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Introduction Expected Possession Value (EPV) Specifics of EPV Results Paper Review: A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes Lee Richardson Sports in Statistics Reading and Research Group Department of Statistics, Carnegie Mellon University November 28, 2017 1

Introduction Expected Possession Value (EPV) Specifics of EPV Results Introduction 1 Expected Possession Value (EPV) 2 Specifics of EPV 3 Results 4 2

Introduction Expected Possession Value (EPV) Specifics of EPV Results Basketball Statistics has gone through Three “Data Epoch’s” Box Score (Points, Rebounds, Assists, etc.) 1 Play-By-Play (Adjusted Plus Minus) 2 Player-Tracking Data 3 We have recently entered the third: Player-Tracking Data 3

Introduction Expected Possession Value (EPV) Specifics of EPV Results This Paper Introduces “Expected Possession Value” Expected Possession Value (EPV) is: A Real-Time Metric of Possession Value 1 Based on Player-Tracking Data 2 Expected Possession Value is analogous to “Win Probability” 4

Introduction Expected Possession Value (EPV) Specifics of EPV Results Defining Expected Possession Value X ( ω ) : Ω → [0 , 2 , 3], Points scored in possession ω ∈ Ω Z t ( ω ) ∈ Z , Tracking data at time t F Z t , Natural Filtration of Z (Everything in Z until time t ) 5

Introduction Expected Possession Value (EPV) Specifics of EPV Results Defining Expected Possession Value X ( ω ) : Ω → [0 , 2 , 3], Points scored in possession ω ∈ Ω Z t ( ω ) ∈ Z , Tracking data at time t F Z t , Natural Filtration of Z (Everything in Z until time t ) Let v t be Expected Possession Value (EPV) at time t : E [ X |F Z = t ] v t 5

Introduction Expected Possession Value (EPV) Specifics of EPV Results A “Coarse Model” Makes Estimation EPV Tractable A Discrete State Model for Basketball Possessions 6

Introduction Expected Possession Value (EPV) Specifics of EPV Results Combining the High Resolution and Coarse Models The author’s make the following simplifying assumptions and definitions: τ t : Time of next decoupling (shot, pass, etc) event δ t : Time decoupling event ends ( min ( s : s ≥ τ t , C s / ∈ C trans ) for all s > δ t , c ∈ C : P ( C s = c | C δ t , F Z t ) = P ( C s = c | C δ t ) These assumptions give a more tractable EPV: � E [ X | C δ t = c ] P ( C δ t = c | F Z v t = t ) c ∈C 7

Introduction Expected Possession Value (EPV) Specifics of EPV Results Four Transition Models used for EPV M ( t ): Event that a decoupling event ( τ t ) happens between ([ t , t + ǫ ]) 8

Introduction Expected Possession Value (EPV) Specifics of EPV Results Four Transition Models used for EPV M ( t ): Event that a decoupling event ( τ t ) happens between ([ t , t + ǫ ]) The first three models correspond to P ( C δ t = c | F Z t ): P ( Z t + ǫ | M ( t ) c , F Z t ): Player Movement Model P ( M ( t ) | F Z t ): Decoupling event in next ǫ time P ( C δ t | M ( t ) , F Z t ): Next “Coarse State” after Decoupling 8

Introduction Expected Possession Value (EPV) Specifics of EPV Results Four Transition Models used for EPV M ( t ): Event that a decoupling event ( τ t ) happens between ([ t , t + ǫ ]) The first three models correspond to P ( C δ t = c | F Z t ): P ( Z t + ǫ | M ( t ) c , F Z t ): Player Movement Model P ( M ( t ) | F Z t ): Decoupling event in next ǫ time P ( C δ t | M ( t ) , F Z t ): Next “Coarse State” after Decoupling Model four corresponds to E [ X | C δ t = c ]: P : Markov Transition Probabilities. P q , r = P ( C n +1 = c r | C n = c q ) 8

Introduction Expected Possession Value (EPV) Specifics of EPV Results The Player Movement Model Predicts Player Movement Works for offense with/without the ball and defense. For example: x l ( t + ǫ ) = x l ( t ) + α l x [ x l ( t ) − x l ( t − ǫ )] + η l x ( t ) Spatial Effect ( η l x ( t )) for offensive players on and off the ball 9

Introduction Expected Possession Value (EPV) Specifics of EPV Results Model Two Shows Spatial Structure of Decoupling Events t ) = � 6 P ( M ( t ) | F Z j =1 P ( M j ( t ) | F Z t ). j = 1 , 2 , 3 , 4 (pass), j = 5 (shot), j = 6 (turnover) Modeled with a “Competing Risks” model: P ( M j ( t ) | F Z t ) λ l = lim j ǫ ǫ → 0 log( λ l [ W l j ] ′ β l j + ξ l j ( z l ( t )) + (˜ j ) = ξ z j ( t )1 j ≤ 4 ) Spatial Likelihood’s of Decoupling events for LeBron James 10

Introduction Expected Possession Value (EPV) Specifics of EPV Results The model requires the following parameters β : Coefficients for hazards (Model Two) (e.g. nearest defender) ξ l j : Spatial effect for player (shot, pass, turnover) for player l ˜ ξ l j : Spatial effect for receiving pass p l ( t ) , ξ l s Shooting probabilities, spatial effect η l x , etc. from player movement model 11

Introduction Expected Possession Value (EPV) Specifics of EPV Results The model requires the following parameters β : Coefficients for hazards (Model Two) (e.g. nearest defender) ξ l j : Spatial effect for player (shot, pass, turnover) for player l ˜ ξ l j : Spatial effect for receiving pass p l ( t ) , ξ l s Shooting probabilities, spatial effect η l x , etc. from player movement model Some small comments on the estimation Parameter’s estimated using Hierarchical Models, and similarity Matrix H . Spatial Effects use a Basis Decomposition of a Gaussian Process Parameters Estimated using Partial Likelihoods and R-INLA 11

Introduction Expected Possession Value (EPV) Specifics of EPV Results “We view such (estimated) EPV Curves as the main contribution . . . ” 12

Introduction Expected Possession Value (EPV) Specifics of EPV Results Useful Summary Statistics can be Computed Using EPV Two Examples Given are: EPV-Added 1 Shot Satisfaction 2 13

Introduction Expected Possession Value (EPV) Specifics of EPV Results Conclusions This paper coherently models EPV using player tracking data Bayesian spatio-temporal hierarchical models are useful for complex Data Throws open the floodgates to more potential research 14