Post on 13-Oct-2020
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!