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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

1

Introduction

2

Expected Possession Value (EPV)

3

Specifics of EPV

4

Results

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

Basketball Statistics has gone through Three “Data Epoch’s”

1

Box Score (Points, Rebounds, Assists, etc.)

2

Play-By-Play (Adjusted Plus Minus)

3

Player-Tracking Data We have recently entered the third: Player-Tracking Data

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

This Paper Introduces “Expected Possession Value”

Expected Possession Value (EPV) is:

1

A Real-Time Metric of Possession Value

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Based on Player-Tracking Data

Expected Possession Value is analogous to “Win Probability”

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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 Zt(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 Zt(ω) ∈ Z, Tracking data at time t F Z

t , Natural Filtration of Z (Everything in Z until time t)

Let vt be Expected Possession Value (EPV) at time t: vt = E[X|FZ

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

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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: τt: Time of next decoupling (shot, pass, etc) event δt: Time decoupling event ends (min(s : s ≥ τt, Cs / ∈ Ctrans) for all s > δt, c ∈ C: P(Cs = c|Cδt, F Z

t ) = P(Cs = c|Cδt)

These assumptions give a more tractable EPV: vt =

• c∈C

E[X|Cδt = c]P(Cδt = c|F Z

t ) 7

Introduction Expected Possession Value (EPV) Specifics of EPV Results

Four Transition Models used for EPV

M(t): Event that a decoupling event (τt) happens between ([t, t + ǫ])

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

Four Transition Models used for EPV

M(t): Event that a decoupling event (τt) happens between ([t, t + ǫ]) The first three models correspond to P(Cδt = c|F Z

t ):

P(Zt+ǫ|M(t)c, F Z

t ): Player Movement Model

P(M(t)|F Z

t ): Decoupling event in next ǫ time

P(Cδt |M(t), F Z

t ): Next “Coarse State” after Decoupling

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

Four Transition Models used for EPV

M(t): Event that a decoupling event (τt) happens between ([t, t + ǫ]) The first three models correspond to P(Cδt = c|F Z

t ):

P(Zt+ǫ|M(t)c, F Z

t ): Player Movement Model

P(M(t)|F Z

t ): Decoupling event in next ǫ time

P(Cδt |M(t), F Z

t ): Next “Coarse State” after Decoupling

Model four corresponds to E[X|Cδt = c]: P: Markov Transition Probabilities. Pq,r = P(C n+1 = cr|Cn = cq)

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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: xl(t + ǫ) = xl(t) + αl

x[xl(t) − xl(t − ǫ)] + ηl x(t)

Spatial Effect (ηl

x(t)) for offensive players on and off the ball

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

Model Two Shows Spatial Structure of Decoupling Events

P(M(t)|F Z

t ) = 6 j=1 P(Mj(t)|F Z t ). j = 1, 2, 3, 4 (pass), j = 5 (shot), j = 6 (turnover)

Modeled with a “Competing Risks” model: λl

j

= lim

ǫ→0

P(Mj(t)|F Z

t )

ǫ log(λl

j)

= [Wl

j]′βl j + ξl j (zl(t)) + (˜

ξzj(t)1j≤4)

Spatial Likelihood’s of Decoupling events for LeBron James

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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) ξl

j: Spatial effect for player (shot, pass, turnover) for player l

˜ ξl

j: Spatial effect for receiving pass

pl(t), ξl

s Shooting probabilities, spatial effect

ηl

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) ξl

j: Spatial effect for player (shot, pass, turnover) for player l

˜ ξl

j: Spatial effect for receiving pass

pl(t), ξl

s Shooting probabilities, spatial effect

ηl

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

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

“We view such (estimated) EPV Curves as the main contribution . . . ”

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Introduction Expected Possession Value (EPV) Specifics of EPV Results

Useful Summary Statistics can be Computed Using EPV

Two Examples Given are:

1

EPV-Added

2

Shot Satisfaction

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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

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