Credits
Paper Puck's methods were learned from published work by others. These are credits, not sources: no number on Paper Puck comes from them; every figure is counted and fitted here from the NHL's own feeds. Which part of the expected-goals model came from which work is set out in What is borrowed, and what is new on Methodology's expected-goals page.
- Shot Quality: a methodology for the study of the quality of a hockey team's shots allowedAlan Ryder, 2004The idea itself: weigh each shot by its chance of going in, from where and how it was taken. Also the first warning that two scorers record the same shot differently.
- Shot Quality Model: A logistic regression approach to assessing NHL shots on goalKen Krzywicki, 2005A logistic regression on distance, shot type, rebound and strength, checked on a season it was not fitted on: the shape of Paper Puck's model.
- Product Recall Notice for 'Shot Quality'Alan Ryder, 2007Scorer bias: rinks record shots longer or shorter than they were. The problem Paper Puck's season terms answer, over time rather than by rink.
- Removing Observer Bias from Shot Distance – Shot Quality Model – NHL Regular Season 2008-09Ken Krzywicki, 2009Correcting recorded distance inside the model, by measuring each shot against its rink's average. Paper Puck's season terms are the same move made by season.
- NHL Shot Quality 2009-10: A look at shot angles and reboundsKen Krzywicki, 2010Shot angle as an input, and the rebound "push": how far the angle moved from the shot before, which the goalie has to cover. He found it too close to the rebound flag to keep; on our shots it helped more than anything else I tried.
- Evaluating NHL Goalies, Skaters, and Teams Using Weighted ShotsBrian Macdonald, Craig Lennon and Rodney Sturdivant, 2012A logistic regression with distance, angle, shot type, rebound, score and home terms, and an angle-on-rebound interaction: nearly Paper Puck's list of inputs.
- Accounting for Rink Effects in the National Hockey League's Real Time Scoring SystemMichael Schuckers and Brian Macdonald, 2014Estimating how much each rink's scorers over- or under-record, and reweighting for it. Related to the season terms; Paper Puck does not adjust by rink.
- Adjusted possession measuresMicah Blake McCurdy, Hockey Graphs, 2014Score and venue adjustment: weigh each shot attempt by how far the league's split in its score state and venue sits from even. The weights here are fitted on our own data.
- Expected goals are a better predictor of future scoring than Corsi, goalsDTMAboutHeart, Hockey Graphs, 2015How to judge an expected-goals model against shot attempts and goals.
- A New Expected Goals Model for Predicting Goals in the NHLJosh and Luke Younggren, Evolving-Hockey, 2018Separate models for even strength, power play, short-handed and empty net; leaving out blocked shots because their location is the block; testing on a season the model never saw. Also the inspiration for these tables. Their model is gradient-boosted trees with inputs on the event before each shot; Paper Puck's is a logistic regression without them.
- Scorer Bias AdjustmentsMicah Blake McCurdy, HockeyViz, 2020Scorer bias estimated for each rink in each season and removed by moving shots. Paper Puck corrects league-wide drift instead, and does not move shots.
- Magnus 6 expected goalsMicah Blake McCurdy, HockeyViz, 2022A ridge-penalised logistic regression as the model, and Paper Puck's rebound (the same team's attempt in the 3 s before) and rush (the event before outside the attacking zone, within 4 s) definitions. Magnus also fits shooter and goalie terms; Paper Puck's does not.
- MoneyPuck methodologyPeter Tanner, MoneyPuckOff-wing as an input: the shooter's hand against the side of the ice he shoots from. Also how the event before a shot (what it was, where, how long before) shapes its chance of going in; Paper Puck keeps rebound and rush flags and a rebound's change of angle. Their model was rebuilt for 2026-27 for how the NHL now records shots, the same drift Paper Puck's season terms answer.