Pythagorean Expectation - "Second-order" and "third-order" Wins

"Second-order" and "third-order" Wins

In their Adjusted Standings Report, Baseball Prospectus refers to different "orders" of wins for a team. The basic order of wins is simply the number of games they have won. However, because a team's record may not reflect its true talent due to luck, different measures of a team's talent were developed.

First-order wins, based on pure run differential, are the number of expected wins generated by the "pythagenport" formula (see above). In addition, to further filter out the distortions of luck, sabermetricians can also calculate a team's expected runs scored and allowed via a runs created-type equation (the most accurate at the team level being Base Runs). These formulas result in the team's expected number of runs given their offensive and defensive stats (total singles, doubles, walks, etc.), which helps to eliminate the luck factor of the order in which the team's hits and walks came within an inning. Using these stats, sabermetricians can calculate how many runs a team "should" have scored or allowed.

By plugging these expected runs scored and allowed into the pythagorean formula, one can generate second-order wins, the number of wins a team deserves based on the number of runs they should have scored and allowed given their component offensive and defensive statistics. Third-order wins are second-order wins that have been adjusted for strength of schedule (the quality of the opponent's pitching and hitting). Second- and third-order winning percentage has been shown to predict future actual team winning percentage better than both actual winning percentage and first-order winning percentage.