NPB Pythagorean Expectation 2026: True Strength and Schedule Difficulty

Data as of Aug 23, 2026

Central League

Largest gap above expectation Yakult +4.2 wins
Largest gap below expectation Chunichi −6.8 wins

Pacific League

Largest gap above expectation ORIX +6.0 wins
Largest gap below expectation SoftBank −4.1 wins

end of Aug 23, 2026 · npbc.media

As of Aug 23, 2026, the largest gap above the Pythagorean expectation belongs to Yakult (+4.2 wins) in the Central League and ORIX (+6.0 wins) in the Pacific League, while the largest gap below it belongs to Chunichi (−6.8 wins) in the Central League and SoftBank (−4.1 wins) in the Pacific League. A positive gap means overperforming the run differential; a negative one, underperforming.

The standings show results, but runs scored and allowed are known to reflect a team's underlying strength more faithfully. This page shows the gap between the Pythagorean expected record and the actual one, the difficulty of each club's remaining schedule, and the biggest over- and underperformances of the last 20 seasons - a view of where each club really stands beyond the win-loss table.

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 Gap vs expectation end of Aug 23, 2026 npbc.media ← Underperforming (actual < expected) Overperforming (actual > expected) → Hanshin −0.9 Yomiuri +1.5 DeNA −4.5 Yakult +4.2 Chunichi −6.8 Hiroshima +1.2
Central League Gap vs expectation end of Aug 23, 2026 npbc.media ← Underperforming (actual < expected) Overperforming (actual > expected) → T −0.9 G +1.5 DB −4.5 S +4.2 D −6.8 C +1.2
Pacific League Gap vs expectation end of Aug 23, 2026 npbc.media ← Underperforming (actual < expected) Overperforming (actual > expected) → SoftBank −4.1 Seibu +3.4 Nippon-Ham −1.0 ORIX +6.0 Lotte +4.9 Rakuten −1.1
Pacific League Gap vs expectation end of Aug 23, 2026 npbc.media ← Underperforming (actual < expected) Overperforming (actual > expected) → H −4.1 L +3.4 F −1.0 B +6.0 M +4.9 E −1.1

Central League

Team Actual RS/RA Pythagorean pct Expected W-L Diff
Hanshin 63 - 47 - 1 417 / 349 .581 63.9 - 46.1 −0.9
Yomiuri 60 - 51 - 2 379 / 357 .527 58.5 - 52.5 +1.5
DeNA 50 - 59 - 3 428 / 428 .500 54.5 - 54.5 −4.5
Yakult 50 - 60 - 1 346 / 416 .416 45.8 - 64.2 +4.2
Chunichi 49 - 65 - 1 386 / 395 .489 55.8 - 58.2 −6.8
Hiroshima 44 - 60 - 4 321 / 390 .412 42.8 - 61.2 +1.2

Pacific League

Team Actual RS/RA Pythagorean pct Expected W-L Diff
SoftBank 69 - 41 - 2 543 / 374 .664 73.1 - 36.9 −4.1
Seibu 65 - 48 - 3 415 / 376 .545 61.6 - 51.4 +3.4
Nippon-Ham 63 - 52 - 1 477 / 421 .557 64.0 - 51.0 −1.0
ORIX 55 - 57 - 2 403 / 462 .438 49.0 - 63.0 +6.0
Lotte 51 - 55 - 3 381 / 440 .434 46.1 - 59.9 +4.9
Rakuten 43 - 67 - 1 359 / 447 .401 44.1 - 65.9 −1.1

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, recent form and head-to-head records against each opponent are not considered.

Central League

Difficulty rank Team Left Avg. opponent pct
1 Hiroshima 35 .494
2 Chunichi 28 .489
3 DeNA 31 .487
4 Yakult 32 .486
5 Yomiuri 30 .463
6 Hanshin 32 .457

Pacific League

Difficulty rank Team Left Avg. opponent pct
1 Rakuten 32 .536
2 Lotte 34 .526
3 ORIX 29 .525
4 Nippon-Ham 27 .507
5 Seibu 27 .502
6 SoftBank 31 .495

Darker cells mean a tougher remaining schedule (a higher average opponent winning percentage).

Biggest overperformers, 2006-2025: top 10

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.

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, 2006-2025: bottom 10

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
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
2011 Hanshin Tigers 68 - 70 - 6 482 / 443 74.3 −6.3

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 rankings at the bottom of the page (covering the last 20 seasons) give a sense of scale: gaps around plus or minus ten wins are among the largest on record there.

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.

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