Hockey in Space!

Hockey in Space!Characterizing team-wise differences in shot locations with

spatial point processes

Devan BeckerThe University of Western Ontario

dbecker7@uwo.ca

September 16, 2018

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Hockey in Space!Introduction

Introduction

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Hockey in Space!Introduction

The Data

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Hockey in Space!Introduction

2017-2018 Season Shot Locations

All Shots, Detroit All Shots, Tampa Bay

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Hockey in Space!Introduction

2017-2018 Season Shot Hexbins

## 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.

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Hockey in Space!Introduction

2017-2018 Season Shot Density

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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.

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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.

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Hockey in Space!LGCP

Variance and Clustering (Simulated)

−2

−1

0

1

2

Diff

Low Variance, Small Clusters

−2

−1

0

1

2

Diff

High Variance, Small Clusters

−2

−1

0

1

2

Diff

Low Variance, Large Clusters

−2

−1

0

1

2

Diff

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.

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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.

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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

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Hockey in Space!Results

Acknowledgments

Thank you to my supervisors: Doug Woolford, Charmaine Dean,and W. John Braun

Thanks for funding:

Thanks for listening! Any further questions: dbecker7@uwo.ca

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