event.

Assignment of Players

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This image shows the breakdown of the median percentile for each cluster for different categories

Fouls Per Minute Meets the Poisson Distribution

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https://www.onlinemathlearning.com/poisson-distribution.html
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The probability density function of a Poisson distribution with lambda equalling 2.4 and X equalling four
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The probability of fouling out of a game when a player has 2 fouls in a game and expects to play another 24 minutes with a foul rate of one foul every ten minutes
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Distribution of fouls per minute of players in each cluster

When A Player Should Actually Be Pulled

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This line graph shows the likelihood of a player fouling out if they were to play X more minutes depending on the number of fouls they have in the game as well as the cluster they belong to. Cluster 1 is a solid line, Cluster 2 is a dashed line, and Cluster 3 is the dotted line.

Conclusion

Appendix

Clustering

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The elbow method that was used to choose the number of clusters for the k-means clustering algorithm.

Poisson Distribution

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