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A Multiresolution Stochastic Process Model forBasketball Possession Outcomes
Dan Cervone, Alex D’Amour, Luke Bornn, Kirk Goldsberry
Harvard Statistics Department
August 11, 2015
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
NBA optical tracking data
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
NBA optical tracking data
(x , y) locations for all 10 players (5 on each team) at 25Hz.
(x , y , z) locations for the ball at 25Hz.
Event annotations (shots, passes, fouls, etc.).
1230 games from 2013-14 NBA, each 48 minutes, featuring 461 players intotal.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
NBA optical tracking data
(x , y) locations for all 10 players (5 on each team) at 25Hz.
(x , y , z) locations for the ball at 25Hz.
Event annotations (shots, passes, fouls, etc.).
1230 games from 2013-14 NBA, each 48 minutes, featuring 461 players intotal.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Expected Possession Value (EPV)
JamesshotNORRIS COLE POSSESSION
RASHARDLEWISPOSS.
LEBRON JAMES POSSESSION
EPV constant whilepass is en route
PassPass
Slight dip in EPV aftercrossing 3 point line
Slight dip in EPV aftercrossing 3 point line
Acceleratestowards basket
Runs behindbasket and
defenders close
Acceleratesinto the paint
Splits the defense;clear path to
basket
0.8
1.0
1.2
1.4
1.6
time
EP
V
0 3 6 9 12 15 18
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
EPV definition
Let Ω be the space of all possible basketball possessions. For ω ∈ Ω
X (ω) ∈ 0, 2, 3: point value of possession ω.
T (ω): possession length
Zt(ω), 0 ≤ t ≤ T (ω): time series of optical tracking data.
F (Z)t = σ(Z−1
s : 0 ≤ s ≤ t): natural filtration.
Definition
The expected possession value (EPV) at time t ≥ 0 during a possession is
νt = E[X |F (Z)t ].
EPV provides an instantaneous snapshot of the possession’s value, given itsfull spatiotemporal history.
νt is a Martingale: E[νt+h|F (Z)t ] = νt for all h > 0.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Calculating EPVνt = E[X |F (Z)
t ]
Regression-type prediction methods:
– Data are not traditional input/output pairs.
– No guarantee of stochastic consistency.
Markov chains:
+ Stochastically consistent.
– Information is lost through discretization.
– Many rare transitions.
Brute force, “God model” for basketball.
+ Allows Monte Carlo calculation of νt by simulating future possession paths.
– Zt is high dimensional and includes discrete events (passes, shots, turnovers).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Calculating EPVνt = E[X |F (Z)
t ]
Regression-type prediction methods:
– Data are not traditional input/output pairs.
– No guarantee of stochastic consistency.
Markov chains:
+ Stochastically consistent.
– Information is lost through discretization.
– Many rare transitions.
Brute force, “God model” for basketball.
+ Allows Monte Carlo calculation of νt by simulating future possession paths.
– Zt is high dimensional and includes discrete events (passes, shots, turnovers).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Calculating EPVνt = E[X |F (Z)
t ]
Regression-type prediction methods:
– Data are not traditional input/output pairs.
– No guarantee of stochastic consistency.
Markov chains:
+ Stochastically consistent.
– Information is lost through discretization.
– Many rare transitions.
Brute force, “God model” for basketball.
+ Allows Monte Carlo calculation of νt by simulating future possession paths.
– Zt is high dimensional and includes discrete events (passes, shots, turnovers).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
A coarsened process
Finite collection of states C = Cposs ∪ Cend ∪ Ctrans.
Cposs: Ball possession states
player × region × defender within 5 feet
Cend: End states
made 2, made 3, turnover
Ctrans: Transition states
pass linking c , c ′ ∈ Cposs,shot attempt from c ∈ Cposs,
turnover in progress,rebound in progress .
Ct ∈ C: state of the possession at time t.
C (0),C (1), . . . ,C (K): discrete sequence of distinct states.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
A coarsened process
Finite collection of states C = Cposs ∪ Cend ∪ Ctrans.
Cposs: Ball possession states
player × region × defender within 5 feetCend: End states
made 2, made 3, turnover
Ctrans: Transition states
pass linking c , c ′ ∈ Cposs,shot attempt from c ∈ Cposs,
turnover in progress,rebound in progress .
Ct ∈ C: state of the possession at time t.
C (0),C (1), . . . ,C (K): discrete sequence of distinct states.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
A coarsened process
Finite collection of states C = Cposs ∪ Cend ∪ Ctrans.
Cposs: Ball possession states
player × region × defender within 5 feetCend: End states
made 2, made 3, turnover
Ctrans: Transition states
pass linking c , c ′ ∈ Cposs,shot attempt from c ∈ Cposs,
turnover in progress,rebound in progress .
Ct ∈ C: state of the possession at time t.
C (0),C (1), . . . ,C (K): discrete sequence of distinct states.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
A coarsened process
Finite collection of states C = Cposs ∪ Cend ∪ Ctrans.
Cposs: Ball possession states
player × region × defender within 5 feetCend: End states
made 2, made 3, turnover
Ctrans: Transition states
pass linking c , c ′ ∈ Cposs,shot attempt from c ∈ Cposs,
turnover in progress,rebound in progress .
Ct ∈ C: state of the possession at time t.
C (0),C (1), . . . ,C (K): discrete sequence of distinct states.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Possible paths for Ct
Cposs
Player 1
Passto
P2 Player 2
Passto
P3 Player 3
Passto
P4 Player 4
Passto
P5 Player 5
Ctrans Turnover Shot Rebound
Cend Made 2pt Made 3pt End of possession
Figure 1: Schematic of the coarsened possession process C, with states (rectangles) and possiblestate transitions (arrows) shown. The unshaded states in the first row compose Cposs. Here, statescorresponding to distinct ballhandlers are grouped together (Player 1 through 5), and the discretizedcourt in each group represents the player’s coarsened position and defended state. The gray shadedrectangles are transition states, Ctrans, while the rectangles in the third row represent the end states,Cend. Blue arrows represent possible macrotransition entrances (and red arrows, macrotransitionexits) when Player 1 has the ball; these terms are introduced in Section ??.
1
τt =
mins : s > t,Cs ∈ Ctrans if Ct ∈ Cposs
t if Ct 6∈ Cposs
δt = mins : s ≥ τt ,Cs 6∈ Ctrans.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Possible paths for Ct
Cposs
Player 1
Passto
P2 Player 2
Passto
P3 Player 3
Passto
P4 Player 4
Passto
P5 Player 5
Ctrans Turnover Shot Rebound
Cend Made 2pt Made 3pt End of possession
Figure 1: Schematic of the coarsened possession process C, with states (rectangles) and possiblestate transitions (arrows) shown. The unshaded states in the first row compose Cposs. Here, statescorresponding to distinct ballhandlers are grouped together (Player 1 through 5), and the discretizedcourt in each group represents the player’s coarsened position and defended state. The gray shadedrectangles are transition states, Ctrans, while the rectangles in the third row represent the end states,Cend. Blue arrows represent possible macrotransition entrances (and red arrows, macrotransitionexits) when Player 1 has the ball; these terms are introduced in Section ??.
1
τt =
mins : s > t,Cs ∈ Ctrans if Ct ∈ Cposs
t if Ct 6∈ Cposs
δt = mins : s ≥ τt ,Cs 6∈ Ctrans.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Stopping times for switching resolutions
τt =
mins : s > t,Cs ∈ Ctrans if Ct ∈ Cposs
t if Ct 6∈ Cposs
δt = mins : s ≥ τt ,Cs 6∈ Ctrans.
Key assumptions:
A1 C is marginally semi-Markov.
A2 For all s > δt , P(Cs |Cδt ,F (Z)t ) = P(Cs |Cδt ).
Theorem
Assume (A1)–(A2), then for all 0 ≤ t < T,
νt =∑
c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Stopping times for switching resolutions
τt =
mins : s > t,Cs ∈ Ctrans if Ct ∈ Cposs
t if Ct 6∈ Cposs
δt = mins : s ≥ τt ,Cs 6∈ Ctrans.
Key assumptions:
A1 C is marginally semi-Markov.
A2 For all s > δt , P(Cs |Cδt ,F (Z)t ) = P(Cs |Cδt ).
Theorem
Assume (A1)–(A2), then for all 0 ≤ t < T,
νt =∑
c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Stopping times for switching resolutions
τt =
mins : s > t,Cs ∈ Ctrans if Ct ∈ Cposs
t if Ct 6∈ Cposs
δt = mins : s ≥ τt ,Cs 6∈ Ctrans.
Key assumptions:
A1 C is marginally semi-Markov.
A2 For all s > δt , P(Cs |Cδt ,F (Z)t ) = P(Cs |Cδt ).
Theorem
Assume (A1)–(A2), then for all 0 ≤ t < T,
νt =∑
c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Stopping times for switching resolutions
τt =
mins : s > t,Cs ∈ Ctrans if Ct ∈ Cposs
t if Ct 6∈ Cposs
δt = mins : s ≥ τt ,Cs 6∈ Ctrans.
Key assumptions:
A1 C is marginally semi-Markov.
A2 For all s > δt , P(Cs |Cδt ,F (Z)t ) = P(Cs |Cδt ).
Theorem
Assume (A1)–(A2), then for all 0 ≤ t < T,
νt =∑
c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Multiresolution models
EPV:νt =
∑c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Let M(t) be the event τt ≤ t + ε.M1 P(Zt+ε|M(t)c ,F (Z)
t ): the microtransition model.
M2 P(M(t)|F (Z)t ): the macrotransition entry model.
M3 P(Cδt |M(t),F (Z)t ): the macrotransition exit model.
M4 P, with Pqr = P(C (n+1) = cr |C (n) = cq): the Markov transition probabilitymatrix.
Monte Carlo computation of νt :
Draw Cδt |F (Z)t using (M1)–(M3).
Calculate E[X |Cδt ] using (M4).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Multiresolution models
EPV:νt =
∑c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Let M(t) be the event τt ≤ t + ε.M1 P(Zt+ε|M(t)c ,F (Z)
t ): the microtransition model.
M2 P(M(t)|F (Z)t ): the macrotransition entry model.
M3 P(Cδt |M(t),F (Z)t ): the macrotransition exit model.
M4 P, with Pqr = P(C (n+1) = cr |C (n) = cq): the Markov transition probabilitymatrix.
Monte Carlo computation of νt :
Draw Cδt |F (Z)t using (M1)–(M3).
Calculate E[X |Cδt ] using (M4).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Multiresolution models
EPV:νt =
∑c∈Ctrans∪Cend
E[X |Cδt = c]P(Cδt = c |F (Z)t ).
Let M(t) be the event τt ≤ t + ε.M1 P(Zt+ε|M(t)c ,F (Z)
t ): the microtransition model.
M2 P(M(t)|F (Z)t ): the macrotransition entry model.
M3 P(Cδt |M(t),F (Z)t ): the macrotransition exit model.
M4 P, with Pqr = P(C (n+1) = cr |C (n) = cq): the Markov transition probabilitymatrix.
Monte Carlo computation of νt :
Draw Cδt |F (Z)t using (M1)–(M3).
Calculate E[X |Cδt ] using (M4).
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Microtransition model
Player `’s position at time t is z`(t) = (x`(t), y `(t)).
x`(t + ε) = x`(t) + α`x [x`(t)− x`(t − ε)] + η`x(t)
η`x(t) ∼ N (µ`x(z`(t)), (σ`x)2).µx has Gaussian Process prior.y `(t) modeled analogously (and independently).
Defensive microtransition model based on defensive matchups[Franks et al., 2015].
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Microtransition model
Player `’s position at time t is z`(t) = (x`(t), y `(t)).
x`(t + ε) = x`(t) + α`x [x`(t)− x`(t − ε)] + η`x(t)
η`x(t) ∼ N (µ`x(z`(t)), (σ`x)2).µx has Gaussian Process prior.y `(t) modeled analogously (and independently).
TONY PARKER WITH BALL DWIGHT HOWARD WITH BALL
Defensive microtransition model based on defensive matchups[Franks et al., 2015].
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Microtransition model
Player `’s position at time t is z`(t) = (x`(t), y `(t)).
x`(t + ε) = x`(t) + α`x [x`(t)− x`(t − ε)] + η`x(t)
η`x(t) ∼ N (µ`x(z`(t)), (σ`x)2).µx has Gaussian Process prior.y `(t) modeled analogously (and independently).
TONY PARKER WITHOUT BALL DWIGHT HOWARD WITHOUT BALL
Defensive microtransition model based on defensive matchups[Franks et al., 2015].
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Microtransition model
Player `’s position at time t is z`(t) = (x`(t), y `(t)).
x`(t + ε) = x`(t) + α`x [x`(t)− x`(t − ε)] + η`x(t)
η`x(t) ∼ N (µ`x(z`(t)), (σ`x)2).µx has Gaussian Process prior.y `(t) modeled analogously (and independently).
TONY PARKER WITHOUT BALL DWIGHT HOWARD WITHOUT BALL
Defensive microtransition model based on defensive matchups[Franks et al., 2015].
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Macrotransition entry model
Recall M(t) = τt ≤ t + ε:Six different “types”, based on entry state Cτt ,∪6
j=1Mj(t) = M(t).
Hazards: λj(t) = limε→0P(Mj (t)|F (Z)
t )ε .
log(λj(t)) = [W`j (t)]′β`j + ξ`j
(z`(t)
)
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Macrotransition entry model
Recall M(t) = τt ≤ t + ε:Six different “types”, based on entry state Cτt ,∪6
j=1Mj(t) = M(t).
Hazards: λj(t) = limε→0P(Mj (t)|F (Z)
t )ε .
log(λj(t)) = [W`j (t)]′β`j + ξ`j
(z`(t)
)
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Macrotransition entry model
Recall M(t) = τt ≤ t + ε:Six different “types”, based on entry state Cτt ,∪6
j=1Mj(t) = M(t).
Hazards: λj(t) = limε→0P(Mj (t)|F (Z)
t )ε .
log(λj(t)) = [W`j (t)]′β`j + ξ`j
(z`(t)
)+ ξ`j (zj(t)) 1[j ≤ 4]
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Hierarchical modeling
Dwight Howard’s shot chart:
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Hierarchical modeling
Shrinkage needed:
Across space.
Across different players.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Basis representation of spatial effects
Spatial effects ξ`j`: ballcarrier identity.
j : macrotransition type (pass, shot, turnover).
Functional basis representation
ξ`j (z) = [w`j ]′φj(z).
φj = (φji . . . φjd)′: d spatial basis functions.
w`j : weights/loadings.
Information sharing
φj allows for non-stationarity, correlations between disjoint regions[Higdon, 2002].
w`j : weights across players follow a CAR model [Besag, 1974] based on playersimilarity graph H.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Basis representation of spatial effects
Spatial effects ξ`j`: ballcarrier identity.
j : macrotransition type (pass, shot, turnover).
Functional basis representation
ξ`j (z) = [w`j ]′φj(z).
φj = (φji . . . φjd)′: d spatial basis functions.
w`j : weights/loadings.
Information sharing
φj allows for non-stationarity, correlations between disjoint regions[Higdon, 2002].
w`j : weights across players follow a CAR model [Besag, 1974] based on playersimilarity graph H.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Basis representation of spatial effects
Spatial effects ξ`j`: ballcarrier identity.
j : macrotransition type (pass, shot, turnover).
Functional basis representation
ξ`j (z) = [w`j ]′φj(z).
φj = (φji . . . φjd)′: d spatial basis functions.
w`j : weights/loadings.
Information sharing
φj allows for non-stationarity, correlations between disjoint regions[Higdon, 2002].
w`j : weights across players follow a CAR model [Besag, 1974] based on playersimilarity graph H.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Basis representation of spatial effects
Basis functions φj learned in pre-processing step:
Graph H learned from players’ court occupancy distribution:
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Basis representation of spatial effects
Basis functions φj learned in pre-processing step:
Graph H learned from players’ court occupancy distribution:
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Inference
“Partially Bayes” estimation of all model parameters:
Multiresolution transition models provide partial likelihood factorization[Cox, 1975].
All model parameters estimated using R-INLA software[Rue et al., 2009, Lindgren et al., 2011].
Distributed computing implementation:
Preprocessing involves low-resource, highly parallelizable tasks.
Parameter estimation involves several CPU- and memory-intensive tasks.
Calculating EPV from parameter estimates involves low-resource, highlyparallelizable tasks.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Inference
“Partially Bayes” estimation of all model parameters:
Multiresolution transition models provide partial likelihood factorization[Cox, 1975].
All model parameters estimated using R-INLA software[Rue et al., 2009, Lindgren et al., 2011].
Distributed computing implementation:
Preprocessing involves low-resource, highly parallelizable tasks.
Parameter estimation involves several CPU- and memory-intensive tasks.
Calculating EPV from parameter estimates involves low-resource, highlyparallelizable tasks.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Inference
“Partially Bayes” estimation of all model parameters:
Multiresolution transition models provide partial likelihood factorization[Cox, 1975].
All model parameters estimated using R-INLA software[Rue et al., 2009, Lindgren et al., 2011].
Distributed computing implementation:
Preprocessing involves low-resource, highly parallelizable tasks.
Parameter estimation involves several CPU- and memory-intensive tasks.
Calculating EPV from parameter estimates involves low-resource, highlyparallelizable tasks.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
New insights from basketball possessions
JamesshotNORRIS COLE POSSESSION
RASHARDLEWISPOSS.
LEBRON JAMES POSSESSION
EPV constant whilepass is en route
PassPass
Slight dip in EPV aftercrossing 3 point line
Slight dip in EPV aftercrossing 3 point line
Acceleratestowards basket
Runs behindbasket and
defenders close
Acceleratesinto the paint
Splits the defense;clear path to
basket
0.8
1.0
1.2
1.4
1.6
time
EP
V
0 3 6 9 12 15 18
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
New insights from basketball possessions0.
81.
01.
21.
41.
6
time
EP
V
0 3 6 9 12 15 18
A
B
C
D
1
2 3
4
5
1
2
34
51
2 3
4
5
1
2
34
51
2 3
4
5
1
2
34
5
A
V 1.42P 0.83
V 1.09P 0.00
V 0.98P 0.04
V 1.01P 0.06
V 1.03P 0.04
TURNOVERV 0.00P 0.02
OTHERV 0.99P 0.02
LEGENDMOVEMENT
Macro History Micro
MACROTRANSITION VALUE (V)
High Medium Low
MACROTRANSITION PROBABILITY (P)High Medium Low
OFFENSE1
2
3
4
5
Norris ColeRay AllenRashard LewisLeBron JamesChris Bosh
DEFENSE1
2
3
4
5
Deron WilliamsJason Terry
Joe JohnsonAndray Blatche
Brook Lopez
1
23
4
5
1
2
3
451
23
4
5
1
2
3
451
23
4
5
1
2
3
45
B
V 1.17P 0.27
V 1.02P 0.03 V 0.98
P 0.04
V 1.01P 0.23
V 1.03P 0.12
TURNOVERV 0.00P 0.16
OTHERV 1.00P 0.16
1
23
4
5
1
23
45
1
23
4
5
1
23
45
1
23
4
5
1
23
45
C
V 1.01P 0.05
V 1.00P 0.13
V 1.01P 0.04
V 1.01P 0.61
V 1.05P 0.04 TURNOVER
V 0.00P 0.01
OTHERV 0.97P 0.13
12
3
4
5
12
3
4
5
12
3
4
5
12
3
4
5
12
3
4
5
12
3
4
5
D
V 1.50P 0.83
V 1.01P 0.01
V 1.09P 0.01
V 0.98P 0.04
V 1.03P 0.00
TURNOVERV 0.00P 0.04
OTHERV 1.06P 0.06
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
New metrics for player performance
EPV-added:
Rank Player EPVA
1 Kevin Durant 3.262 LeBron James 2.963 Jose Calderon 2.794 Dirk Nowitzki 2.695 Stephen Curry 2.506 Kyle Korver 2.017 Serge Ibaka 1.708 Channing Frye 1.659 Al Horford 1.55
10 Goran Dragic 1.54
Rank Player EPVA
277 Zaza Pachulia -1.55278 DeMarcus Cousins -1.59279 Gordon Hayward -1.61280 Jimmy Butler -1.61281 Rodney Stuckey -1.63282 Ersan Ilyasova -1.89283 DeMar DeRozan -2.03284 Rajon Rondo -2.27285 Ricky Rubio -2.36286 Rudy Gay -2.59
Table : Top 10 and bottom 10 players by EPV-added (EPVA) per game in 2013-14,minimum 500 touches during season.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
New metrics for player performance
Shot satisfaction:
Rank Player Satis.
1 Mason Plumlee 0.352 Pablo Prigioni 0.313 Mike Miller 0.274 Andre Drummond 0.265 Brandan Wright 0.246 DeAndre Jordan 0.247 Kyle Korver 0.248 Jose Calderon 0.229 Jodie Meeks 0.22
10 Anthony Tolliver 0.22
Rank Player Satis.
277 Garrett Temple -0.02278 Kevin Garnett -0.02279 Shane Larkin -0.02280 Tayshaun Prince -0.03281 Dennis Schroder -0.04282 LaMarcus Aldridge -0.04283 Ricky Rubio -0.04284 Roy Hibbert -0.05285 Will Bynum -0.05286 Darrell Arthur -0.05
Table : Top 10 and bottom 10 players by shot satisfaction in 2013-14, minimum 500touches during season.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Acknowledgements and future work
Our EPV framework can be extended to better incorporate unique basketballstrategies:
Additional macrotransitions can be defined, such as pick and rolls, screens,and other set plays.
Use more information in defensive matchups (only defender locations, notidentities, are currently used).
Summarize and aggregate EPV estimates into useful player- or team-specificmetrics.
Thanks to:
Co-authors: Alex D’Amour, Luke Bornn, Kirk Goldsberry.
Colleagues: Alex Franks, Andrew Miller.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
Acknowledgements and future work
Our EPV framework can be extended to better incorporate unique basketballstrategies:
Additional macrotransitions can be defined, such as pick and rolls, screens,and other set plays.
Use more information in defensive matchups (only defender locations, notidentities, are currently used).
Summarize and aggregate EPV estimates into useful player- or team-specificmetrics.
Thanks to:
Co-authors: Alex D’Amour, Luke Bornn, Kirk Goldsberry.
Colleagues: Alex Franks, Andrew Miller.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015
References I
[0] Besag, J. (1974).Spatial interaction and the statistical analysis of lattice systems.Journal of the Royal Statistical Society: Series B (Methodological), 36(2):192–236.
[0] Cox, D. R. (1975).A note on partially bayes inference and the linear model.Biometrika, 62(3):651–654.
[0] Franks, A., Miller, A., Bornn, L., and Goldsberry, K. (2015).Characterizing the spatial structure of defensive skill in professional basketball.Annals of Applied Statistics.
[0] Higdon, D. (2002).Space and space-time modeling using process convolutions.In Quantitative Methods for Current Environmental Issues, pages 37–56. Springer, New York, NY.
[0] Lindgren, F., Rue, H., and Lindstrom, J. (2011).An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach.Journal of the Royal Statistical Society: Series B (Methodological), 73(4):423–498.
[0] Rue, H., Martino, S., and Chopin, N. (2009).Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations.Journal of the Royal Statistical Society: Series B (Methodological), 71(2):319–392.
Dan Cervone (Harvard) Multiresolution Basketball Modeling August 11, 2015