Saber-Slant #14: Fun With wOBA

Last week in the All-Star Game lineup optimization piece, I mentioned a stat called wOBA, an acronym for Weighted On-Base Average. I did not explain much about it last week in order to get to the lineup optimization, but today I will discuss the stat in detail and display its usefulness in encompassing all offensive characteristics.

What is wOBA?

Don’t be fooled by the name “Weighted On-Base Average.” The statistic is scaled to look like on-base percentage (OBP), and indeed the idea behind it was to get the stat to work in a binomial (success or failure) fashion like OBP. However, there is a key difference between wOBA and a stat like OBP. The explanation can be seen in this quote from stat innovator Tom Tango, explaining the history of wOBA.

Anyway, while OBP initially satisfied our objective for The Book, it became quite clear very early that we simply couldn’t always treat a walk and a HR equally. In OBP, each safe event counts as “1”. So, we needed something else, something that could align itself to OBP to make comparisons straightforward in The Book, be binomial-like, and better weight each event.

Tango nails the problem on the money there. In order for a stat to be comprehensive, the weight of each event could not possibly be “1.” Otherwise, we would be treating walks, doubles, and homers all equally, when intuitively we know they are not equal events.

How can we resolve this problem? Remember linear weights? Linear weights provides average run values for each event in baseball. This allowed for the relative values of events to be labeled correctly. For Tango’s initial purposes, it was important that the “safe” (i.e. good) events averaged to a value of 1 (just as in OBP), while the outs were all worth 0 (again, just as in OBP). To do this, Tango took the difference between the value of an out and the value of each safe event and used those as the weights for each event. As a result, you get something like this basic weights as provided in The Book.

Non-intentional BB: 0.62
1B: 0.77
2B: 1.08
3B: 1.37
HR: 1.70

In order to scale the stat to OBP, Tango multiplied all the weights by a multiplier (1.15, for this generic example) such that the average wOBA would equal the average OBP, resulting in the weights you see here. These weights actually change year-to-year based on the run environment, but as you can see in this list of historical weights, recently there has not been much in the way of changes.

The Good Stuff

Now that we have gone through some of the technical explanation (about which you can read more in the links provided), let’s get to the cool advantages. What wOBA provides is a rate stat that is based on linear weights, scaled to something that is somewhat familiar. While the familiarity factor was not the reason for it being scaled to OBP, I do find the scale a little easier to get used to, as compared to getting used to something like linear weights runs/PA (average is 0.12). As we talked about last week, the scale is moderately easy to understand:

Awful: below .300 (2010 example: Yuniesky Betancourt, .292)
Bad: .300-.320 (Miguel Tejada, .304)
Average: .320-.340 (the average is always around .330)
Good: .350-.370 (Brandon Phillips, .356)
Great: .370-.400 (Scott Rolen, .385)
Amazing: above .400 (Albert Pujols, .414)

If you can keep that in mind, then you should be able to easily compare players and their offensive production. In addition, not only can we compare qualitatively (Albert Pujols is better than Yuniesky Betancourt), but the calculation to compare quantitatively is a breeze. When converting wOBA to linear weights runs, all you have to do is to take the difference between two wOBA (usually done with a player’s or team’s wOBA versus the average wOBA), divide by the multiplier that scales to OBP, and multiply by the number of plate appearances.

For example, assume both Pujols and Betancourt had 400 PA with those wOBA. The multiplier for this season is about 1.21. We can now find how many more runs Pujols contributed over Betancourt.

(0.414 – 0.292) * 400 / 1.21 = 40.3 runs

This can be done against a league average or by comparing individual players such as in the example. With wOBA, the comparison is easily made.

The Comparison Power of wOBA

A few weeks ago, I posed this example as a point against using batting average as a tool for evaluating players.

Player A (Justin Upton): .300/.366/.532
Player B (Shin-Soo Choo): .300/.394/.489
Player C (A.J. Pierzynski): .300/.331/.425

Each player had the same .300 AVG in 2009, but with radically different OBP and SLG. As a result, we can qualitatively tell the difference in the value of these batting lines. It should be obvious that Pierzynski is not in the same league offensively as Upton and Choo. However, how can we compare the difference between Upton and Choo? Which was better? wOBA can provide that answer.

Upton: .388 wOBA
Choo: .389 wOBA
Pierzynski: .326 wOBA

As you can see, without park-adjustment there is little difference between Upton’s .300/.366/.532 line and Choo’s .300/.394/.489. Upton’s superior power numbers were more or less evened out by Choo’s ability to avoid more outs that season. Furthermore, we can quantitatively tell how much better Upton/Choo and their .300 BA were over Pierzynski’s .300 BA season.

(.388 – .326) *600 / 1.21 = approx. 31 runs per 600 PA better

As you can see, because wOBA weighs all of the events correctly, we can use it as a rate stat to more accurately determine the comparative quality of hitters. Glancing at Upton’s and Choo’s lines, it would have been difficult to say who was better. Using their wOBA tells us quite certainly that they hit the same. Beyond that, the conversion from a qualitative measurement to a quantitative one is really simple, and gives us an answer in runs, a meaningful baseball denomination. Quite simply, wOBA is one of the best total offensive stats out there, and something that I use all the time in my analysis.