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

▶
a simple bayesian game prediction model
SMART_READER_LITE
LIVE PREVIEW

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

Aug 22, 2023 562 likes •850 views

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 +

slide-1
SLIDE 1

A Simple Bayesian Game Prediction Model

By: Jake Flancer

slide-2
SLIDE 2

The Motivation

2

Quantify Team Performance With Uncertainty Estimates Using Limited Data

slide-3
SLIDE 3

Bayesian Statistics

  • Incorporating beliefs not “in” data
  • Prior “padding” data + Observed data = Estimate
  • Parameters under uncertainty

3

slide-4
SLIDE 4

Using the Poisson Distribution

4

slide-5
SLIDE 5
  • Prior: Gamma(𝛃, 𝜸)
  • Data: Goals Scored = Poisson
  • Posterior: Gamma(𝛃+Goals, 𝜸+GP)

Poisson-Gamma Conjugacy

5

https://www4.stat.ncsu.edu/~reich/st590/code/PoissonGamma

slide-6
SLIDE 6

Team A: 1 Game / 5 Goals Scored Team B: 50 Games / 250 Goals Scored Which team is better at scoring?

How does this help?

6

slide-7
SLIDE 7

How does this help?

7

slide-8
SLIDE 8

Translating to Hockey...

  • Using two team specific parameters
  • Goals For Per Game (GF Rate)
  • Goals Against Per Game (GA Rate)

8

slide-9
SLIDE 9

Prior Distribution

  • Gamma(“Prior GF”, “Prior GP”)
  • Previous Season Regressed to League Average
  • 20 Games of “Padding”

9

slide-10
SLIDE 10

Prior Distribution

10

slide-11
SLIDE 11
  • 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)

Posterior Distribution

11

slide-12
SLIDE 12

Posterior Distribution

12

slide-13
SLIDE 13

Posterior Distribution

13

slide-14
SLIDE 14

Posterior Distribution

14

slide-15
SLIDE 15

Prior Distribution

15

slide-16
SLIDE 16

Posterior Distribution

16

slide-17
SLIDE 17

Interpreting the Posterior

17

slide-18
SLIDE 18
  • Posterior only yields P(Team A > Team B)
  • Make probability statements about team parameters
  • “The distribution of the expectation”

18

Current

slide-19
SLIDE 19
  • Estimate Game Outcomes
  • “The distribution of the outcomes”

19

Goal

slide-20
SLIDE 20

Game Prediction

20

slide-21
SLIDE 21

Game Prediction

21

slide-22
SLIDE 22

Game Prediction

22

slide-23
SLIDE 23

Game Prediction

23

*Home Advantage Added

slide-24
SLIDE 24

Game Prediction

24

slide-25
SLIDE 25
  • 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)

Key Assumptions and Issues

25

slide-26
SLIDE 26

In Summary

  • Team level uncertainty estimates
  • Make straightforward probabilistic team comparisons
  • Game outcome distributions
  • Works with limited data
  • Cool plots!

26

slide-27
SLIDE 27

Thank You!

Feel Free To Reach Out

jflancer@wharton.upenn.edu @jakef1873 github.com/jflancer/gameModel Use even-strength.com!!!

27

slide-28
SLIDE 28
  • Data via nhl.com
  • “Full” Presentation (w/ math): https://tinyurl.com/RITgamemodel

Appendix

28