Expected by Whom? A Skill-Adjusted Expected Goals Model for NHL Shooters and Goaltenders

TL;DR

This paper tackles predicting NHL shot outcomes by incorporating skill-adjusted expected goals that account for both shooter and goaltender abilities across three dimensions: overall, locational, and situational. Using a stacked, light gradient-boosted framework and data from 2010–2022, the authors compare baseline xG models to skill-adjusted variants across skill brackets, employing novel feature engineering methods such as shot weighting, shot binning, and Gower distance. The results show consistent, modest improvements in log loss, AUROC, and Brier score for the skill-adjusted models, with the largest gains among high-skill players, indicating that both players’ skills and the context of the shot meaningfully influence outcomes. The approach advances xG modeling in hockey by explicitly modeling goaltender skill and location/situation-specific effects, offering potential extensions to other game states and sports.

Abstract

This study outlines a light gradient boosted model aimed at predicting shot outcomes in the NHL. The model uses the NHL's spatiotemporal data to account for both the skill of shooters and goaltenders. This approach involves isolating and engineering features for different aspects of shooter and goaltender skill. These aspects include the overall skill, the locational skill, which is engineered using a shot binning technique previously outlined by Shuckers and Curro, and the situational skill, which is engineered using Gower distance. Three separate datasets were created based on the skill of the shooter and goaltender. For each, a baseline model was created in order to compare and contrast its performance with the skill-adjusted model. The results seen in this study show performance increases for the skill-adjusted model over the baseline model in log loss, brier scores, and area under the ROC curve. These performance increases have a high of 5\% and outperform previous works, which have attempted to account only for player skill. This highlights the importance of accounting for both player and goaltender skill, while also accounting for different aspects of their skill. In future works, a skill-adjusted expected goals model could benefit models interested in predicting other aspects of the game, such as scoring leaders or individual game outcomes.

Figures (3)

• Figure 1: Feature importance based on gain for the low-skill model.
• Figure 2: Feature importance based on gain for the mid-skill model.
• Figure 3: Feature importance based on gain for the high-skill model.