A Simple Bayesian Game Prediction Model By: Jake Flancer The - PowerPoint PPT Presentation

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A Simple Bayesian Game Prediction Model By: Jake Flancer The Motivation Quantify Team Performance With Uncertainty Estimates Using Limited Data 2 Bayesian Statistics Incorporating beliefs not in data Prior padding data +

A Simple Bayesian Game Prediction Model By: Jake Flancer
The Motivation Quantify Team Performance With Uncertainty Estimates Using Limited Data 2
Bayesian Statistics ● Incorporating beliefs not “in” data ● Prior “padding” data + Observed data = Estimate ● Parameters under uncertainty 3
Using the Poisson Distribution 4
Poisson-Gamma Conjugacy ● Prior: Gamma( 𝛃 , 𝜸 ) ● Data: Goals Scored = Poisson ● Posterior: Gamma( 𝛃 +Goals, 𝜸 +GP) https://www4.stat.ncsu.edu/~reich/st590/code/PoissonGamma 5
How does this help? Team A: 1 Game / 5 Goals Scored Team B: 50 Games / 250 Goals Scored Which team is better at scoring? 6
How does this help? 7
Translating to Hockey... ● Using two team specific parameters ● Goals For Per Game (GF Rate) ● Goals Against Per Game (GA Rate) 8
Prior Distribution ● Gamma(“Prior GF”, “Prior GP”) ● Previous Season Regressed to League Average ● 20 Games of “Padding” 9
Prior Distribution 10
Posterior Distribution ● Gamma(“Prior GF” + Cumulative GF, “Prior GP” + Total GP) ● Game 0 (Prior): Gamma(60 + 0, 20 + 0) ● Game 10: Gamma(60 + 30, 20 + 10) ● ... ● Game 82: Gamma(60 + 246, 20 + 82) 11
Posterior Distribution 12
Posterior Distribution 13
Posterior Distribution 14
Prior Distribution 15
Posterior Distribution 16
Interpreting the Posterior 17
Current ● Posterior only yields P(Team A > Team B) ● Make probability statements about team parameters ● “The distribution of the expectation” 18
Goal ● Estimate Game Outcomes ● “The distribution of the outcomes” 19
Game Prediction 20
Game Prediction 21
Game Prediction 22
Game Prediction *Home Advantage Added 23
Game Prediction 24
Key Assumptions and Issues Goal scoring is not truly poisson (score effects) ● ○ 16% in OT, reality is 21% ● Parameters equally weighted Team strength stays the same (game 1 and game 82 equally weighted) ● 25
In Summary Team level uncertainty estimates ● ● Make straightforward probabilistic team comparisons ● Game outcome distributions Works with limited data ● Cool plots! ● 26
Thank You! Feel Free To Reach Out jflancer@wharton.upenn.edu @jakef1873 github.com/jflancer/gameModel Use even-strength.com!!! 27
Appendix - Data via nhl.com “Full” Presentation (w/ math): https://tinyurl.com/RITgamemodel - 28

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