643 runs scored and 649 allowed give a Pythagorean win percentage of .496
The Pythagorean win percentage is the winning percentage that a team's runs scored and runs allowed predict. The formula is runs scoredx ÷ (runs scoredx + runs allowedx), and baseball commonly uses an exponent x of 1.83. The 2025 Cleveland Guardians scored 643 runs and allowed 649, which gives .496. Over 162 games that is an expected record of 80.3 wins and 81.7 losses (the calculator uses the unrounded percentage).
Cleveland actually went 88-74. That is 7.7 wins more than expected, the largest positive gap among the 30 MLB teams. Even though they were outscored by 6 runs, the Guardians won more games than any other AL Central team (the Tigers won 87). Wins that scoring does not explain are often put down to luck, but close-game results, bullpen use and runs bunched into a few games are all mixed in. The calculator above loads 52 teams from the 2025 KBO, MLB and NPB seasons and shows where each one sits on a curve and in a bar chart.
What the Pythagorean win percentage tells you
- Record versus roster strength: two teams with the same record can have very different run margins. The 2025 Yankees and Blue Jays both finished 94-68, but New York outscored opponents by 164 runs and Toronto by 77, so the method expects 96.7 wins for the Yankees and 88.5 for the Blue Jays. A large margin is a signal that a team is better than its record, and a small one that the record is ahead of the team. The standings alone do not show that.
- A rough read on the rest of the season: midseason, add "remaining games × Pythagorean win percentage" to the wins a team already has to estimate where it will finish. The calculator shows this for a 162-game MLB season (144 games for the KBO, 143 for NPB).
- The size of an upgrade: you can work out how many more runs scored, or how many fewer runs allowed, add one win. An average 2025 MLB team needed about 9.7 runs per win. It is a way to turn the expected effect of a signing or a defensive upgrade into wins.
How it is calculated
- Pythagorean win percentage: runs scoredx ÷ (runs scoredx + runs allowedx). Computing the same thing as 1 ÷ (1 + (runs allowed ÷ runs scored)x) keeps the numbers from overflowing in basketball, where scores are large.
- Choosing the exponent: 1.83 is the value Baseball-Reference uses for pythWL in its standings. Calculated with 1.83, all 30 MLB teams in 2025 match pythWL; calculated with 2, only 8 do. 2 is the exponent of Bill James's original formula, and Pythagenpat sets the exponent from the scoring environment as (runs scored + runs allowed, per game)0.287.
- Ties: MLB standings have no ties, so expected wins are simply the win percentage times games played. Leagues with ties handle them differently. Article 2 of the KBO league rules sets win percentage as wins ÷ (wins + losses), and NPB standings use the same method, so expected wins there are the win percentage × (games − ties). The NFL counts a tie as half a win and half a loss.
- Gap from actual: actual wins − expected wins, shown to one decimal place.
- Value of one win: the calculator measures how much expected wins rise for one more run scored and shows the reciprocal, which is the number of runs it takes to add a win. Runs allowed work the same way.
| Sport · method | Exponent | Basis |
|---|---|---|
| Baseball (default) | 1.83 | Baseball-Reference pythWL (matches all 30 MLB teams in 2025) |
| Baseball (original formula) | 2 | Bill James's original formula |
| Baseball (Pythagenpat) | (runs per game, scored + allowed)0.287 | FanGraphs Projected Standings |
| NBA | 14 | Basketball-Reference glossary |
| NFL | 2.37 | Pro-Football-Reference Expected W-L (matches the four 2025 teams checked) |
The 2025 MLB teams, one by one
These are the 2025 regular-season records (162 games each) calculated with exponent 1.83. A plus sign in the Difference column marks a team that won more than its runs scored and allowed predicted.
| Team | W-L | Runs scored | Runs allowed | Actual win% | Pythagorean win% | Expected wins | Difference |
|---|---|---|---|---|---|---|---|
| Brewers | 97-65 | 806 | 634 | .599 | .608 | 98.5 | −1.5 |
| Phillies | 96-66 | 778 | 648 | .593 | .583 | 94.4 | +1.6 |
| Blue Jays | 94-68 | 798 | 721 | .580 | .546 | 88.5 | +5.5 |
| Yankees | 94-68 | 849 | 685 | .580 | .597 | 96.7 | −2.7 |
| Dodgers | 93-69 | 825 | 683 | .574 | .586 | 94.9 | −1.9 |
| Cubs | 92-70 | 793 | 649 | .568 | .591 | 95.7 | −3.7 |
| Mariners | 90-72 | 766 | 694 | .556 | .545 | 88.3 | +1.7 |
| Padres | 90-72 | 702 | 621 | .556 | .556 | 90.0 | 0.0 |
| Red Sox | 89-73 | 786 | 676 | .549 | .569 | 92.1 | −3.1 |
| Guardians | 88-74 | 643 | 649 | .543 | .496 | 80.3 | +7.7 |
| Astros | 87-75 | 686 | 665 | .537 | .514 | 83.3 | +3.7 |
| Tigers | 87-75 | 758 | 691 | .537 | .542 | 87.8 | −0.8 |
| Mets | 83-79 | 766 | 715 | .512 | .531 | 86.1 | −3.1 |
| Reds | 83-79 | 716 | 681 | .512 | .523 | 84.7 | −1.7 |
| Royals | 82-80 | 651 | 637 | .506 | .510 | 82.6 | −0.6 |
| Giants | 81-81 | 705 | 684 | .500 | .514 | 83.2 | −2.2 |
| Rangers | 81-81 | 684 | 605 | .500 | .556 | 90.1 | −9.1 |
| D-backs | 80-82 | 791 | 785 | .494 | .503 | 81.6 | −1.6 |
| Marlins | 79-83 | 709 | 798 | .488 | .446 | 72.3 | +6.7 |
| Cardinals | 78-84 | 689 | 754 | .481 | .459 | 74.3 | +3.7 |
| Rays | 77-85 | 714 | 683 | .475 | .520 | 84.3 | −7.3 |
| Athletics | 76-86 | 733 | 817 | .469 | .451 | 73.0 | +3.0 |
| Braves | 76-86 | 724 | 734 | .469 | .494 | 80.0 | −4.0 |
| Orioles | 75-87 | 677 | 788 | .463 | .431 | 69.8 | +5.2 |
| Angels | 72-90 | 673 | 837 | .444 | .402 | 65.0 | +7.0 |
| Pirates | 71-91 | 583 | 645 | .438 | .454 | 73.5 | −2.5 |
| Twins | 70-92 | 678 | 773 | .432 | .440 | 71.3 | −1.3 |
| Nationals | 66-96 | 687 | 899 | .407 | .379 | 61.5 | +4.5 |
| White Sox | 60-102 | 647 | 742 | .370 | .438 | 70.9 | −10.9 |
| Rockies | 43-119 | 597 | 1,021 | .265 | .272 | 44.1 | −1.1 |
Source: MLB Stats API, 2025 regular season. Runs scored total = runs allowed total = 21,614 across the 30 teams. Sorted by wins; difference = actual wins − expected wins.
Cleveland's +7.7 was the largest gap, followed by the Angels (+7.0) and the Marlins (+6.7). The White Sox were furthest the other way at −10.9, then the Rangers at −9.1. Texas outscored opponents 684 to 605, a margin of 79 runs and the fewest runs allowed in MLB, and was expected to win 90.1 games, but finished 81-81. The Padres, at 90-72, landed almost exactly on their expected total (90.0).
KBO and NPB teams with the largest gaps
The same calculation covers the other two leagues in the tool, where ties are left out of the win percentage. Records are shown as wins-losses-ties.
| League | Team | W-L-T | Runs scored | Runs allowed | Expected wins | Difference |
|---|---|---|---|---|---|---|
| KBO | Samsung | 74-68-2 | 775 | 647 | 82.6 | −8.6 |
| KBO | NC | 71-67-6 | 732 | 766 | 66.1 | +4.9 |
| KBO | LG | 85-56-3 | 788 | 584 | 89.4 | −4.4 |
| KBO | Lotte | 66-72-6 | 676 | 749 | 62.5 | +3.5 |
| NPB | Rakuten | 67-74-2 | 446 | 526 | 59.9 | +7.1 |
| NPB | Orix | 74-66-3 | 502 | 519 | 67.9 | +6.1 |
| NPB | Nippon-Ham | 83-57-3 | 548 | 409 | 88.3 | −5.3 |
| NPB | Hanshin | 85-54-4 | 496 | 352 | 90.6 | −5.6 |
Samsung went 74-68-2 with 775 runs scored and 647 allowed. Its expected 82.6 wins is 8.6 more than it won, the largest gap among the 10 KBO teams. NC scored 732 and allowed 766 yet finished 71-67-6, 4.9 wins better than expected. In NPB, Rakuten had the biggest positive gap (+7.1) and Hanshin the biggest negative one (−5.6). Hanshin allowed 352 runs, the fewest of NPB's 12 teams, and was expected to win 90.6 games but won 85. Switch the league in the calculator to load any KBO or NPB team.
How well did each formula fit?
For each formula, this is the average absolute gap between actual and expected wins across the 52 teams of the 2025 KBO, NPB and MLB seasons.
| Formula | KBO | NPB | MLB | All 52 teams |
|---|---|---|---|---|
| Exponent 1.83 | 3.23 | 3.48 | 3.65 | 3.53 |
| Exponent 2 | 3.91 | 4.36 | 4.05 | 4.09 |
| Pythagenpat | 3.59 | 2.94 | 3.77 | 3.55 |
Across the three leagues combined, 1.83 and Pythagenpat came out about even and 2 had the largest gap. In MLB itself, 1.83 had the smallest average gap (3.65 wins, against 3.77 for Pythagenpat and 4.05 for 2). In NPB, Pythagenpat had the smallest average gap, but that is one season of 12 teams. NPB teams score and allow 6.59 runs per game combined, fewer than the KBO (9.46) or MLB (8.89), and a lower-scoring league gives a lower Pythagenpat exponent, about 1.72 here. One season cannot rank the formulas, so read this table as a 2025 observation, not as proof that one formula is better.
How many runs is one win worth?
Put in a league-average team, with runs scored equal to runs allowed, and the number of runs needed for one more win differs from league to league.
| League (2025) | Average team runs scored | Scored + allowed per game | Value of one win (1.83) |
|---|---|---|---|
| KBO | 681.3 | 9.46 | 10.7 |
| MLB | 720.5 | 8.89 | 9.7 |
| NPB | 471.2 | 6.59 | 7.4 |
The fewer runs a league scores, the more each run is worth, so a win takes fewer of them. A team's own scoring level matters too: Cleveland, with just 643 runs scored, needed about 8.7 more runs scored or 8.8 fewer runs allowed per win, below the MLB average of 9.7. When a team's scored and allowed totals are far apart, the two sides differ more; the 2025 Samsung needed about 12.3 more runs scored or 10.2 fewer runs allowed.
Common mistakes
- Entering per-game averages: exponents 1.83 and 2 depend only on the ratio of runs scored to runs allowed, so the win percentage would come out the same. Pythagenpat, though, divides season totals by games to set its exponent, so averages throw it off. Enter season totals in the fields.
- Counting ties in the denominator: Samsung's 74-68-2 divided by all 144 games is .514, but the KBO's win percentage is 74 ÷ 142 = .521, and expected wins should be applied to those 142 games as well. This matters in the KBO, NPB and NFL; MLB has no ties.
- Earned runs instead of runs allowed: the runs allowed in this formula (R) include unearned runs, such as those that score because of errors. Pitching stats also list earned runs (ER), which are fewer, and entering them inflates expected wins.
- Judging from the first few games: over 10 games, a 10-run edge is a full run per game, so the percentage swings widely. It settles as games pile up.
- Mixing in the postseason or spring training: to compare with the standings, enter regular-season numbers only.
Limits and cautions
- The Pythagorean win percentage looks at two numbers, runs scored and runs allowed. FanGraphs notes that calling a team with more wins than expected "lucky" is only a loose approximation, though the gap does tend to move back toward average.
- It does not account for one-run-game results, the bullpen or how many games the runs were bunched into. If the lineup changed during the season, full-season totals do not describe the current roster.
- Team data are from the 2025 regular season. The 2026 season is not included, because the KBO regular season was still in progress on October 12, 2026, when this page was written. For a season in progress, enter the numbers yourself and the calculator also gives a projected season finish.
- The projected season finish assumes the remaining games are played at the current Pythagorean win percentage, with no ties. For the NBA and NFL the calculator offers one example team and the exponent, without team data.
Sources
- 01KBO: 2025 League RulesArticle 1: 144 games and ties. Article 2, how to calculate win percentage: wins ÷ (wins + losses)
- 02KBO Records Room: team standings, team batting and team pitching (2025 regular season)Wins, losses and ties for 10 teams, runs scored (team batting R), runs allowed (team pitching R); totals 6,813 = 6,813
- 03NPB: 2025 Central League standings (std_c)Pacific League (std_p); runs scored from team batting (tmb_c, tmb_p), runs allowed from team pitching (tmp_c, tmp_p), 12 teams
- 04MLB Stats API: 2025 regular-season standingsWins, losses, runs scored and runs allowed for 30 teams (runs scored total = runs allowed total = 21,614)
- 05Baseball-Reference: 2025 MLB StandingsExpanded standings, pythWL: all 30 teams match the exponent 1.83 calculation
- 06FanGraphs: The Tigers Have Been Kicked in the Pythagoras (2026-09-03)Uses the Pythagenpat exponent ((RS + RA)/G)^0.287 in Projected Standings
- 07FanGraphs Library: Pythagorean Win-Loss"Luck" is only a loose label, and gaps from expected tend to regress
- 08Basketball-Reference: GlossaryPythagorean Wins = G × PTS14 ÷ (PTS14 + Opp PTS14); the 2024–25 Lakers example comes from the NBA_2025 season table
- 09Pro-Football-Reference: GlossaryExpected W-L: the 2025 Chiefs, Bills, Lions and Giants match the exponent 2.37 calculation. The Chiefs example (6-11, 362 scored, 328 allowed) matches the NFL.com 2025 standings
- 10NFL: Tiebreaking ProceduresA tie counts as half a win and half a loss for both teams
Frequently asked questions
How is the Pythagorean win percentage calculated?
It is runs scored^x ÷ (runs scored^x + runs allowed^x). In baseball the default exponent x is 1.83, the value Baseball-Reference uses, and expected wins are that percentage multiplied by games played, minus ties in leagues that leave them out. The 2025 Cleveland Guardians (643 runs scored, 649 allowed, 88-74) come to .496, which is 80.3 expected wins over 162 games using the unrounded percentage.
Should I use an exponent of 1.83 or 2?
Start with 1.83. Baseball-Reference uses it for the pythWL column in its standings, and calculated with 1.83 all 30 MLB teams in 2025 match that column, while with 2 only 8 do. In the 2025 season the average gap from actual wins across the 52 teams of the KBO, MLB and NPB was 3.53 with 1.83 and 4.09 with 2, but that is one season, not proof. The exponent 2 comes from Bill James's original formula.
What is Pythagenpat?
It is a method that does not fix the exponent but sets it as (runs scored + runs allowed per game)^0.287. FanGraphs uses it in its Projected Standings. A league that scores fewer runs gets a lower exponent: 2025 NPB (6.59 runs per game combined) comes to about 1.72. In 2025 Pythagenpat had the smallest average gap of the three formulas in NPB, which is one season of 12 teams and does not show it is the better formula.
How are ties handled?
MLB standings have no ties, so expected wins are the win percentage times games played. Article 2 of the KBO league rules sets win percentage as wins ÷ (wins + losses), and NPB standings do the same, so expected wins there are the Pythagorean win percentage × (games − ties). The NFL counts a tie as half a win and half a loss, so the calculator adds half the ties to actual wins before comparing.
If a team wins more than expected, was it lucky?
People often say so, but it is only a rough label. Close-game results, the bullpen and runs bunched into a few games are all mixed in. FanGraphs advises against treating the gap as a strict measure of skill, while noting that the gap itself tends to move back toward average. The 2025 Guardians won 7.7 more games than expected, the largest positive gap in MLB.
How many runs does it take to add a win?
It depends on the team and the league's scoring environment. For a league-average 2025 team, with runs scored equal to runs allowed, it comes to about 9.7 runs in MLB, 10.7 in the KBO and 7.4 in NPB. The Value of one win row in the calculator shows the scored side and the allowed side separately for the team you enter.
Can I use it in the middle of a season?
Yes. Enter the runs scored, runs allowed, games played and actual wins so far, and the calculator estimates the final record as actual wins + remaining games × the Pythagorean win percentage. It uses 162 games for MLB, 144 for the KBO and 143 for NPB, and the result swings a lot when few games have been played.
Does it work for basketball or football?
Yes. The NBA uses the exponent 14 from Basketball-Reference, and the NFL uses 2.37, the same value as Pro-Football-Reference's expected win-loss record. For any other sport, choose Custom exponent and enter an exponent from 0.5 to 30.