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.
Scroll right to see the full chart
Pacific League
Scroll right for more
| Team | Actual | RS/RA | Pythagorean pct | Expected W-L | Diff |
|---|---|---|---|---|---|
| SoftBank | 84 - 47 - 3 | 652 / 429 | .683 | 89.4 - 41.6 | −5.4 |
| Seibu | 74 - 56 - 4 | 471 / 430 | .542 | 70.4 - 59.6 | +3.6 |
| Nippon-Ham | 73 - 59 - 3 | 563 / 500 | .554 | 73.1 - 58.9 | −0.1 |
| ORIX | 63 - 70 - 2 | 467 / 565 | .414 | 55.0 - 78.0 | +8.0 |
| Lotte | 58 - 68 - 3 | 453 / 537 | .423 | 53.3 - 72.7 | +4.7 |
| Rakuten | 52 - 78 - 1 | 432 / 519 | .417 | 54.2 - 75.8 | −2.2 |
Biggest overperformers, 2006-2025: top 2
Reference values based on archived game results (runs) and official final standings. Club names are shown as they were at the time; years within the last 50 seasons link to that season's pennant race page.
Scroll right for more
Biggest underperformers, 2006-2025: bottom 4
Scroll right for more
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 move back toward the expectation in following seasons.
The list at the bottom of the page (covering the last 20 seasons) gives a sense of scale: gaps around plus or minus ten wins are among the largest on record there.
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.