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## Sunday, April 20, 2014

#### Studeman: Why wOBA Works

Why wOBA Works

Let’s say you have a player, let’s call him Al Trout, who has hit six singles in 10 plate appearances (making an out every other time) and the league, on average, hits three singles every 10 plate appearances (again, making an out every other time). To use linear weights to figure out how many more runs Al contributed above the league average, you’d…

Calculate the extra runs Al contributed by hitting more singles, which equals the difference in singles times the run value of a single, or (6-3) times 0.48, or 1.44.  Then you’d…
Calculate the extra runs that Al contributed by making fewer outs, which equals the difference in outs made times the run value of an out, or (4-7) times -0.30 (that’s a negative 0.30), or 0.9. Then you’d…
Add the two together. 1.44 plus 0.9 equals 2.34. In his 10 plate appearances, Al contributed 2.34 runs more than the average player.

Okay, I have to add a technical footnote here. I have shown you this way of calculating linear weights because it will make it easier to understand the wOBA formula But, in reality, you only have to multiply Al’s singles and outs by the appropriate linear weights of that league and year to calculate the number of runs he contributed above average.

Anyway, that’s the hard linear weights way to calculate the difference.  Here’s the wOBA way:

Multiply the difference in singles times the wOBA multiplier, or (6-3) times 0.78, or 2.34.

That’s it; one simple step. wOBA shows that Al contributed 2.34 runs more than the average player, the same outcome as the linear weights.

Why does this happen? Because wOBA weights include the impact of the hit AND the impact of turning an out into a hit. When you keep the number of plate appearances even, you’re not just adding a hit to the hit total.  You’re also reducing an out from the out total. wOBA captures the impact of both event changes.

wOBA fundamentally works because it is a rate stat.  Its divisor is plate appearances. When you compare two players’ wOBA you have equalized their total plate appearances.

Thanks to Los.

Repoz Posted: April 20, 2014 at 05:27 AM | 1 comment(s) Login to Bookmark
Tags: sabermetrics

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1. Walt Davis Posted: April 21, 2014 at 06:09 PM (#4690582)
wOBA is just oRAR/PA, pointlessly (and incorrectly) re-scaled to an OBP-like measure. (or the hitting-only component of oRAR if you don't want to include baserunning) That's it, nothing special.

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