Skater Influence on Shot Location in the NHL

Micah Blake McCurdyhockeyviz.com

Stevens Point, WIGreat Lakes Analytics in Sports Conference

July 13, 2017

Shot Locations

How much of what happens on the ice in a hockey game is underthe control of an individual player?

Shot Locations

How much of what happens on the ice in a hockey game is underthe control of an individual player?

I Isolate player impact on shot location and frequency.

I Consolidate impact into convenient units.

I Measure correlation from season to season.

Least-Squares Regression

I α a collection of observations

I X a design matrix

I β a collection of (imagined) individual isolated impacts

Xβ = α

Least-Squares Regression

I α a collection of observations

I X a design matrix

I β a collection of (imagined) individual isolated impacts

Xβ = α

XTXβ = XTα

Least-Squares Regression

I α a collection of observations

I X a design matrix

I β a collection of (imagined) individual isolated impacts

Xβ = α

XTXβ = XTα

β = (XTX )−1XTα

Least-Squares Regression

I α a collection of observations

I X a design matrix

I β a collection of (imagined) individual isolated impacts

Xβ = α

XTXβ = XTα

β = (XTX )−1XTα

Elements of α and β can be taken from any inner product spaceand the usual proof goes through.

Observations - Ottawa with Erik Karlsson

Closed form solutions

Usually, we compute (XTX )−1XT numerically, with computers.However, in our case, we can work it out by hand:

Closed form solutions

Usually, we compute (XTX )−1XT numerically, with computers.However, in our case, we can work it out by hand:

βp = 5(α with p) − 4(α without p)

Closed form solutions

Usually, we compute (XTX )−1XT numerically, with computers.However, in our case, we can work it out by hand:

βp = 5(α with p) − 4(α without p)

βp(NZ ) βp(OZ ) βp(DZ ) βp(OTF )

Closed form solutions

Usually, we compute (XTX )−1XT numerically, with computers.However, in our case, we can work it out by hand:

βp = 5(α with p) − 4(α without p)

β′p = 0.17βp(NZ ) + 0.13βp(OZ ) + 0.11βp(DZ ) + 0.59βp(OTF )

Erik Karlsson (attacking)

Erik Karlsson (defending)

Erik Karlsson (isolated)

Threat

To compare different players we weight their isolated shotcontributions according to league average shooting percentagesfrom given locations to obtain threat.

Threat

To compare different players we weight their isolated shotcontributions according to league average shooting percentagesfrom given locations to obtain threat.

I Expected Goals per hour, purely from individual impact onshot locations.

Threat

To compare different players we weight their isolated shotcontributions according to league average shooting percentagesfrom given locations to obtain threat.

I Expected Goals per hour, purely from individual impact onshot locations.

For Karlsson this season:

I Threat For: +2.4 goals per hour

I Threat Against: +1.3 goals per hour

Threat

To compare different players we weight their isolated shotcontributions according to league average shooting percentagesfrom given locations to obtain threat.

I Expected Goals per hour, purely from individual impact onshot locations.

For Karlsson this season:

I Threat For: +2.4 goals per hour (Actual: 2.4)

I Threat Against: +1.3 goals per hour (Actual: 2.1)

Correlations - Offensive Threat Created

Correlations - Defensive Threat Allowed

Correlations - Net Threat

Conclusions

I Players have small but noticeable individual effects on shotlocations.

I Effects are strongest when net threat is considered.

Future Work

I Isolate interactions with goaltending metrics.

I Take into account shooter quality.

I Consider quality-of-competition and score state.

I Isolate coaching impacts.

I Consider non-linear effects.

Thanks!