The Stats We Use: wOBA

Several people on Another Cubs Blog had asked us to write something that explained some of the stats that we often reference in articles and comments. It was always something that I wanted to do, but never got around to it. Since several have asked before and now that we’ve created a new blog with Tim and Adam, it seems more appropriate than ever to finally stop being lazy and get it done.  Maybe we’ll even convince a few more of you of the value of advanced statistics compared to the traditional ones. No big deal if we don’t.

To keep things as simple as possible, Berselius and I are going to break this down into several parts.  We can’t possibly cover all the stats that may show up here at times, but we can cover the majority of them.

The most oft-cited offensive statistic is going to be weighted on-base average (wOBA). It’s a fantastic statistic, but to explain why it’s needed let’s back up and look at OBP and SLG. Each of those stats values a certain aspect of hitting. OBP measures the rate at which a player has reached base safely via hit, walk and hit by pitch. Some people, usually myself if I take time to calculate it, will also include reached on errors while excluding intentional walks. It’s the rate at which batters reach base. It has its flaws. It considers a walk and a home run equally. We know they are not.

Slugging measures the total bases a batter has hit for per at-bat. It’s the measure of how many bases were advanced on the base hits. However, SLG does not even consider how often a batter gets on base. We have two stats that provide two valuable pieces of information, but each piece by itself ignores much about hitting.

To make up for these flaws, people began adding them together to create OPS. The problem with OPS is that it treats OBP and SLG equally, but the most valuable aspect of hitting is not making outs. Football, basketball and hockey are measured in time. After a set amount of time the game is over. Each minute is hugely important. Baseball’s clock is outs. Each team gets 27 of them and each one brings you closer to the end of the game. OBP is more important than SLG yet OPS considers them equal.  This is why we needed a new statistic and thanks to The Book authors tangotiger, MGL and Dolphin, we have that stat.

It’s called wOBA. It weights the value of reaching base and the number of bases advanced to create a rate statistic that is then scaled to OBP because we’re so familiar with what are good and bad OBP’s.  wOBA starts by calculating the run value of each offensive event in baseball. No, not all hits are going to result in runs while sometimes they may result in 2 or 3 runs, but each single helps produce runs while each out does not. The same thing is true for any event.

Don’t be afraid of the formula though. It may seem overwhelming at first: wOBA = (.72*(BB – IBB) + .75*HPB + .90*S + .92*ROE + 1.24*D + 1.56*T + 1.95*HR)/PA. The first thing you may be wondering is why aren’t the value of the walk and hit by pitch the same? It has to do with the control of the pitcher. The single is more valuable than the walk because singles can score runners from 2nd and sometimes there are errors after a single. Everything else is rather straightforward in terms of the values of each event.

The reason I say not to be afraid of that formula, is that it’s actually a more simple formula than something like OPS, which almost all baseball fans are familiar with at this point. OPS is based on two stats and each of those stats has a formula. Below are the formula for each.

OBP=(Hits+BB+HBP)/(AB+BB+HBP+SF)

SLG=(1B+2B*2+3B*3+HR*4)/AB

That makes the formula for OPS (see below):

OPS=((Hits+BB+HBP)/(AB+BB+HBP+SF)) + ((1B+2B*2+3B*3+HR*4)/AB)

Compare that to wOBA

wOBA=(.72*BB+.75*HBP+.9*1B+.92*ROE+1.24*2B+1.56*3B+1.95*HR)/PA

There are also versions of wOBA that incorporate stolen bases and caught stealings. Fangraphs wOBA figures include each. It’s important to note that the values above change slightly from year to year based on the run evironment during the season. A .335 league average OBP (also league average wOBA) could be .328 the following year or .323. Maybe it will be .338. This changes the value of each event.

If the formula is still overwhelming, focus more on the processes of the the three metrics I’ve referenced. When calculating OBP, HR=1, BB=1 and so on. All the stats used in OBP are equal to 1 even though some of those events are less than others. For SLG, single=1, double=2, triple=3, and home run=4. SLG assumes each additional base is twice as valuable as the previous one, which is also not true. A home run is not four times as valuable as a single.

wOBA uses the more accurate weights for each event, relative to the out, and combines both aspects of hitting (reaching base and bases gained) into a rate statistic we’re all familiar with. The stat is then adjusted so that the leaguve average wOBA is equal to whatever the league average OBP is.

Why should you care about wOBA? Because it has a direct relationship with the the number of runs produced. Runs, as you know, lead to wins. So rather than being a number like OBP that only tells us the rate at which a player reached base safely, wOBA tells us exaclty how many runs the player was worth. We can then convert those runs to wins, which is really what we want to know.

To convert wOBA into runs we simply subtract league average wOBA (equal to whatever league OBP is) from the player’s wOBA, divide the total by 1.15, add in league runs per plate appearance and then multiply it all by the number of PA the player had. In simpler terms, the formula is below.

wRC (weighted runs created)=((wOBA-lgwOBA)/1.15+lgR/PA)*PA

We now have the number of runs the player contributed based on his wOBA. We can also compare the player’s wOBA to the average player in terms of runs above average.

wRAA (weighted runs above average)=(wOBA-lgwOBA)/1.15*PA

The 1.15 is the scale used to adjust wOBA so that it’s on the OBP scale and it changes slightly from one year to the next, but is always around 1.15.

Still having trouble swallowing all this? Try to think of the various events in terms of how excited you get when the Cubs are batting. Imagine a close game in the 7th, 8th or 9th inning with 1 out. A single will get you to think that they have something going, but they’re a long way from scoring that run. A double though, now you’re got a guy in scoring position who can score on a single. You’re more excited because that run is more likely to score. Imagine a triple. You’re very excited now because that runner can come home on a base hit, wild pitch, passed ball, infield grounder or sac fly. The chance of scoring that much needed run is pretty good. A home run. You’re as happy with that plate appearance as possible. Now add in the emotions you may feel for a walk, hit by pitch, and so forth. In that particular situation a hit and BB or HBP woud be the same, but over the course of a game that’s obviously not true.

The weights used in wOBA reflect how excited you got after each event.

As mentioned, the great thing about having the value in runs is that we can easily convert it to wins. That’s another post and we have to look at defense and baserunning before that one anyway.


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