The stats we use: wOBA

Just because people term a statistic “advanced” doesn’t mean it requires an overly complex calculation. Last week we examined UZR, and that might have given off the wrong impression. UZR is complex out of necessity. A baseball field contains 78 zones, and to calculate defense we must account for multiple zones per player. This involves not only balls hit into the zones, but also the type of ball hit into the zones and the rate at which other players converted those balls into outs. Offensive statistics, however, are a bit more straight forward. It helps, too, that we’re already familiar with the components.

This week we’re going to dive into weighted on base average, or wOBA. Developed by Tom Tango, the stat attempts to reconcile OBP and SLG, two of the most important offensive statistics. They both measure one thing while ignoring others. OBP measures how many times a player reaches base while ignoring the difference between a walk and a home run. SLG measures total bases while ignoring walks. wOBA weighs both and combines them for an offensive statistic that more accurately represents a player’s value.

What about OPS?

At this point you might be saying, “But they already have OPS. That combines OBP and SLG. So what gives?” True, OPS stands for on-base plus slugging, so why the need for a more advanced calculation? The answer deals with the scales upon which each metric is based.

The denominator in OBP is plate appearances, while the denominator in SLG is at-bats. True, they’re expressed in decimal format, and that might make it easier to slap them together. That doesn’t mean it is correct. Beyond the denominator issue, we also have an issue of scale. OBP is almost always going to be lower than SLG, because OBP is binary. You either reached base or you didn’t, meaning you get a 1 if you succeed and a 0 if you fail. SLG, on the other hand, measures total bases, so a player receives 4 for a home run, 3 for a triple, 2 for a double, and 1 for a single. And, again, it works with a smaller denominator, since at-bats is a subset of plate appearances.

By merely adding together OBP and SLG, we get a number that greatly favors power hitters. High on base guys will still climb the OPS charts, but their lack of power will keep them away from the top. What we want an on-base plus slugging stat to accomplish is to properly weigh these two aspects and provide us a proper valuation of offensive contribution.

How do we weigh events?

Instead of working with OBP and SLG, Tango decided to start from scratch with wOBA. This makes perfect sense. Statistics are just a recording of what happened on the field. OBP examines walks, hits, and outs. SLG examines singles and extra base hits. Why take those two pre-made calculations when the available data allows you to weigh the individual components of these stats before their OBP and SLG calculations? That’s exactly what Tango did.

In last week’s UZR primer, we looked at linear run estimators, which assigns a certain run value to each offensive event. This comes into play again for wOBA. After breaking offense down into its individual components, we can then weigh the value of those components and combine them for a rate stat. With wOBA, however, we’re looking at the runs above the run value of an out, which is zero in an OBP calculation. So here’s an updated linear run estimator, in terms of runs above the value of an out.

Event	Value
Single	0.77
Double	1.08
Triple	1.37
Home run	1.70
Walk	0.62

The only step left is to scale the stat to OBP. This isn’t necessary — in fact, the league-average hitter under this situation would be around .300, which seems like a neat, round number. But, since we’re talking about a weighted OBP, Tango decided to scale it so the league average is around .340. That requires adding 15 percent to each weight. Again, not a big deal. It just makes the end result easier to understand.

Stolen bases

Yes, wOBA includes stolen bases. Successful stolen bases weigh at 0.20, while a caught stealing around -0.44. Tango provides a full list of linear weight events here.

Runs above average

Using wOBA, we can easily determine how many runs above average a player contributed. All we have to do is subtract the league-average wOBA from the player’s wOBA. But, because of the 15 percent weight added for scale, we need to divide by 1.15 to strip that out.

No adjustments?

No, there is no wOBA adjustment for park, position, or league. Individuals can make these calculations, but wOBA is meant as a context-neutral stat. Again, just as OPB and SLG are not park adjusted, nor is wOBA.

What about OPS+?

On Big League Stew, Alex Remington is running his own series of articles on advanced statistics. I try not to use what he writes in mine, especially because we’re trying for different purposes. In his wOBA primer he makes a statement with which Tango takes issue. Alex says that wOBA is “superior to non-weighted stats like OPS and OPS+.” The statement is inaccurate, because OPS+ is weighted. But, as Tango notes, it is weighted improperly.

Sean Forman, proprietor of Baseball Reference, leads the charge with OPS+. He essentially weighs OBP to SLG at a 1.2 to 1 ratio. That appears to improperly undervalue OBP, and Tango argues that the ratio should be more like 1.7 or 1.8 to 1. Because OPS+ does park and league adjust, that would make OPS+, as he says, “(almost always) superior to wOBA.” Again, this comes from the man who created wOBA.

To remember

Unlike all-in-one stats like WAR and WARP3, wOBA doesn’t try to tell us everything. What it does try to tell us is the value of a player’s offensive contribution. It doesn’t necessarily favor guys who walk a lot, like OBP, or guys who hit for a lot of power, like SLG and OPS. It breaks down offense into its core events, weighs those events, and then adds up the value. It also adjusts to a familiar scale, making it easier for us to understand, at a glance, the value of a player’s contribution.

Resources

wOBA from The Book
Getting to know wOBA
The history of wOBA, part 1 (to which there seems to be no part 2)