Pythagorean expectation
Expected records from runs scored and allowed, prorated over decisions and compared with the actual record. Ties drop out of the denominator, as in the official NPB percentage.
Central League
| Team | Actual | RS/RA | Pythagorean pct | Expected W-L | Diff |
|---|---|---|---|---|---|
| Hanshin | 59-46-1 | 402 / 338 | .579 | 60.8-44.2 | −1.8 |
| Yomiuri | 57-48-2 | 361 / 346 | .519 | 54.5-50.5 | +2.5 |
| Yakult | 49-55-1 | 333 / 399 | .418 | 43.5-60.5 | +5.5 |
| DeNA | 48-56-3 | 416 / 410 | .507 | 52.7-51.3 | −4.7 |
| Chunichi | 46-62-1 | 369 / 372 | .496 | 53.6-54.4 | −7.6 |
| Hiroshima | 40-58-4 | 301 / 375 | .401 | 39.3-58.7 | +0.7 |
Pacific League
| Team | Actual | RS/RA | Pythagorean pct | Expected W-L | Diff |
|---|---|---|---|---|---|
| SoftBank | 67-39-1 | 517 / 356 | .664 | 70.4-35.6 | −3.4 |
| Seibu | 60-47-3 | 393 / 362 | .537 | 57.5-49.5 | +2.5 |
| Nippon-Ham | 62-49-0 | 458 / 395 | .567 | 63.0-48.0 | −1.0 |
| ORIX | 53-54-2 | 390 / 444 | .441 | 47.2-59.8 | +5.8 |
| Lotte | 48-53-3 | 366 / 421 | .436 | 44.1-56.9 | +3.9 |
| Rakuten | 41-63-1 | 340 / 428 | .396 | 41.2-62.8 | −0.2 |
Remaining schedule difficulty
The average current winning percentage of remaining opponents, weighted by games remaining against each. Higher means a tougher run-in. Home/away, travel, schedule density and recent form are not considered.
Central League
| Difficulty rank | Team | Left | Avg. opponent pct |
|---|---|---|---|
| 1 | Hiroshima | 41 | .494 |
| 2 | DeNA | 36 | .493 |
| 3 | Yakult | 38 | .482 |
| 4 | Chunichi | 34 | .480 |
| 5 | Hanshin | 37 | .459 |
| 6 | Yomiuri | 36 | .456 |
Pacific League
| Difficulty rank | Team | Left | Avg. opponent pct |
|---|---|---|---|
| 1 | ORIX | 34 | .535 |
| 2 | Rakuten | 38 | .533 |
| 3 | Lotte | 39 | .519 |
| 4 | Nippon-Ham | 32 | .515 |
| 5 | SoftBank | 36 | .500 |
| 6 | Seibu | 33 | .494 |
Biggest overperformers in history: top 10 (2005-2025)
Reference values based on archived game results (runs) and official final standings. Club names are shown as they were at the time; each year links to that season's pennant race page.
| Year | Team | Record | RS/RA | Expected wins | Diff |
|---|---|---|---|---|---|
| 2015 | Hanshin Tigers | 70-71-2 | 465 / 550 | 59.8 | +10.3 |
| 2020 | Chunichi Dragons | 60-55-5 | 429 / 489 | 50.6 | +9.4 |
| 2007 | Hanshin Tigers | 74-66-4 | 518 / 561 | 64.9 | +9.1 |
| 2012 | Chunichi Dragons | 75-53-16 | 423 / 405 | 66.5 | +8.5 |
| 2011 | Tokyo Yakult Swallows | 70-59-15 | 484 / 504 | 62.1 | +7.9 |
| 2024 | Tohoku Rakuten Golden Eagles | 67-72-4 | 492 / 579 | 59.2 | +7.8 |
| 2024 | Chunichi Dragons | 60-75-8 | 373 / 478 | 52.4 | +7.6 |
| 2022 | Yokohama DeNA BayStars | 73-68-2 | 497 / 534 | 65.9 | +7.1 |
| 2025 | Tohoku Rakuten Golden Eagles | 67-74-2 | 446 / 526 | 59.9 | +7.1 |
| 2022 | Chunichi Dragons | 66-75-2 | 414 / 495 | 59.1 | +6.9 |
Biggest underperformers in history: bottom 10 (2005-2025)
| Year | Team | Record | RS/RA | Expected wins | Diff |
|---|---|---|---|---|---|
| 2022 | Hanshin Tigers | 68-71-4 | 489 / 428 | 77.9 | −9.9 |
| 2023 | Tokyo Yakult Swallows | 57-83-3 | 534 / 567 | 66.2 | −9.2 |
| 2007 | Tokyo Yakult Swallows | 60-84-0 | 596 / 623 | 69.1 | −9.1 |
| 2021 | Fukuoka SoftBank Hawks | 60-62-21 | 564 / 493 | 68.5 | −8.5 |
| 2013 | Fukuoka SoftBank Hawks | 73-69-2 | 660 / 562 | 81.4 | −8.4 |
| 2005 | Chiba Lotte Marines | 84-49-3 | 740 / 479 | 91.7 | −7.6 |
| 2008 | Tohoku Rakuten Golden Eagles | 65-76-3 | 627 / 607 | 72.6 | −7.6 |
| 2008 | Yokohama BayStars | 48-94-2 | 552 / 706 | 55.3 | −7.3 |
| 2018 | Yomiuri Giants | 67-71-5 | 625 / 575 | 74.3 | −7.2 |
| 2023 | Hokkaido Nippon-Ham Fighters | 60-82-1 | 464 / 496 | 66.7 | −6.7 |
What the Pythagorean expectation is
The Pythagorean expectation is an empirical formula devised by Bill James, the father of sabermetrics: it estimates a team's expected winning percentage from the ratio of runs scored to runs allowed. The original insight - winning percentage roughly tracks runs squared over the sum of runs squared and runs allowed squared - gave the formula its theorem-like name; in practice the exponent is tuned slightly away from 2.
The expected records on this page multiply the Pythagorean percentage by the number of decisions. Ties drop out of the denominator, exactly as in the official NPB percentage, so expected wins plus expected losses always equal actual wins plus losses.
Reading the gap: it is not all luck
Overperforming the expectation reflects an ability to win close games - bullpen quality, late-game management - as well as the bounce of one-run games. Underperformance often comes from a mix of blowout wins and narrow losses. Not all of the gap is luck, but extreme gaps are known to regress toward the mean in following seasons.
The historical rankings at the bottom of the page give a sense of scale: gaps around plus or minus ten wins are among the largest ever recorded.
Strength of schedule: the same games left can weigh differently
Down the stretch, who you still have to play matters as much as how many games remain. The difficulty shown here (SoS, strength of schedule) is the average current winning percentage of remaining opponents, weighted by the number of games left against each. Higher means more strong opponents ahead.
It is a deliberately simple definition: home/away splits, travel, schedule density and recent form are not considered. Note that the odds board's simulation already bakes in the remaining matchups themselves.
Frequently asked questions
What is the Pythagorean winning percentage?
An empirical formula by Bill James that estimates a team's expected winning percentage from runs scored and allowed; its theorem-like shape gave it the name.
Why do actual records differ from expected records?
Because the same run totals can be distributed differently - winning the close ones versus piling up blowouts. Bullpen quality, late-game management and one-run-game fortune all show up in the gap, and extreme gaps tend to regress the following season.
How do ties affect the expected records?
They do not. Expected records are prorated over decisions only, so the number of ties leaves them unchanged - the same convention as the official NPB winning percentage, where ties drop out of the denominator.
How is the schedule difficulty (SoS) computed?
It is the weighted average of remaining opponents' current winning percentage, with games remaining against each opponent as weights. Home/away, travel, schedule density and recent form are not considered.