Converting OPS to wOBA

Does it get any more exciting than this?  I bet not.  Why write about this?  OPS is used by everyone but Joe Morgan as shorthand representation for batter skill.  wOBA, on the other hand, has no such following, as much as fangraphs has helped. 

So what is wOBA?  It's short for weighted On Base Average.  It takes all possible batter outcomes (single, double, strikeout, etc.) and weights them according to their run value.  The total number of runs is divided by plate appearances to give, in effect, runs per plate appearance.  The final figure has been manipulated to an on base percentage scale where .340 is about average. 

Using the standard approximation of 10 runs per 1 win, we can find the value of a batter's plate appearances.  OPS was never designed with that in mind, but it turns out that wOBA and OPS correlate very very well.




The graph is the correlation of OPS to wOBA of 125 major league hitters over the last 3 calendar years, the data for which I nabbed from fangraphs.  If you can't see, the r-squared value is 0.967 and the exact equation provided is

wOBA = 0.362*OPS+0.059

For ease of remembering, .36 and .06 are perfectly acceptable values.  Plugging .340 for league average wOBA, we get that an average bat is about .775 OPS.  20 runs worse over the course of a season (600 PA), or about replacement level, is about .670.  As long as we're talking about a fairly standard line (the regression had 3 consecutive seasons per batter, which significantly normalized batting lines), this conversion should not only be useful, but show perhaps that more advanced stats aren't getting us as far away from the hoi as we think. 

On the other hand, that's an extremely high r-squared value, almost absurdly so.  Perfect correlation is 1.  Why so high?  Power and on base percentage are dependent on each other.  Pitchers tend to stay away from big sluggers, but don't mind busting weak hitters inside.  So, there's a margin of error associated with avoiding the big bats.  I would bet this holds particularly for those who mash fastballs.  As support for this notion, I ran a second regression comparing ISO and BB% using the same data set and found an r-squared of .314, which is fairly robust.  There are obviously skills involved outside of hitting for power that allow some to take more or fewer walks than opportunity allows, but there's a reason why you don't see any .300/.400/.400 hitters.

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