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
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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
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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
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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
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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.
