How player Elo splits a game
After every game the team’s rating moves by one Elo step, sized by how surprising the result was. That step is shared out by the night’s net goals, weighted by how much each moment could swing the game: after a loss the team’s best performer takes none of the drop and the weakest performers take the most; after a win the worst performer gets none of the gain. Measured the way the model weighs lineups, by leverage ice time, the team still moves exactly one step, and at the start of every season each rating is pulled 15% of the way back toward 1500. Pick a game where one player was brilliant in a loss, or one who piled on goals after a blowout was decided, and compare with net goals as measured, the rule in use for one day.
The settle-up, step by step
These are the model’s real numbers for this game (K = 9, home ice worth 30 Elo points; ratings going in are the live model’s, Players shows everyone’s current rating). Change the result to see how the same performances would have been credited with a different ending.
Where ÷ Σ(share × responsibility) comes from
Step 5 splits the team’s step under two requirements. The divisor is what makes both hold at once.
- Responsibility decides who carries it. Each player’s change is proportional to his responsibility share r: changei = λ × ri
- The team moves by exactly one step. The team’s rating is its players’ ratings weighted by leverage ice time share s, so its change is the s-weighted average of theirs, and that has to equal Δ: Σ si × changei = Δ
- Put 1 into 2. λ × Σ si ri = Δ ⇒ λ = Δ ÷ Σ(s × r) Responsibility sets who moves; ice time sets how much each player counts toward the team, so the divisor mixes the two.
| Split rule | Team rating moves |
|---|
Where the leverage was
Every player’s share
Click a row to follow that player. NG is net goals for this game from the model’s components (goalies: goals saved above expected); Lev. NG weights its finishing, goaltending, penalty and faceoff events by the leverage of the moment, and is what the model uses. The underlined column is in use. Adj. is NG measured from the team’s best performer after a loss, or its worst after a win. Resp. is Adj. as a share of the team total, and Lev. is the leverage ice time share that weights the team rating. Change = step × Resp. ÷ Σ(Lev. × Resp.) (why).
Why share by net goals?
A result belongs most to the players who drove it. Net goals measure each player’s part of the night: shots and chances for and against, finishing, saves, penalties, faceoffs, playmaking and suppression. A goalie who stops 40 of 42 in a loss is not blamed for it, and a passenger on a winning night collects less.
Does it predict better?
On every game 2010-26, each predicted only from earlier games, the full game model’s log-loss moves from 0.66651 with the ice-time split to 0.66604 with this rule: responsibility from leverage-weighted net goals plus the season pull. Each piece is small and hockey stays close to a coin flip, but together they are the best version tested. It became the model’s rule on 2026-09-29.
Why leverage-weighted net goals?
The on-ice parts of net goals are already priced by how much each chance could swing the game. Finishing, goaltending, penalties and faceoffs are not, so a goal at 7–1 would count as much as a tying goal. The model weights each of those events by the leverage at that second, relative to an average second (a tied third period counts about double, the last minutes of a 7–1 game close to zero), so the credit for a result goes to the players who decided it.
Why pull ratings back each season?
Players who post strong nights on winning teams climb game after game. Without a pull, ratings drifted apart season after season (one standard deviation reached about 175 points). Moving every rating 15% back toward 1500 before each season’s first game keeps one standard deviation near 90 points and predicts better, because last season’s results say less about this one.