The Pythagorean Theorem of Baseball, created by Bill James, relates a winning percentage for a team using its run scored and runs surrendered to its actual winning percentage. James found that using runs scored compared to runs allowed is a better indicator of a team’s future performance than its actual winning percentage. The formula is:
Pyth = Runs Scored ^ 2 / (Runs Scored ^ 2 + Runs Allowed ^ 2)
The formula has since been updated to include either 1.81 or 1.83 as the exponent instead of 2.
As you can see in the chart above the Athletics and Blue Jays have both vastly underachieved their expected win total, while the White Sox have vastly overachieved their total. The theorem does not necessarily indicate that these teams will dramatically reverse their season over the second half, but it does indicate that their current record does not necessarily reflect how good our bad the team has played.