# Third Order Winning Percentage: Nuts and Bolts

Earlier I said that it was important to examine the inner workings of third order winning percentage to determine its predictive value, so here goes.

Baseball Prospectus, who produces the statistic, describes it as ” a team’s projected winning percentage, based on underlying statistics and adjusted for quality of opponents.” The underlying statistics, it turns out, are in fact two statistics, adjusted equivalent runs scored and adjusted equivalent runs allowed.  Each is a statistic that attempts to encompass the entirety of one phase of a game.

The offensive statistic is calculated by adjusting a team’s batting runs above average and runs per plate appearance for their opponents’ ability to prevent runs.  Batting runs above average is not precisely described on baseball prospectus. All that it says is that it “is the number of runs a hitter produces relative to an average hitter, adjusted for park.”  Both FanGraphs and Tango Tiger use an equation that uses the same weights and statistics as wOBA.

wOBA calculates run values for every outcome at the plate and uses these as multipliers for each hit type.  For instance, in 2011 a single was worth 0.89 runs, so wOBA would award a player with .89 runs for every single that he hit. Likewise, but with a different run value, for walks, doubles, triples, home runs, and outs.  The formula for wOBA in 2011 was:

wOBA = (0.69×uBB + 0.72×HBP + 0.89×1B + 1.26×2B + 1.60×3B +
2.08×HR + 0.25×SB -0.50×CS) / PA

*note: some equations for wOBA or batting runs above average do not include stolen bases or caught stealings.

Batting runs above average simply adjusts the figure for league average. No other aspect of player performance is included. Therefore, the only offensive statistics that affect third order winning percentage are walks, hit by pitches, singles, doubles, triples, home runs, outs, and (in some cases) steals and caught stealings.

How defense and pitching are evaluated in third order winning percentage is less clear because of how the Baseball Prospectus glossary works. However, I am assuming that since offense used batting runs above average, preventing runs will be measured with pitching and defense runs above average.  Pitching runs above average are derived from the pitching portion of RAA.  This means that runs allowed per inning is the only statistic used to judge a pitcher’s performance.

FR = .20*(PO+2A-E+DP) – ((team PO – team K) * AVG(POS,LG) * %PT)

As a result, the only defensive statistics that affect third order winning percentage are put outs, assists, errors, and double plays.

This is as close as I was able to get to reconstructing third order winning percentage. I was unable to find anything that I left out, such as the precise method that Baseball Prospectus uses to adjust for opponent performance. I will examine what this means for whether the Pirates can expect to outperform their third order winning percentage in my next post on the subject.