Year End Pythagorean Records

Bill James, famous for his "Baseball Abstract" and advancement of sabermetric baseball statistics, created a formula called Pythagorean Win Expectation. It uses a team's runs scored and runs allowed to calculate how many wins a team "should" have at any given time in a season. The theory is that a team's won-loss record (particularly at year's end) does not necessarily reflect how good or bad that team is.

Comparing a team's actual W-L record to their Pythagorean record can measure how "lucky" or "unlucky" a team is. A great recent example is the 2007 Arizona Diamondbacks, who, despite being outscored by 20 runs by season's end, finished with a record of 90-72 and the NL West Division title. According to their Pythagorean Expecation, they should have finished 79-83, giving them a +11 Luck.

The formula, for those interested, is:

1 / 1 + (Runs Allowed/Runs Scored)^2

This will give you the expected winning %, and, when multiplied by 160 games, will give you the expected # of wins for a team based on their Run Differential (defined as Runs Scored minus Runs Allowed).

Some argue that using a power of 1.81 is more accurate, but for the purpose of this article, we'll keep it simple and use 2.

The following are the final standing for 2018 SLB based on Pythagorean records.

NORTH DIVISION

TEAM               PyW  PyL   RS    RA   DIFF   ActW  ActL  LUCK
-----------------------------------------------------------------
Halifax Sailors     97   63  905   734   +171   98    62    (+)1
Philly Fever        81   79  895   888   +7     77    83    (-)4
Bedford Crunch      77   83  790   823   -33    77    83    EVEN
Cleveland Dawgs     68   92  811   942   -131   69    91    (+)1


SOUTH DIVISION

TEAM               PyW  PyL   RS    RA   DIFF  ActW  ActL   LUCK
-----------------------------------------------------------------
Atlanta Flyers      99   61  1004  785   +219   98    62    (-)1
San Juan Senadores  90   70  876   777   +99    94    66    (+)4
Baltimore Panthers  80   80  787   788   -1     77    83    (-)3
Savannah Sabers     79   81  768   778   -10    73    87    (-)6


EURO DIVISION

TEAM               PyW  PyL   RS    RA   DIFF  ActW  ActL   LUCK
-----------------------------------------------------------------
London Knights     104   56  954   704   +250   102   58    (-)2
Paris Pimpernels    86   74  889   825   +74     90   70    (+)4
Scotland Rebels     70   90  729   833   -104    78   82    (+)8
Ireland Invaders    52  108  649   936   -287    52  108    EVEN


FAR EAST DIVISION

TEAM               PyW  PyL   RS    RA   DIFF  ActW  ActL   LUCK
-----------------------------------------------------------------
Kyoto Bushido       85   75  800   754   +46    79    81    (-)6
Taipei Tai Fong     80   80  758   765   -7     83    77    (+)3
Chiang Mai Kwaan    78   82  852   869   -17    74    86    (-)4
Osaka Ronin         58  102  821  1085   -264   59   101    (+)1

Overall, the software does a good job of keeping teams' records within a reasonable margin to their Pythagorean expectations. Two teams were exactly right, while 4 more were with a win or two of their projected win totals. Impressive.

Only the Far East saw a team "outluck" their way to the playoffs; the actual records between Taipei and Kyoto are 9 games off of what the run differentials say they should be, with Kyoto underperforming their way out of the post season.