## The Joy of wOBA

Last night, David announced that FanGraphs is officially carrying wOBA as our newest statistical addition. For those of you who have read The Book, you’ll be familiar with wOBA, but for those of you who aren’t, here’s a brief introduction and some reasons why you should give this new, funny sounding stat a try.

First off, wOBA is a linear weight formula presented as a rate statistic scaled to On Base Percentage. Essentially, what that means is that average wOBA will always equal average OBP for any given year. If you know what the league’s OBP is, you know what the league’s wOBA is. Usually, league average falls in the .335 range – it was .332 last year, but offense was down around the game in 2008, which may or may not continue.

So, why should you care about wOBA? What makes it better than OPS or any of the more famous rate statistics that measure offensive value? The beauty of wOBA lies in linear weights. Essentially, every outcome has a specific run value that is proportional to other outcomes – a home run is worth a little more than twice as much a single, for instance. What wOBA does, as all linear weights formulas do, is value these outcomes relative to each other so that they are properly valued.

OPS, as you probably know, significantly undervalues the ability of a hitter to get on base. It treats a .330 OBP/.470 slug as equal to a .400 OBP/.400 slug, when the latter is more conducive to scoring runs. wOBA gives proper weight to all the things a hitter can do to produce value, and is a more accurate reflection of a hitter’s value.

For a practical example, let’s look at Ryan Ludwick versus Hanley Ramirez. Ludwick had a .966 OPS versus a .940 OPS for Ramirez – not a huge difference, but one most people would consider significant. If you put a lot of stock in OPS, you’d probably argue that Ludwick had a better offensive season.

However, Ramirez actually had a slightly higher wOBA, .403 to .401. This is due to the fact that Ramirez posted a .400/.540 line compared to Ludwick’s .375/.591 mark. Ramirez’s 25 point advantage in OBP was slightly more valuable than Ludwick’s 51 point advantage in SLG, and wOBA reflects this.

The other great advantage wOBA has is that it’s extremely easy to convert into run values. Simply take a player’s wOBA difference from the league average, divide by 1.15, and multiply that by how many plate appearances he got, and you have a run value above or below average for that player.

For instance, using Ramirez, who we already said had a .403 wOBA, which is 72 points higher than the 2008 NL average of .331. 0.072 / 1.15 = 0.063. 0.063 * 700 = 43.82 runs above average.

wOBA – league average wOBA divided by 1.15 times plate appearances = runs above average by linear weights. Simple, easy, and accurate. This is the joy of wOBA.

If you want a solid, context-neutral statistic that values hitting properly, wOBA is a great place to start. Some of the other great stats here on FanGraphs, such as WPA/LI and WPA, take context into account to add or subtract value based on how a hitter did in certain situations, but there are times when you just want to know how a batter did at the plate, regardless of who was on base or what the score was at the time. For those, wOBA is the perfect answer.

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Forgive my ignorance of wOBA, but is it any different than BP’s EQA.

Something that doesn’t make sense to me is that, if I understood correctly, wOBA has the same value has OBP?

If that’s the case, then why go through all this trouble. Why not just check OBP?!

wOBA is only ‘scaled’ to look like OBP.

Thus, we grade wOBA the same way as OBP:

0.310 and below is under average

0.320 is marginally average

0.330 is average

0.340 is slightly above average

0.350 is good

.360 and above is very good

A player’s wOBA may or may not be the same as their OBP.

This is just awesome.

Ever since I learned about wOBA, I wished there was a sortable leaderboard that I can organize and compare between players. Of course, EQA is a good all-in-one offensive metric, but I had a distaste for BP’s leaderboards and was reluctant to go there. Fangraphs has been my favorite Baseball website for some time now, and now the addition of wOBA will secure its place. Every hardcore stathead should be doing backflips right now.

I salute you, David Appelman. (Oh and of course, Tango)

Also, great post about the specifics of wOBA, Dave.

Thank you for the formula to calculate wins above average, what is the conversion to get wins above replacement level? Is there a position adjustment for that?

wOBA and EqA are both linear weights formulas, so the only major difference between them is the scale – wOBA is scaled to OBP, EqA is scaled to BA. There’s some minor differences in the formulas, but they don’t add up to much.

There’s nothing wrong with EqA, per se, but the formula to convert wOBA into runs and wins is readily available while the same is not true of EqA. So I prefer wOBA.

As for replacement level, the generally accepted mark is that it is about 20 runs below average per full season. So, you can just add 20 runs to whatever your +/- average mark comes out to be. The position adjustments are separate – a good place to start reading about those is Sean Smith’s recent article over at THT.

One significant difference is that EqA includes SB/CS, while wOBA doesn’t, no?

wOBA does include SB and CS on FanGraphs.

Thanks for clearing that up Dave.

Interesting, thanks David.

Will league averages for wOBA be posted?

This is outstanding. I have come to love wOBA after the StatCorner guys made it readily available on their site.

Speaking of that site, maybe Matthew can answer this: Does StatCorner’s wOBA factor in SB’s and CS’s?

Great stuff. Very good explanation, also. I’m not much of a sabre-head when it comes to wrapping my head around most of it, but even I understood all of that. Should be put to great use here at FanGraphs.

David, Just curious…. Whats the process like to add a stat to the fangraphs site? What things do you consider? Who is involved in the decision making process. Thanks in advance

For 500 PA replacement level comes out to a wOBA of .285

700PA => 0.298

I really hope a replacement level player never accumulates 700PA in a season.

Roughly speaking, replacement level is around .300 wOBA.

The league average wOBA is similar to the “official” OBP, and is identical to how I calculate OBP.

drew: There’s no real process for adding stats to FanGraphs. There were a lot of requests to add wOBA and Dave Cameron made an argument to me sometime last week that “sealed the deal” so to speak. Then Tangotiger walked me (and anyone who reads his blog) through the math to scale the formula from year to year and it was finally put up on the site.

Personally I try to put up stats that we either don’t have anything like or are a lot better than we already have. I think wOBA fit mainly in the “a lot better category” in terms of a context neutral player valuation.

I ran the numbers against the official OBP this morning and it’s very close. At most it’s .005 off in any given year, but for most years it’s even closer.

Is there a wOBA for pitchers anywhere?

Like I mean specific values for stat categories adding or subtracting to run prevention.

FIP would be the equivalent. It’s linear weights put on an ERA scale.

I thought about that after I posted the 2nd time, and said duh, thanks!

Maybe a stupid question, but it sounds like wOBA is not adjusted for park and league effects?

Quick question- why divide by 1.15? I was following everything in this formula up until that. Is that just arbitrary to even it out to the OPS for the year?

Because they linear weights run values of the events (e.g, walk, home run, etc.) have been altered so that when they’re added up and divded by plate appearances, the resulting number “looks” like on-base percentage, with an average of around .330-.340.

I believe (correct me if I’m wrong) that FanGraphs uses a custom linear weights version of wOBA that 1) calculates the specific value of each event in a given year, and 2) alters the “wOBA scale” (the “1.15” in the original formula) so that league average wOBA = league average OBP. So the wOBA scale in recent years has been more like 1.2.

Hope that helps.

OH, sorry…

I skipped a step — when calculating the wOBA rate stat, the linear weights values are already multiplied by a “wOBA scale,” (e.g, 1.15, 1.2, whatever) so when you convert to a runs scale, you need to divide it back.

Bernie Williams had a career wOBA of .371 – this is historically above average? still learning wOBA

Is there anywhere I can see a nice, simple definition of wOBA? I’m trying to trim this down to what would be in a baseball dictionary…

wOBA gives proper weight to all the things a hitter can do to produce value, and is a more accurate reflection of a hitter’s value. a home run is worth a little more than twice as much a single

wOBA has its pros and cons, from what I can tell.

The pro is it makes perfect sense. It’s based on linear weights to particular statistics. EqA is weirdly constructed.

The con is, it’s weak in the points where EqA is strong: comparing across eras, and park adjustments.

Fortunately, fangraphs also now includes adjusted weighted runs created, or wRC+. You’re probably familiar with OPS+. This is kind of the same thing, only a lot more detail and accurate (in that OPS+ overrates low OBP, big HR total sluggers like Gary Gaetti, and underrates guys who succeeded by maintaining a high OBP, or base stealers, like Tim Raines and Rickey Henderson).

To put it back to Williams for a second, his career wRC+ was 128. Essentially saying he was a 28% better than average hitter in his career. Which is good. But it’s also the same wRC+ as Al Ferrara (.346 in a short career in a pitchers era) and Rick Monday (.358 wOBA). Also just one behind Hank Sauer (.380 wOBA in an extreme hitter’s era).

But yeah, to sum up your original question, wOBA is everything contributed by a hitter, scaled into a number equivalent to the league average OBP for that season. Good number to see how much a player produced in a season, just not recommended as a 1:1 comparison for a Rockie and a Padre (use wRC+ for that). Good example is how Carlos Gonzalez edged Kyle Blanks in wOBA .378 to .372, but Blanks crushed CarGo in wRC+, 138 to 125.

Not sure if anyone will notice this at this point, but on what basis can a HBP and a base on balls have different values? For a leadoff hitter, wouldn’t a single and a walk have the same value, at least for the first at-bat? So for a leadoff hitter, walks are somewhat more valuable than the formula allows?