Hockey in Space! Hockey in Space! Characterizing team-wise differences in shot locations with spatial point processes Devan Becker The University of Western Ontario [email protected]September 16, 2018 Devan Becker University of Western Ontario 1 / 20
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Hockey in Space!
Hockey in Space!Characterizing team-wise differences in shot locations with
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
Devan Becker University of Western Ontario 5 / 20
Hockey in Space!Introduction
2017-2018 Season Shot Density
Devan Becker University of Western Ontario 6 / 20
Hockey in Space!Introduction
Objective
Fit a parametric statistical model to determine:
• Where do different teams shoot from?• Are the patterns consistent? (Variance!)• Which shots go in?• What can goalies expect?
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Hockey in Space!LGCP
LGCP
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Hockey in Space!LGCP
Log-Gaussian Cox Processes (Yay math!)
log(Λ(x , y)) = µ+ βC(x , y) + S(x , y)
The log of the rate of points in a given location is modelled as anintercept plus a spatial covariate plus a random process.
• “Random” doesn’t mean unstructured!• The random process is a smooth function based on the normal
distribution.
Devan Becker University of Western Ontario 9 / 20
Hockey in Space!LGCP
Log-Gaussian Cox Processes (Yay math!)
log(Λ(x , y)) = µ+ βC(x , y) + S(x , y)
The log of the rate of points in a given location is modelled as anintercept plus a spatial covariate plus a random process.
• “Random” doesn’t mean unstructured!• The random process is a smooth function based on the normal
distribution.
Devan Becker University of Western Ontario 9 / 20
Hockey in Space!LGCP
Variance and Clustering (Simulated)
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Low Variance, Small Clusters
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High Variance, Small Clusters
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Low Variance, Large Clusters
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High Variance, Large Clusters
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Hockey in Space!LGCP
League Average as a Spatial Covariate
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Hockey in Space!LGCP
League Average as a Spatial Covariate
Our interpretation becomes:
log(Λ(x , y)) = µ+ C(x , y) + S(x , y)
The log of the rate of shots is modelled as an intercept plus theleague average plus a team specific deviation.
• S(x , y) can be seen as the intended strategy difference.• The variance and range illustrate the team’s consistency.
Devan Becker University of Western Ontario 12 / 20
Hockey in Space!LGCP
League Average as a Spatial Covariate
Our interpretation becomes:
log(Λ(x , y)) = µ+ C(x , y) + S(x , y)
The log of the rate of shots is modelled as an intercept plus theleague average plus a team specific deviation.
• S(x , y) can be seen as the intended strategy difference.• The variance and range illustrate the team’s consistency.
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Hockey in Space!LGCP
Estimation of LGCP
oh no
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Hockey in Space!LGCP
Estimation of LGCP
oh no
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Hockey in Space!Results
Results
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Hockey in Space!Results
Random Processes - S(x,y)
−0.1 0.0 0.1 0.2 0.3Diff
Diff. from League − Detroit
−0.5 0.0 0.5 1.0Diff
Diff. from League − Tampa Bay
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Hockey in Space!Results
Variance at Every Location
0.08 0.10 0.12SD
SD − Detroit
0.15 0.20 0.25SD
SD − Tampa Bay
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Hockey in Space!Results
All Results - Shiny App
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Hockey in Space!Results
Limitations
• Differences from league are often minor
• One dense cluster means small clusters estimated everywhere
• Needs a lot of data• Can’t just look at one team’s goals
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Hockey in Space!Results
Final Notes
Conclusions• This method can indicate the manifested strategy• Variance and cluster size indicate a teams consistency
• Careful interpretation
Future Work• Different play types (e.g. first shot after possession)• Statistical comparison of teams• Spatially varying range parameter• All the things that the audience suggests
Devan Becker University of Western Ontario 19 / 20
Hockey in Space!Results
Acknowledgments
Thank you to my supervisors: Doug Woolford, Charmaine Dean,and W. John Braun