Methodology · NHL
How NHL luck is measured, and how well it holds up
The same question as for football: with the way both teams actually played, how often does each win a replay of the game in which every chance event happens at its expected rate? The difference between that and the result is luck. In hockey most of it is shooting and goaltending: how many of a game’s chances went in. This page sets out how that is measured, what hockey changes, and every test, including the parts that failed and were dropped.
How much better than the standings?
Halfway through a season, the luck-adjusted record predicts 18% more of how the second half goes than the standings do, and after 10 games 84% more.
Why 18% is still a lot: by halfway, much of the luck in a hockey record has evened out over 41 games, and the second half has so much luck of its own that even perfect knowledge of every team would predict only about 59% of it. There is little left to find, and the luck-adjusted record finds 31% of it. Halfway through an NFL season the gain is about the same, 19%. Earlier, when a record is mostly luck, hockey’s gain is the bigger one, as a luckier game should give: a quarter of the way in, after 20 games, it is 49%, against the NFL’s 24% after four games, and after 10 games 84%. And it is not chance: halfway, it beats the standings in 7 of 8 seasons and in 97% of 2,000 resamples of the team-seasons.
| Games | Standings | Luck-adjusted | Better by | Most |
|---|---|---|---|---|
| 10 | 17.3% | 31.9% | +84% | 70% |
| 20 | 27.2% | 40.6% | +49% | 71% |
| 30 | 33.2% | 43.1% | +30% | 66% |
| 41 | 37.6% | 44.4% | +18% | 59% |
Share of the rest of the season’s differences between teams each predicts (r²), points percentage in the standings against coin-flip replay points. Games: how far into the season. Most: what perfect knowledge of every team would predict, from how well the rest of the season’s odd and even games agree. Every measure tested.
1. What’s different in hockey
The luck index (100 × (result − replay win probability)) and the four numbers on every game are the NFL’s, set out in full on the NFL methodology page. What changes:
- Points, not wins. The NHL gives two points for a win and one for a loss after regulation, so the standings here are in points: each replay says how often a team wins and how often it’s level after regulation, and a game’s expected points are 2 × the win chance + the tie chance × the chance of losing it after regulation.
- Shots, not plays. The replay is built from each team’s unblocked shot attempts and our own expected-goals model, not from drives.
- The data. Play-by-play from fastRhockey’s releases (SportsDataverse) for finished seasons and the NHL’s own feed for the season under way. We use no outside expected-goals figures.
- No betting lines yet. Closing lines from ESPN are switched off until we could test reading them, so every game page says it has no line, and “before puck drop” and “same teams, fresh game” are blank.
2. Expected goals
The chance that an unblocked shot attempt (on goal or missed) goes in, from a logistic model of its distance (a spline), angle, shot type, whether it was a rebound (within 3 seconds of the same team’s last attempt) or off the rush (within 4 seconds of an event 50 feet away), the strength on the ice, and whether the net was empty. Fitted on 2021-22 to 2024-25 (480,312 attempts) and checked on 2025-26 (117,680): log loss 0.2268 against 0.2447 for distance alone and 0.2564 for the league rate, AUC 0.755.
Arena scorers differ and the league’s shot locations drift, so each season gets its own level, fitted on its own attempts (for the season under way, week by week on the weeks before, so a game’s numbers never change after it). A shot’s chance is then shifted by the shooter’s and the goalie’s records before the game, shrunk toward average by 40 expected goals for shooters and 320 for goalies (fitted by log loss): what a shooter or goalie has shown over hundreds of shots is skill, the rest is luck. Goalies need far more shots than shooters before their record says much.
| Season | Attempts | Goals | Expected | With records |
|---|---|---|---|---|
| 2018-19 | 116,027 | 7,851 | 7,853 | 7,890 |
| 2019-20 | 102,475 | 6,967 | 6,978 | 7,025 |
| 2020-21 | 77,273 | 5,334 | 5,324 | 5,337 |
| 2021-22 | 119,810 | 8,511 | 8,509 | 8,508 |
| 2022-23 | 120,027 | 8,570 | 8,572 | 8,605 |
| 2023-24 | 120,888 | 8,384 | 8,345 | 8,397 |
| 2024-25 | 118,240 | 8,221 | 8,198 | 8,220 |
| 2025-26 | 117,306 | 8,343 | 8,377 | 8,431 |
3. Luck events
Each event has a value in goals: the outcome against its chance. Each kind counts at its luck share (section 4).
| Kind | Luck share | Repeats, r |
|---|---|---|
| Shooting Every unblocked shot attempt of regulation, a goal or not, against its chance: our expected goals with the shooter’s and goalie’s records. A team’s own attempts are its finishing; its opponents’ are its goaltending. Posts and crossbars are misses like any other. | 0.75 | 0.00 |
| Empty-net goals Attempts at an empty net after the trailing team pulled its goalie, at their own chance. | 1.00 | 0.13 |
| Overtime The result of overtime (3-on-3 in the regular season, 5-on-5 in the playoffs) against the winner’s chance before it started. Worth two goals of margin: a one-goal loss becomes a one-goal win. | 1.00 | 0.01 |
| Shootout The same for the shootout. | 1.00 | 0.12 |
| Penalty calls Each call that gave a power play, worth what a power play is worth (0.116 goals a minute). Calls at the same moment offset. | 0.00 | 0.37 |
| Overturned goals Goals taken off the board by a coach’s challenge or the league’s review, worth the goal. | 0.00 | 0.03 |
Repeats: the correlation of a team’s total of that kind in one half of a season with the other half’s, 2018-19 to 2024-25. Shooting splits into finishing (own attempts, 0.01) and goaltending (opponents’ attempts, 0.12).
4. Luck shares
How much of each kind is luck is fitted, not assumed: the shares that make the luck-adjusted goal differential of one half of a season best predict the other half’s, on 2018-19 to 2024-25 (seven seasons: with fewer the shares jumped from fit to fit), and checked on 2025-26. Half-season to half-season, goal differential correlates 0.67 in training and 0.46 in the holdout; adjusted at the fitted shares, 0.70 and 0.55 (every share at 1: 0.56).
What was dropped. Penalties repeat (a team’s penalty differential in one half correlates 0.37 with the other’s) and their fitted share is 0: drawing and taking penalties is mostly skill and discipline. Overturned goals are too rare to fit and get 0 too. Both stay on the game pages as context, but neither counts as luck. Shooting is 0.75 rather than 1 because goaltending repeats a little.
Unbiasedness. For each all-or-nothing chance, the outcomes should happen at the rate the model gives them:
| Kind | Events | Expected | Happened | z |
|---|---|---|---|---|
| Empty-net goals | 6,317 | 59.3% | 58.2% | −1.85 |
| Overtime | 1,631 | 51.1% | 50.8% | −0.20 |
| Shooting | 885,729 | 6.6% | 6.6% | −0.72 |
| Shootout | 713 | 49.5% | 49.1% | −0.22 |
Within ±2 is what chance alone gives. An earlier version used one home-ice share for overtime and the shootout together and failed (z −2.55 and −2.84): home teams win overtime more often than shootouts. They now have their own.
5. The replay with the same day’s form
Resampling. Each team’s unblocked attempts of regulation are drawn again by strength state (5-on-5, power play, short-handed, 4-on-4): as many as a Poisson draw around the number it took, each from its own attempts in that state (with few of them, partly from all its attempts of the game), each a goal at its chance. Power plays are the ones the penalties actually drawn gave.
Score effects. A leading team sits back and gives up more attempts; a trailing one pushes. Each attempt is weighted by the league’s share of attempts at that lead: +1: 1.032, +2: 1.052, +3: 1.056, -3: 0.949, -2: 0.953, -1: 0.970. With the weights the replay’s holdout log loss fell from 0.683 to 0.668.
The end of regulation. A team down one pulls its goalie for the league’s 94 seconds, down two for 143, and both sides score at the league’s empty-net rates: empty-net goals follow the replayed score.
Calibration. The raw replay is too sure of itself, as in the other leagues. A logit scale and a home shift correct it, π̂ = σ(T · logit π̂raw + h): T = 0.74, h = 0.033, fitted on 2018-19 to 2024-25 and checked on 2025-26: log loss 0.677 raw, 0.668 calibrated, against 0.693 for a coin flip. 4,000 replays a game on the site.
When the replay says 90%, it happens about 90% of the time
Every game 2018-19 to 2025-26, grouped by the replay’s win probability for the home team: what it predicted against how often the home team actually won.
Show as a table
| Bin | Games | Predicted | Actually won |
|---|---|---|---|
| 10%–25% | 178 | 20.7% | 21.3% |
| 25%–50% | 3991 | 40.9% | 41.1% |
| 50%–75% | 5742 | 60.7% | 60.5% |
| 75%–90% | 591 | 79.0% | 77.7% |
6. Overtime and the shootout
Regular-season overtime (3-on-3) and the shootout are as close to coin flips as hockey gets: since 2015-16 the home team has won 51.2% of overtimes and 49.5% of shootouts. The replay plays them at those rates, tilted a little toward the stronger team. Playoff overtime is 5-on-5 until someone scores; there the team with more of the game’s 5-on-5 expected goals gets 60% of that edge (fitted on 247 playoff overtimes, log loss 0.684 against 0.693 for a coin flip). Over 2,344 games that went past regulation, the replay gave the eventual winners 51.1% on average.
7. The other three numbers
- Before puck drop: the closing moneyline without the bookmaker’s margin. Blank until lines are on.
- Same teams, fresh game: the line plus this game’s expected-goals evidence. Needs the line, so blank too.
- Only coin-flips re-rolled: every shot, overtime and shootout redrawn at its chance, penalties re-flipped; the rest as played. It is the number behind coin-flip points. It keeps each game’s own attempts, so it is a statement about that game’s luck rather than a forecast, and isn’t calibrated against results.
8. Penalties and reviews
Each call that gave a power play is valued at the goals a power play is worth, 0.116 a minute (a team scores 8.0 goals per 60 minutes on the power play, 2.5 at 5-on-5). They are shown on every game page, but at a luck share of 0 (section 4) they don’t count toward luck; overturned goals likewise.
9. Momentum
Not counted. The NFL and college tests found no sign that a lucky break changes what comes next, and hockey’s breaks come too often to carry one, so it wasn’t fitted for the NHL and the game pages don’t offer the setting.
10. What the “adjust the assumptions” panel changes
It reruns the coin-flip replay and luck in goals under your shares and your choice of what counts, overtime and the shootout included. It doesn’t move the replay with the same day’s form, which draws every shot at its expected chance already.
11. Validation
Does luck predict the rest of the season?
The test that matters: if what we call luck is luck, a record with it taken out should say more about the games still to come. For each team-season, each measure over the first 41 games against points percentage over the last 41, with PDO regression (shot differential at the league’s shooting percentage, the usual way to read PDO) as the benchmark:
| First half → second half, r | 2018-19 to 2025-26 (253) | 2025-26 (32) |
|---|---|---|
| Coin-flip replay (our luck-adjusted record) | 0.666 | 0.492 |
| Goal differential | 0.636 | 0.430 |
| Replay with the same day’s form | 0.633 | 0.478 |
| Expected-goal differential, with records | 0.631 | 0.490 |
| Actual wins | 0.630 | 0.445 |
| Points percentage | 0.614 | 0.429 |
| Expected-goal differential, xG alone | 0.602 | 0.492 |
| PDO regressed (shot differential at league shooting) | 0.560 | 0.409 |
The luck-adjusted record predicts the rest of a season better than the standings, goal differential and PDO regression, pooled and in the held-out season. PDO itself barely carries over: a team’s first-half PDO correlates 0.33 with its second-half PDO. In one season of 32 teams the expected-goal differentials are as good as the coin-flip replay; the pooled seasons separate them.
Holdout
Every fitted number (expected goals, the records, the shares, the calibration, overtime) was fitted without 2025-26 and checked on it: the results are in the sections above.
Luck and the closing line
Not run yet: it needs the betting lines (section 1).
Win probability
The line through each game page is a model of the goal difference minute by minute, with the league’s scoring rates by score and time left (pulled goalies included). Checked on 77,433 moments of 2025-26: log loss 0.512.
12. Forecasts and power rankings
Each team is rated each week on its goal margins (capped at 4) and its expected-goal margins, against the opponents it has played, starting from last season’s rating. Tested on every game from 2021-22 to 2025-26, each forecast from the games before it (6,993 games): 58.8% of winners picked, log loss 0.6646; goals alone 0.6705, expected goals alone 0.6646, the home team always 0.6905. Expected goals carry the forecast. The power rankings are the same ratings. Predictions · Power rankings
13. Limitations
- No betting lines yet, so two of the four numbers are blank.
- Expected goals know where and how a shot was taken, not the passes before it, which the public play-by-play doesn’t record. Part of what looks like finishing luck or skill is that.
- Shot locations come from each arena’s scorers; the season level corrects the league’s drift, not one arena’s.
- Blocked shots have no shooter location and are left out.
Data: fastRhockey (SportsDataverse) and the NHL’s own feed; our own expected-goals model. The full record, with the decisions behind it, is in the repository’s docs/METHOD-NHL.md.