From Expected Goals to Wins Above Replacement

Three Parts, One Number

Each of the first three articles produced an independent metric. RAPM gives each skater a Net xG: their contribution to their team's expected goal differential at 5v5, controlling for linemates, opponents, score state, and venue. GSAx gives each goalie a goals-saved-above-expected figure. Both are denominated in goals. Both are independent by construction: RAPM uses pre-goalie expected goals, so it measures shot suppression without crediting or blaming the goalie.

Adding them together gives a team-level combined value: the sum of all skater Net xG plus all goalie GSAx. If this framework is any good, combined value should predict which teams win games.

Do the Metrics Predict Wins?

Across the 2025-26 regular season (120 games), the correlation between combined value and standings points: R² = 93.0%.

The framework captures the vast majority of team-level variation. Boston and Montréal cluster at the top with massive combined values (+31.9 and +29.2), separated by 9+ points from the rest of the league. Seattle sits at the bottom, negative in both components.

The most interesting case is Ottawa: +11.8 combined (third-best) driven almost entirely by Philips' +15.7 GSAx, while their skater Net xG is actually negative (-3.9). One goalie is holding up the entire team's analytical profile. The remaining variance is likely power play/penalty kill performance, which the 5v5 model doesn't capture.

Deriving Goals Per Win

Knowing that the metrics predict wins is useful. Knowing the exchange rate is more useful. How many goals of combined value equals one win?

We derive this from the Pythagorean expectation, the formula relating a team's goal differential to its expected winning percentage:

WPct = GF^exp / (GF^exp + GA^exp)

The exponent determines how efficiently goal differential converts to wins. We tested two approaches:

• Hockey standard: exp = 2.0. Used in most NHL Pythagorean models.
• Pythagenpat dynamic: exp = totalGPG^0.287. Adapts to the scoring environment. With the PWHL averaging 4.67 goals per game, this yields exp = 1.898.

Both exponents produce R² = 95.7% against actual winning percentage. The Pythagorean formula is an excellent fit for the PWHL's scoring environment. With identical R², we use the fixed exponent (2.0) for simplicity and consistency with the broader hockey analytics literature.

From the Pythagorean exponent, we derive Goals Per Win:

GPW = (4 × avgGPG) / exp = (4 × 2.33) / 2.0 = 4.67 goals per team per win

When both teams are included, each additional goal of combined value is worth approximately 1/9.33 of a win (since GPW for the full game is 9.33). For context, the NHL's equivalent figure is roughly 5.0-5.5 goals per team per win. The PWHL's figure is slightly lower, consistent with a marginally higher-scoring environment.

What Counts as Replacement Level?

WAR requires a baseline: what would a freely available, replacement-level player produce? In the NHL, this is typically set at a .300 winning percentage. We can't borrow that number. The PWHL has different roster depth, a different talent pool, and a different economic structure. We need to derive it.

The approach: invert the Pythagorean formula. For a given target replacement winning percentage, solve for the per-game goal deficit that produces it:

targetWPct = (avgGPG − d)^exp / ((avgGPG − d)^exp + (avgGPG + d)^exp)

Then check pool balance: the sum of all individual player WARs should equal the sum of all team-level wins above replacement. If the pool of player WAR doesn't match the pool of team WAR, the replacement level is wrong.

We select .350, where 79% of qualified players produce above replacement. This is slightly higher than the NHL's typical .300. With only 8 teams and roughly 200 players, the talent pool is concentrated. The gap between an average player and a freely available replacement is smaller than in a 32-team league with thousands of professionals in the pipeline.

At .350 replacement, a replacement-level player produces 2.28 goals below average over a full season. The per-game deficit is 0.36 goals. A team of replacement-level players would win roughly 35% of their games, about 10-11 wins in a 30-game season.

The WAR Leaders

Skaters

Top 20 skaters by WAR (Net xG above replacement, divided by 9.33 goals per win):

Nylén Persson leads at +1.05 WAR, meaning her 5v5 play alone was worth just over one additional win over a replacement-level player in a 30-game season. That might sound modest, but in a league where the gap between first and last is 12 wins, a single win matters.

Defenders dominate the top of the list: 6 of the top 10, 10 of the top 20. This is consistent with how RAPM works. Defenders play more 5v5 minutes and have more opportunity to accumulate impact. Forwards like Butorac and Carpenter are notable precisely because they produce elite value in fewer minutes.

Minnesota places four skaters in the top 13 (Butorac, Zumwinkle, Curl-Salemme, Roese). That depth of above-average contributors is how they finished third despite split goaltending.

Goalies

All 12 goalies, ranked by WAR:

The top three goalies are worth more than any individual skater. Desbiens at +2.67 WAR is worth nearly three additional wins over a replacement goalie. That is roughly the same value as Minnesota's top three skaters combined. Goaltending leverage in the PWHL is enormous: one player, touching every defensive play, with a wide performance range.

The gap between Desbiens (+2.67) and Osborne (-0.77) is 3.4 wins. In a league where the standings gap between first and last is 12 wins, goaltending alone explains a significant chunk of team separation.

Team WAR vs Actual Wins

The ultimate validation: does the bottom-up, player-level WAR reconstruct team-level outcomes? We sum each team's individual player WARs and compare to actual wins above replacement (actual WPct minus .350, times games played).

The league-wide pool balances: 51.00 team WAR vs 51.01 player WAR. That is by construction (we derived the replacement level to make this hold).

The per-team picture is more interesting. The top four teams (Boston, Montréal, Minnesota, Ottawa) all have player WAR that undershoots their actual wins above replacement. These teams won more games than their 5v5 xG metrics explain. The gap is likely special teams: strong power plays and penalty kills that the 5v5-only RAPM doesn't capture.

The bottom four teams show the reverse: player WAR exceeds team WAR. Seattle's gap is the largest (+3.75), meaning they had above-average 5v5 talent that didn't translate into proportional wins. Power play futility, penalty kill breakdowns, or poor performance in one-goal games could explain the leak.

Limitations

• 120 games, 8 teams.The Pythagorean fit looks strong (R² = 95.7%), but 8 data points is small. The replacement level is derived from one season. Multi-season calibration would be more robust.
• 5v5 only.RAPM excludes power play and penalty kill, where significant value is created and destroyed. The 3-4 win gap between team WAR and player WAR for Boston/Montréal is likely special teams contribution that the model misses.
• Ridge regularization compresses extremes. RAPM pulls all coefficients toward zero. The true best and worst players are probably further from average than the model shows, which means the WAR range is likely wider than reported.
• Replacement level from one season. The .350 WPct comes from fitting 79% of qualified players above replacement. With more seasons, this threshold can be calibrated against actual call-up and free-agent performance rather than a percentage target.
• No pre-shot movement data.The xG model doesn't know about screens, cross-ice passes, or goalie positioning. Some WAR variance reflects shot difficulty the model can't measure.
• Season-to-season stability unknown. We can't yet test whether a player's WAR persists across seasons. The 2026-27 season (now with 12 teams) will be the first opportunity.

What’s Next

We now have a single number, WAR, that converts each player's contribution into wins. In Part 5, we connect WAR to salary. The PWHL published every player's base salary in April 2026. With WAR in hand, we can measure which contracts are wins-per-dollar bargains, which are overpays, and how teams navigated the average-salary system to build their rosters.