# Saber-Terms Series: wOBA

#### By Michael Jong

I’ve gone for much of my time here on Marlin Maniac eschewing doing something like this. I had always run on the assumption that if readers wanted to know what things like wOBA and FIP meant, they could travel on down to FanGraphs to find out. But this process seems a bit impersonal and perhaps still difficult to understand, so I’m going to take over the reins of explaining all the crazy acronyms I call “stats” really mean. Call it the ** Saber-Terms Series**!

(Here I’ll remind you that my other blog, Intro to Sabermetrics 101, has more in-depth, but still easy-to-understand, explanations on these terms and more on sabermetrics. Go check it out!)

Today, I’ll start with what is now one of the most popularly used terms in saber-speak, the offensive stat wOBA.

**wOBA**

Here’s a glossary piece I wrote on Intro to Sabermetrics, and here is the general explanation as found on The Book site.

Tom Tango was the originator of the statistic wOBA, but its roots go a while back. Essentially, wOBA is a linear weights model for run scoring. Linear weights models are simple to understand: for each offensive event, a run total above some baseline is determined. Then, the totals of all the events are multiplied by their respective run coefficients or “weights,” and the sum becomes a value in runs above or below the determined baseline. Linear weights was initially championed by one Pete Palmer, but since then many other models have come out, all quite similar and with good accuracy.

So why do we use wOBA? Well, there’s certainly nothing wrong with using other linear weights systems. Pete Palmer’s original Batting Runs system has weights for each event that very closely mirror empirical weights determined for time periods. Batting Runs is also adjustable over different eras, though its method of correction is not right (it adjusts the value of the out only, but empirically the value of all events changes over different run environments). What does wOBA provide that something like Batting Runs or its descendants doesn’t?

Well, first off wOBA is determined as a rate stat fit to the OBP scale with a denominator of plate appearances. The reason Tango did this was to allow him to use a binomial model for the various research studies published in *The Book: Playing the Percentages in Baseball*. What comes out practically from this to the casual observer is that wOBA looks like a statistic that general fans recognize (OBP) and thus are perhaps more comfortable with. This is not a design by Tango,who needed the OBP scale to make his research easier, but it does work out nicely for us. Baseball Prospectus’ Clay Davenport does a translation to the batting average scale for his statistic Equivalent Average, another linear weights model disguised as a rate stat.

OK, so it’s easier to recognize. What else? The fact that it is a rate stat makes comparison between players much easier. With a traditional linear weights system, the end result of a calculation is a value of runs above or below a baseline, let’s say the average player. This would give you a total, but it had no context for playing time. On the other hand, wOBA has playing time considered in its denominator, so it is easy to determine which player hit better in a comparison. For example, two players in a straight linear weights model could have earned two runs above average. However, when examining wOBA, you could find that one player had a much higher wOBA than the other, signaling a difference in playing time.

The appeal of combining the power of linear weights as a run estimator combined with a rate stat that is easy on the eyes, recognizable, and comparable, makes wOBA an excellent choice. But there is one aspect about it that makes it even better than Equivalent Average, a very similar model in design. It is extremely easy to convert wOBA into linear weights runs above average (thus taking out the playing time component). The conversion is done as follows:

wOBA Runs Above Average (wRAA) = (wOBA – league wOBA) * PA / wOBAScale

where wOBA scale is the multiplier used to fit the rate to the OBP scale. You can also find the total runs by just adding:

wOBA Total Runs = wRAA + (league R/ league PA)*player PA

The calculations are simple, once you’re given the wOBA scale conversion. For ease of use, 1.15 is the typical wOBA scale given, and 1.21 has been the scale for the last few seasons.

A couple of final notes:

– wOBA does not directly use the linear weights values for each event. Rather, to each weight, they subtract the weight of an out, thus each wOBA weight is the run value of an event over the run value of an out. This, of course, zeroes the value of an out and allows us to use plate appearances rather than outs as our denominator.

– A shorthand way to park-adjust wOBA is to divide it by the square root of the park factor. I’m not sure why this works, (if anyone can help me on that one) but by doing so I get very close numbers compared to park-adjusted wOBA totals elsewhere. It was originally suggested to me by Colin Wyers.

– The linear weights for wOBA can be easily determined each season using basic baseball statistics found on database such as the Baseball Databank. Here are the directions on how to do it on MySQL, if you’re interested.

– If you’re like me and you’re too lazy to figure it out, here are all the weights for each season, from 2008 all the way down to 1871.

Thanks for reading up on the favorite offensive total stat for us baseball geeks. I hope you guys use wOBA as much as possible to talk about a player’s offensive contributions. It’s readily available on FanGraphs, so we shouldn’t have to use OPS too much now. Enjoy wOBA and check in every Friday for more of these definitions in our Saber-Terms series.