## Introducing Statistics: Weighted On Base Average

Today, I want to focus on a sabermetric stat that has replaced OPS in many circles as the best statistic to measure hitting performance. OPS was a little crude, simply adding to pre-existing statistics, and a little lopsided, as it gives a decided advantage to slugging percentage. It also had the misfortune of double counting hits. Weighted On Base Average (wOBA) was developed to be a stat that lacked these difficulties.

wOBA grows out of the linear weights formula developed by Pete Palmer and expounded in its longest form in Palmer and John Thorn’s 1984 book*The Hidden Game of Baseball*. Linear weights attempted to transform all batting outcomes into numbers weighted by the likelihood of producing a run. For example, slugging percentage counts a home run as four times more valuable than a singe (4 total bases to 1). Linear weights scaled singles as worth .77 and home runs worth 1.7, acknowledging that home runs do produce an instant run, giving them greater worth, but the fact that a single provides a base runner *and* another hitter at the plate, while also advancing runners already on the bases, makes it closer to the value of a home run than slugging percentage presents. (The comparison group is outs, which are worth 0.)

Using the run expectancy values from linear weights and diving by plate appearances gets you a statistic that averages .300. To put it on nearly the same scale as OBP, sabermetrician Tom Tango added 15% to each of the values, giving an average of .320, nearly identical with the league average On Base Percentage. The formula at this point looks like this:

(0.72xNIBB + 0.75xHBP + 0.90x1B + 0.92xRBOE + 1.24x2B + 1.56x3B + 1.95xHR) / PA

RBOE is reached base on error, and NIBB are non-intentional walks.

To give you a broad sense of wOBA, an average player is around .320, above average in the range of .340-.360, and excellent players hover above .400. For this season, Albert Pujols led the majors at .449, while Joe Mauer led the American League at .438. The most notable difference of wOBA from OPS is that it gives substantially more weight to OBP while OPS is weighted in favor of slugging percentage. The question then becomes, which is more valuable, reaching base or hitting for power? As Joe Posnanski recently argued, the essence of successful hitting is not making outs. While power is certainly better than its absence, if all else is equal, that is rarely the case. Getting on base is the first thing you have to do to score runs and win games, and that highlights the relative strength of wOBA.

**Explore posts in the same categories:**Baseball, Statistics

**Tags:** Albert Pujols, Joe Mauer, Joe Posnanski, Statistics, Tom Tango

10/07/2009 at 12:52 pm

Baseballbriefs.com tracking back Introducing Statistics: Weighted On Base Average…Baseballbriefs.com tracking back Introducing Statistics: Weighted On Base Average…

10/07/2009 at 7:23 pm

“The Hidden Game of Baseball”- what a book

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