MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV....

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SALO Intro MARKOV The Matrix Results MARKOV The New Road to WAR Gordon Arsenoff 2018-08-10 Gordon Arsenoff MARKOV

Transcript of MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV....

Page 1: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

MARKOVThe New Road to WAR

Gordon Arsenoff

2018-08-10

Gordon ArsenoffMARKOV

Page 2: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

SALO 2.0: Bayesian ordered logit for SoG and penalties

Pr(away shot) = Λ(αsa − Xβs − Zγs)Pr(home shot) = Λ(αsh + Xβs + Zγs)

Pr(away pen) = Λ(αpa − Xβp − Zγp)Pr(home pen) = Λ(αph + Xβp + Zγp)

(likelihood)

γs ∼ N(0, σs) γp ∼ N(0, σp) (prior)

GP ∼ BB(82, αG + γsβG , φ) ([name?])

Gordon ArsenoffMARKOV

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SALO Intro MARKOV The Matrix Results

WAR: combining multiple abilities into an overall value

Gordon ArsenoffMARKOV

Page 4: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

cWAR linearly maps micro ability to macro results

Ability Events Goals Wins

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SALO Intro MARKOV The Matrix Results

Wins (added) aren’t linear in goals (added)G <- (0:100) / 100W <- skellam::pskellam(-1, (1 - G) * 6, G * 6)W <- W / (1 - skellam::dskellam(0, (1 - G) * 6, G * 6))

0.00

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1.00

0.00 0.25 0.50 0.75 1.00

GF%

W%

I bWAR 2.x accounts for thisGordon ArsenoffMARKOV

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SALO Intro MARKOV The Matrix Results

Goals (added) aren’t (globally) linear in ability, either!

Ability Events

Goals

Score Effects

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SALO Intro MARKOV The Matrix Results

A Markov chain randomly changes state in discrete timeaccording to a matrix of transition probabilities

M =[

Mjj MjkMkj Mkk

]

Gordon ArsenoffMARKOV

Page 8: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

Markov property: Distribution of Yt given Y0 equals M t

Gordon ArsenoffMARKOV

Page 9: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

SALO defines a game state space and transition matrix

Period

Lead

Strength

Gordon ArsenoffMARKOV

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SALO Intro MARKOV The Matrix Results

Transition matrices defined separately for each period

M∗ = (M1)2400 × (M2)2400 × (M3)2400

Gordon ArsenoffMARKOV

Page 11: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

Lead change prob. is SALO shot prob. × (constant) Sh%

Gordon ArsenoffMARKOV

Page 12: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

Penalties, PPG, and expiration cause strength changes

Gordon ArsenoffMARKOV

Page 13: MARKOV - The New Road to WAR · 2018-08-13 · Corsica WAR Rates + Pen / 82 GordonArsenoff MARKOV. SALO Intro MARKOV TheMatrix Results \begin{appendix} GordonArsenoff MARKOV. Title:

SALO Intro MARKOV The Matrix Results

Assumptions are added for finiteness and completeness

I M is cropped to 135 × 135 (15 leads, 9 strength states)I Average ice time: forwards 15:00, defensemen 20:00I Model-based replacement player

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SALO Intro MARKOV The Matrix Results

Top players mostly D (ice time assumption is severe)

season player pos mean sd

20152016 KRIS LETANG D 4.055 1.55020152016 PAVEL DATSYUK C 3.916 1.26720132014 MARK GIORDANO D 3.880 1.57220152016 JAKE MUZZIN D 3.741 1.58220152016 HAMPUS LINDHOLM D 3.740 1.57320152016 COLTON PARAYKO D 3.727 1.57420142015 PATRICE BERGERON C 3.701 1.25820172018 RADKO GUDAS D 3.449 1.60220152016 OLIVER EKMAN-LARSSON D 3.382 1.54720152016 CARL HAGELIN L 3.356 1.248

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SALO Intro MARKOV The Matrix Results

WAR is almost linear in shots and unrelated to penaltiesgamma_p gamma_s

−0.08 −0.04 0.00 0.04 −0.10 −0.05 0.00 0.05 0.10 0.15−2

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OV

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SALO Intro MARKOV The Matrix Results

Corsica WAR is not quite linear in MARKOV WAR

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SALO Intro MARKOV The Matrix Results

https://www.salohockey.net

\begin{appendix}Gordon ArsenoffMARKOV