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

 

 

Leave a Reply

Your email address will not be published. Required fields are marked *