Motivation and Problem

• Goals are arguably the most important statistic in hockey, because the team that has the most goals at the end of the game wins

• Unfortunately, there aren't many goals scored in hockey so there is limited data, which means anything based on goals would have lots of variability

• Shots could be used, but that's assuming all shots are equally valuable

• An expected goals model estimates the probability of a goal based on location and other factors

• Analysts use these models to predict overall team and player performance

• One issue with the public expected goals models is they don't factor in how shot location might change over time

Purpose

Search for best practices in expected goals through creating our own models

Data

• Used NHL shots data from MoneyPuck from 2010-11 season to 2020-21 season

• Each observation is a shot

  • Shot on goal, missed the net, goal

• Only using shots during 5-on-5 play

• Used player data to calculate each players age as of Sept. 15 of that season

Our Expected Goals Models

Began with a logistic regression modeling goals as a function of shot distance, shot angle, if the shot occurred on a rush, and if the shot was a rebound

Individual Season Model: ran the model separately for each season

Logistic Regression Model: ran the model over the data from all seasons

• Looked to see if there was a trend in shot angle and distance coefficients over the seasons

Individual Season Model

• Predictors: shot angle, shot distance, rush, rebound
• Average Brier Score: 0.05036

Logistic Regression Model

• Predictors: shot angle, shot distance, rush, rebound
• Brier Score: 0.05035

Distance Coefficient trends over season

Angle Coefficient trends over season

Expected Goals Model including Player Effects

• Used a hierarchical logistic model to predict goals and added in player effects

  • Shooter effects and goalie effects

Why a hierarchical model?

• Information is pulled across all players and serves as regularization, shooters and goalies involved with fewer shots will be pulled towards group mean

More variation in shooter ability than goalie ability

Best and Worst Players by Player Effect

Expected Goals Model including Player Age

• Taking the same model that was used for player effects and adding in 2 variables for shooter and goalie age

• Used a quadratic polynomial term for ages since there were few goalie observations between the ages 18-20 and 38+

Model Performance

Used leave one season out cross validation to assess our four models

Calculated Brier score for overall hold out performance and across seasons

• Individual Season Model
  • Predictors: shot angle, shot distance, rush, rebound
  • Average Brier Score: 0.05036
• Logistic Regression Model
  • Predictors: shot angle, shot distance, rush, rebound
  • Brier Score: 0.05035
• Player Effects Hierarchical Model
  • Predictors: shot angle, shot distance, rush, rebound, shooter effect, goalie effect
  • Brier Score: 0.05029
• Player Effects Model with Ages (Cross Validation using 10% of data)
  • Predictors: shot angle, shot distance, rush, rebound, shooter effect, goalie effect, shooter age, goalie age
  • Brier Score: 0.05069

Comparing Brier Scores

Discussion and Next Steps

Results

• The Player Effects Hierarchical model performed the best with a Brier Score of 0.05029

Future Work

• Creation of one large model allowing distance and angle coefficients to vary across seasons

• Alternative approaches for including player ages

• Adjustments for rink bias

• Addition of player tracking data if/when it becomes available