Written by Sharp edge picks• March 15, 2023• 8:16 am• Value bets and sports thoughts • 1,003 Comments

Flawed James’ Pythagorean Theorem – Offensive Teams Beware!

Bill James developed a theory that run differential (squared) would long term approximate a MLB’s teams win %. Appears to make sense – long term, if you score a lot more runs than you give up, you will win more games than you lose.

HOWEVER, there is a BIG EXCEPTION – strong offensive teams. If you score a lot of runs, your run scoring becomes ‘clumpy’, you are a positively skewed outlier, and you will end up appearing ‘unlucky’ based on James’ calculation. Specifically, you will consistently win LESS games than the James model predicts. How many less games? 3 per year. Looking at the data for 3 MLB seasons (2013-15), laid out below, the top 20% of teams in offence, measured by runs scored, average losing 3 MORE games per year than Bill James model predicts. Its remarkably consistent as the top 6 offences each of the 3 years combined to lose exactly 18 MORE games than James model predicts each year.

Furthermore, each year there is a .3-.45 correlation between runs scored and being ‘unclutch’ (or winning less games than James model predicts). This is further evidence that if you score a lot of runs, you positively skew your +/- causing your team to win less games than expected.

Finally, homerun hitting teams are ‘unclutch’ using James’s model. Over the same 3 yrs, the 4 best homer hitting teams, the O’s, Jays, Mariners, and Astros combined to win 24 LESS games than Bill James model predicts.

Power hitting = unclutch based on Bill James model due to the positive skew of piling on runs.

2 Lessons to be Learned:

1 – for sabermetrics, or anyone obsessed with blindly following stats, always question the formuls. There are sometimes major errors.

2 – for offensive teams, beware, you will consistently underperform expectations. This is NOT due to bad luck, but the clumping nature of offense (scoring 12 runs doesn’t increase your chances of winning a game much more then 8 runs, but does help your +/-). Come playoff time, 1 run is precious, building high powered offences may disappoint as the team isn’t built to execute.

2015	Wins	RS	EW	Uncluctch
Toronto Blue Jays	93	891	103	10	Correlation
New York Yankees	87	764	88	1	0.455826098
Texas Rangers	88	751	83	-5
Boston Red Sox	78	748	80	2	top 20% of RS
Colorado Rockies	68	737	70	2	teams avg 3
Houston Astros	86	729	94	8	LESS wins than EV
Kansas City Royals	95	724	91	-4
Arizona Dbacks	79	720	82	3
Baltimore Orioles	81	713	83	2
Washington Nationals	83	703	89	6
Pittsburgh Pirates	98	697	94	-4
Minnesota Twins	83	696	91	8
SF Giants	84	696	89	5
Oakland Athletics	68	694	77	9
Detroit Tigers	74	689	68	-6
Chicago Cubs	97	689	91	-6
New York Mets	90	683	90	0
Cleveland Indians	81	669	84	3
LA Dodgers	92	667	90	-2
LA Angels	85	661	79	-6
Seattle Mariners	76	656	73	-3
Milwaukee Brewers	68	655	71	3
San Diego Padres	74	650	72	-2
St. Louis Cardinals	100	647	98	-2
Tampa Bay Rays	80	644	81	1
Cincinnati Reds	64	640	68	4
Philadelphia Phillies	63	626	61	-2
Chicago White Sox	76	622	71	-5
Miami Marlins	71	613	73	2
Atlanta Braves	67	573	59	-8

2014	Wins	RS	EW	Uncluctch
LA Angels	98	773	97	-1	Correlation
Detroit Tigers	90	757	87	-3	0.300129449
Colorado Rockies	66	755	75	9
Oakland Athletics	88	729	100	12	top 20% of RS
Toronto Blue Jays	83	723	85	2	teams avg 3
LA Dodgers	94	718	93	-1	LESS wins than EV
Minnesota Twins	70	715	74	4
Baltimore Orioles	96	705	95	-1
Washington Nationals	96	686	98	2
Pittsburgh Pirates	88	682	87	-1
Cleveland Indians	85	669	83	-2
SF Giants	88	665	87	-1
Chicago White Sox	73	660	70	-3
Kansas City Royals	89	651	84	-5
Milwaukee Brewers	82	650	80	-2
Miami Marlins	77	645	77	0
Texas Rangers	67	637	66	-1
Seattle Mariners	87	634	92	5
Boston Red Sox	71	634	71	0
New York Yankees	84	633	77	-7
New York Mets	79	629	82	3
Houston Astros	70	629	70	0
St. Louis Cardinals	90	619	83	-7
Philadelphia Phillies	73	619	73	0
Arizona Dbacks	64	615	66	2
Chicago Cubs	73	614	70	-3
Tampa Bay Rays	77	612	79	2
Cincinnati Reds	76	595	79	3
Atlanta Braves	79	573	78	-1
San Diego Padres	77	535	75	-2

2013	Wins	RS	EW	Uncluctch
Boston Red Sox	97	853	102	5	Correlation
Detroit Tigers	93	796	100	7	0.462414758
St. Louis Cardinals	97	783	103	6
Oakland Athletics	96	767	97	1	top 20% of RS
Baltimore Orioles	85	745	85	0	teams avg 3
Cleveland Indians	92	745	91	-1	LESS wins than EV
LA Angels	78	733	81	3
Texas Rangers	91	730	93	2
Toronto Blue Jays	74	712	76	2
Colorado Rockies	74	706	75	1
Tampa Bay Rays	92	700	88	-4
Cincinnati Reds	90	698	95	5
Atlanta Braves	96	688	99	3
Arizona Dbacks	81	685	80	-1
Washington Nationals	86	656	85	-1
New York Yankees	85	650	78	-7
LA Dodgers	92	649	90	-2
Kansas City Royals	86	648	87	1
Milwaukee Brewers	74	640	75	1
Pittsburgh Pirates	94	634	89	-5
SF Giants	76	629	73	-3
Seattle Mariners	71	624	66	-5
New York Mets	74	619	73	-1
San Diego Padres	76	618	71	-5
Minnesota Twins	66	614	61	-5
Houston Astros	51	610	55	4
Philadelphia Phillies	73	610	65	-8
Chicago Cubs	66	602	70	4
Chicago White Sox	63	598	66	3
Miami Marlins	62	513	63	1