Valuing Offense: The Elegant Simplicity of wOBA
by Steve Slowinski on Jul 13, 2010 4:31 PM EDT
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PrintEver since "Moneyball" was published, there have been two lines of thoughts on walks. On one hand, the sabermetrically-inclined have harped upon how valuable walks are; on the other, traditionalists have stuck by their guns, claiming that, "A walk isn't as good as a hit!" Saberists have rebutted the argument, pointing out how there are a limited number of outs in a game and good players don't make outs...and calling the other person a dumb-bat in the process. The traditionalists followed with a shot across the bow and a right hook to the face, and hence the enmity between the two camps grew.
And so, I'm here today to settle the debate once and for all: is a walk as good as a hit? No, it is not. Walks are good and they're better than making an out, but a walk isn't as valuable as a single because singles have the potential to move runners multiple bases at a time. This is a marginal difference, considering that there aren't always runners on base and both instances still get you a runner on first, but a difference nonetheless. Traditionalists, you were right.
Similarly, not all hits are created equal. This makes intuitive sense to us; a homerun is more valuable than a single, for instance. If you had to choose between two players with the same batting averages but one player hit 40 homeruns and the other 5 homeruns, you'd take the player that hit 40 homeruns in a heartbeat, right? Singles are more valuable than walks, doubles are more valuable than singles, triples more valuable than doubles, and homeruns are more valuable than all of them. I don't think you'll find any baseball fans disputing this fact - again, it's common sense.
The question, then, is how much better? Say you have these two players and you need to determine which one of them is a more valuable offensive player:
Player A: 190 hits, 150 singles, 30 doubles, 2 triples, 8 homeruns, 100 BB, 0 HBP, .333 BA
Player B: 190 hits, 130 singles, 35 doubles, 0 triples, 25 homeruns, 25 BB, 0 HBP, .333 BA
Which player is more valuable? Does Player B's extra power make up for his lack of walks? How valuable are Player A's triples in comparison with Player B's doubles? Is a double worth exactly twice the amount of value as a single? Is a triple exactly three times the value of a single? Slugging percentage would have you believe it's that simple, but where's the proof? Here's my favorite question again: why is that true? Is it?
These are the sort of questions that plagued saberists for a number of years, until someone (Tom Tango, I believe) decided to run some empirical tests and establish - once and for all - the value of different offensive outcomes. Once these values had been established, it was just an extra step to turn the results into a formula that weighed each offensive event for its proper value. This statistic is called Weighted On-Base Average (wOBA) and it's the greatest thing since sliced bread. So now, instead of looking at oodles and oddles of numbers to determine who is a more valuable hitter, we can just look at a final number like this:
Player A: .392 wOBA
Player B: .381 wOBA
Oh, so Player A's walks did make up for his lack of power, and he was the more valuable player. Simple, huh? That's the basic premise behind wOBA: it's one statistic that encapsulates a player's offensive performance. Think of it like OPS, but only more accurate because real mathematicians came up with the proper values for each hit. Some versions of wOBA (like the version over at FanGraphs) include stolen bases in their calculations, giving players added value if they steal bases at a high rate of success. Weighted One-Base Average is scaled to look like On-Base Percentage, with league-average coming in around .335. Just like with OBP, a wOBA of .400 is quite high and a wOBA below .300 is horrendously low.
And this is why I love wOBA - that's all there is to it! I don't know how the mathematicians established the proper weights, but I don't need to; that's their job. This is a statistic that says, "Okay, so we know that singles are more valuable than walks, doubles are more valuable than singles, triples more valuable than doubles, and homeruns are more valuable than all of them. I'll do all the work for you and show you how productive your player has been in one simple, easy-to-understand stat. Okie dokie?"
If you're still attached to batting average, OBP, SLG%, and OPS, that's fine. They're perfectly good statistics, but realize that each of them only gives you a small piece to the puzzle. Only wOBA puts the puzzle pieces together for you.
For more on wOBA, check out its page at The Sabermetrics Library or ask questions below. Also, for those of you that like more hands-on experience, feel free to play around with this wOBA calculator. Put in different inputs and watch how the wOBAs change.
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Baby steps, my friend, baby steps.
wRC+ is excellent. Tougher to explain and understand at first, though, which is why I like wOBA as a gateway.
I love Casey Fossum. Now try and take me seriously.
by Steve Slowinski on Jul 13, 2010 4:37 PM EDT up reply actions
On the contrary, I think wRC+ is extremely easy to understand.
Just like I think OPS+ is easier to understand than OPS (wRC+ to wOBA and OPS+ to OPS have a very analogous relationship). It’s just a rate stats that tells how how much better or worse a player was compared to league average, and it has a very sensible and easily understood scale.
A large part of the struggle in using new stats is learning the new scale.
Everyone knows a .300 AVG is good, but what’s a good OPS? wOBA? The “+” versions are all on the same scale with the same average. So once you trust the stat, it’s easier to compare players.
Thank you for dredging up the painful memories of being called a dumb-bat
The caller said the boy, after removing the bulb from its socket, left the building and threw the bulb on the ground. When the bulb broke, the caller said the boy screamed "I am the cat and I am here to steal."
by Top Gun Numba 1 on Jul 13, 2010 4:50 PM EDT reply actions
"You are a f#cking punk." - SF1, 7/13/10
Boom. Outta Here.
by Ryan Gilliss on Jul 13, 2010 4:54 PM EDT up reply actions
Awesome articles so far
Coming in I had no idea what some of these numbers meant aside from “higher = good”.
In my day lots of messy tissues over her
by sternfan1 on Jun 18, 2010 6:30 AM PDT
Are the wieghting factors different from year to year?
I think adding in a factor for stolen bases makes sense, from my background in data analysis. A single and a stolen base is just about the same as a double…not exactly, but very close.
One other trivial difference between a single and a walk is that there is a possibility of and extra base (or more) on a single if there is a fielding error…but then I remember my old man (RIP dad!) grousing about “not being able to defend” against a walk…
Just some of the many aspects of baseball that make the game fascinating to me! Nice articles Steve!
The thing I love about base-stealers is that their value goes beyond what they do on the bases. It forces the defense to play differently and the pitcher to pitch differently, which inherently creates better at bats for the guy behind you. I don’t know if this is taken into consideration in wOBA but but it certainly makes a difference.
by Jeffrey Borbas on Jul 13, 2010 7:21 PM EDT up reply actions
Research has shown that for the majority of batter/pitcher/baserunner situations that the baserunner is just as distracting to the batter as the pitcher.
Might I suggest: http://amzn.to/cdVYBN
The great thing about baseball is that it requires careful observation not simply attendance and it rewards the analytical person while consistently befuddling the superficial.
Help others while helping yourself by purchasing this Trade Deadline Primer:
http://dockoftherays.com/2010/07/03/2010-trade-deadline-primer/
by Andy Hellicksonstine on Jul 14, 2010 5:45 AM EDT up reply actions
ROE has a weight of .92 while a single has a weight of .90
So the possibility of an extra base on an error is accounted for. Additionally, a walk has a weight of .72, so those complaining about this aspect should probably do their homework first. Might I suggest reading Tango, Lichtman, & Dolphin’s excellent The Book.
The great thing about baseball is that it requires careful observation not simply attendance and it rewards the analytical person while consistently befuddling the superficial.
Help others while helping yourself by purchasing this Trade Deadline Primer:
http://dockoftherays.com/2010/07/03/2010-trade-deadline-primer/
by Andy Hellicksonstine on Jul 14, 2010 5:43 AM EDT up reply actions
Actual wOBA values
Single 0.77
Double 1.08
Triple 1.37
Home run 1.70
Walk 0.62
SB 0.2
CS -0.44
Linear weights.
This has a great description:
http://sports.yahoo.com/mlb/blog/big_league_stew/post/Everything-you-always-wanted-to-know-about-wOBA?urn=mlb,208135
The exact math is beyond me, but the basic gist is that it’s derived from past historical data. What’s the average run value for all singles? Doubles? etc etc.
Here are some other things worth reading (although they’re a bit tougher, so take your time):
http://www.insidethebook.com/woba.shtml
http://www.insidethebook.com/ee/index.php/site/article/getting_to_know_woba/
I love Casey Fossum. Now try and take me seriously.
by Steve Slowinski on Jul 13, 2010 9:08 PM EDT up reply actions
No, I don't know where you got these from, but they aren't correct.
The great thing about baseball is that it requires careful observation not simply attendance and it rewards the analytical person while consistently befuddling the superficial.
Help others while helping yourself by purchasing this Trade Deadline Primer:
http://dockoftherays.com/2010/07/03/2010-trade-deadline-primer/
by Andy Hellicksonstine on Jul 14, 2010 5:48 AM EDT up reply actions
I assume that all scenarios were taken into account.
Various runners on vs. nobody on. I am surprised that there isn’t a bigger difference between a walk and a single. The outcome is so much better if there are runners on base. How many games would the Rays have won this year with one more single with runners on, but instead they took a walk, and did not get the runners in?
I wonder if they assumed the runner at first would only advance one base on a single. I wonder if they take into account the greater number of pitches for a starting pitcher a walk would require, thus forcing him from the game sooner. Too deep?
I believe the first has to be accounted for..
If not, there would be no difference between the value of a walk and a single.
The second would be impossible (or nearly) to quantify since the impact, if there is one, would depend multiple variables.
Completely impossible since the strength of teams bullpen greatly influences the value of a pitch.
by Jeffrey Borbas on Jul 13, 2010 8:39 PM EDT up reply actions
What in the shit are you talking about
The great thing about baseball is that it requires careful observation not simply attendance and it rewards the analytical person while consistently befuddling the superficial.
Help others while helping yourself by purchasing this Trade Deadline Primer:
http://dockoftherays.com/2010/07/03/2010-trade-deadline-primer/
by Andy Hellicksonstine on Jul 14, 2010 5:49 AM EDT up reply actions
It accounts for the difference
But it doesn’t account for lineup effect. I realize lineup effect isn’t HUGE, but it is real, and it becomes more exaggerated when you get men on base. A team that is generally high in OBP is going to get more value out of a player who gets more hits and less walks, but has the same OBA as a player with less hits and more walks (controlling for power).
Bad Left Hook - The SB Nation boxing blog
"Baseball is played on the field, not on a calculator."
I think this is a very underrated issue
I brought this up in an earlier thread. In many ways it is specific team affects and what is the variation on the likelihood of men on base between teams.
Basically, while running on OLS over the entire league’s number to gauge standard weights for wOBA is great, it only actually matters in the context of your team. Simply, the higher your team’s OBA, the more the weights value hits over walks, so walks have diminishing returns. This cannot be captured by using a linear equation (as the derivative of BBs is constant). Therefore wOBA is not really accurate.
Because the stat-heads (and for the record I have an advanced theoretical math degree and do data analysis for a living, so am certainly one) generally assume baseball is an individual sport for ease of analysis, this means that in evaluating a single vs a walk, they assume a standard probability distribution of men on base. Basically a randomly selected at bat will have .33 of a man on first, .11 on second, and .05 on third (or whatever the real numbers are). Some teams that only look at OBP and not BA may actually have much higher rates of men on first and second, which can have a significant impact on the weights (also the weights of GIDP which is some function of ground ball rate)
Since lines can approximate curves over short distances, one way to overcome the shortcomings of wOBA being linear instead of curved is to make sure we estimate and place the line near the spot in the curve we are interested in. The punchline is that we should really have a Rays-specific wOBA. It will essentially make sure we are near the actual wOBA curve and give us much better estimates of a players value to our team
Plus in the Rays team events and this will spit back custom linear weights.
You can compare them to the league average and/or compute a custom wOBA.
Ideally you’d take into account lineup interactions, but, well, good luck.
by Sky Kalkman on Jul 14, 2010 11:42 AM EDT up reply actions
The way I see it, that's a heck of a lot more work for maybe a marginal difference in accuracy.
If someone wants to do it, fine. But wOBA works perfectly fine as its constructed, and its much more accurate than any other traditional stat. It has a lot more strengths than weaknesses.
I love Casey Fossum. Now try and take me seriously.
by Steve Slowinski on Jul 14, 2010 11:52 AM EDT up reply actions
I agree, Steve.
That heck of a lot more work is worth it to teams, but not me/us.
by Sky Kalkman on Jul 14, 2010 11:54 AM EDT up reply actions
It may be a lot of work, but maybe not
I will take a look, but I believe you just need to adjust the odds of men being on base and rerun the regression with the same run values of a walk v single v double coming from the different situations… which is the difficult part of the math (the part involving Markov chains).
Just based on watching the Rays this year, I think it is actually statistically significant.
And strengths vs weaknesses is all relative, but I agree that wOBA is great overall.
Would love to see a fanpost of your findings
Would front page it if you do it.
Follow Me on Twitter @FreeZorilla
I was reading up on it more. Basically it calculates the values in every situation separately and then averages it out. So in a situation like you described, yes a hit would have a higher value to scale, but it would be lower with no men on.
by Jeffrey Borbas on Jul 13, 2010 8:36 PM EDT up reply actions
I don't believe that is true.
Unless I’ve missed something recently.
When calculating a player’s wOBA the weight of each outcome would be multiplied by the number of occurrences. The base/out state is not considered.
That would be a problem with this stat, no?
Under-valuing hits with runners on vs walks?
by terp12 on Jul 13, 2010 9:56 PM EDT via mobile up reply actions
Sure, but that isn't the purpose really.
The purpose was to find a better measure of production than OPS. The stat attempts to quantify offense of the batter by assigning values to each outcome (ultimately based on expected run production of each outcome). It accounts for the differences between a walk and a single by assigning a greater value to the single than the walk. That accounts for the difference with runners on, since there is no difference (outcome based) between a single and a walk with no one on.
It just improves on OBP and SLG. Neither of those stats account for out/base states either. It’d be extremely difficult to create and continuously update a stat that gives a varying value to a hit based on the out or baserunner state and you would run into numerous other issues if you tried to dig that deep.
And so does Fangraphs ;)
They also have RE24, which accounts for the base-out stat, but not the score/inning.
I love RE24
And I am comfortable with wOBA. What is the difference between WPA/LI and RE24 in terms of calculation? Isn’t WPA just RE24 with inning and margin applied?
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Short answers: yes.
Longer answer: Leverage (LI) takes into account for things that context-neutral stats like wOBA do not: runners on base, outs in inning, inning, and score. So, if you combine wOBA and LI, you get WPA (sort of — there’s a re-scaling going on.)
If you only use runners on base and outs in inning as your “leverage” then you’ve (sort of) converted wOBA into RE24.
WPA/LI adjusts the weights on each event just like WPA does, except it doesn’t count some PAs more than others. WPA takes a really important PA and counts it as multiple PAs, while unimportant PAs are weighted a lot less than 1 PA. WPA/LI treats every PA as equally important, but observes that a single with a runner on second in a tie game in the bottom of the ninth is (nearly) just as valuable as a home run.
You could also do RE24/LI_RE24 if you wanted, which is like WPA/LI except that it only adjusts the wOBA weights for runners on base and outs. It would ignore inning and score. Like WPA, RE24 doesn’t treat all PAs as equally important. RE24/LI_RE24 would.
So you kind of have two things going on here: adjusting the value of each event for various situations (the four listed above) and adjusting the importance of each PA. RE24 and WPA do both (for different sets of situations) while WPA/LI and RE24/LI_RE24 only do the first one.
by Sky Kalkman on Jul 14, 2010 11:34 AM EDT up reply actions
Which is why you should be using this statistic in larger samples
The great thing about baseball is that it requires careful observation not simply attendance and it rewards the analytical person while consistently befuddling the superficial.
Help others while helping yourself by purchasing this Trade Deadline Primer:
http://dockoftherays.com/2010/07/03/2010-trade-deadline-primer/
by Andy Hellicksonstine on Jul 14, 2010 5:50 AM EDT up reply actions
What I was describing was how they calculate the weight itself, not an individual players wOBA.
by Jeffrey Borbas on Jul 14, 2010 10:06 AM EDT up reply actions
Yes, one way to derive linear weights is to find how valuable a single is all the various base-out combinations, then average them together.
Then you have the average value of each event, which is what you almost always see listed and used in general calculations (like wOBA).
But there are times you really want to know how valuable a single/HR/whatever is in a specific situation, like to make in-game decisions or to do lineup analyses.
Something wOBA doesn’t include that I think makes a difference is the type of out. A ground-out is more damaging than strikeout which is more damaging than a pop-fly.
A ground out is only worse than a strikeout in a double play situation
Otherwise it is the same or significantly better. Runs batted in, runners moved over, etc.. I would think that overall, the ground out is better than a strike out.
by terp12 on Jul 13, 2010 9:13 PM EDT via mobile up reply actions
Run values of events:
Groundout: -0.24
Fly out: -0.28
Strikeout: -0.30
Line-drive out: -0.33
Double Play: -1.06
I love Casey Fossum. Now try and take me seriously.
by Steve Slowinski on Jul 13, 2010 9:23 PM EDT up reply actions
So .06 run difference between ground out and strike out.
If someone cut their strikeouts by 100 and converted them all to ground outs, that’s six runs. That’s the same converting 5 HRs into 2.5 doubles and 2.5 fly outs.
Don't forget the DP
That’s a ground out… if you knew it was not a DP. Once you bring the DP into the ground out, the differences are not worth noting.
why is a line-out so bad?
It’s completely luck-driven. We value a batter with a high LD% but if he hits one at a defender it hurts his wOBA worse than a groundout or pop fly? That doesn’t make much sense to me. Technically you could say the same about a grounder, but BABIP is higher on average for liners than grounders.
Longo! (Ah-a-ah!) Fighter of the Upton! (Ah-a-ah!) Champion of the Rays! He's the master of batting and defense for everyone!
High incidence of doubling off with no little to no chance of runner advancement
Line drives are good, poor luck on a line drive is bad
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But they separated Double Play from the rest of it so the likelihood of a DP should have no effect. Other than the likelihood of moving runners over, I don’t see what else could cause the values to be different which makes me wonder why a line-drive out is worse than a K.
by Jeffrey Borbas on Jul 14, 2010 9:54 AM EDT up reply actions
Borbas has a point here though
That DPs are calculated differently. I thought wOBA was measuring the skills of a player, not necessarily luck which would be more like BABIP. Of course luck plays a factor in everything in baseball, but I always took wOBA as more of a true gauge of how well a player was doing at the plate. In a SSS I will take a player with 4 lineouts over one with 2 strikeouts and a bloop base hit.
Longo! (Ah-a-ah!) Fighter of the Upton! (Ah-a-ah!) Champion of the Rays! He's the master of batting and defense for everyone!
I believe wOBA counts all outs as equals
These are just the weights per out type
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by FreeZorilla on Jul 14, 2010 10:31 AM EDT up reply actions
DP was an oversight on my part, but again not factored in wOBA b/c only looking at events where player reaches base
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by FreeZorilla on Jul 14, 2010 10:31 AM EDT up reply actions
what stat are these "weighted outs" factored into, then?
Longo! (Ah-a-ah!) Fighter of the Upton! (Ah-a-ah!) Champion of the Rays! He's the master of batting and defense for everyone!
I don't know
They might just be the values.
Follow Me on Twitter @FreeZorilla
by FreeZorilla on Jul 14, 2010 10:50 AM EDT up reply actions
I think they're just the values.
If you want a stat that weighs each out depending upon its importance and magnitude, though, WPA is what you’d want.
I love Casey Fossum. Now try and take me seriously.
by Steve Slowinski on Jul 14, 2010 10:59 AM EDT up reply actions
Yup, exactly.
I love Casey Fossum. Now try and take me seriously.
by Steve Slowinski on Jul 14, 2010 10:59 AM EDT up reply actions
Harder for runner to advance than on the others
Bad Left Hook - The SB Nation boxing blog
"Baseball is played on the field, not on a calculator."
It depends what you're trying to measure.
Line drives are really good and a line-drive out is uncommon/unlucky/whatever. But for wOBA (or any backwards-looking metric that isn’t trying to get at talent or what “should” have happened) a line-drive out is an out.
If you wanted to create a metric to more judge skill, then yeah, you might very well want to do more of a xwOBA where you use xBABIP methodologies for balls-in-play. You could take it further and regress HR/FB rates, K rates, etc. And weight multiple years of data. At that point, you’ve got a full-blown projection.
Many ways of doing it, for many questions to be answered.
by Sky Kalkman on Jul 14, 2010 11:37 AM EDT up reply actions
Isn't a double play really just a variety of ground out, 9 times out of 10?
Bad Left Hook - The SB Nation boxing blog
"Baseball is played on the field, not on a calculator."
Just to be clear
wOBA does just like OBP and SLG wants to do: measure results, not skill. And measure it irrespective of the actual impact when they occurred (inning, score, base, out), and just presume the events occurred randomly during a game.
by tangotiger on Jul 14, 2010 12:06 PM EDT reply actions 1 recs
That's not to say there's no value in doing that extra stuff
You have other metrics for that, like RE24 and WPA and WPA/LI. wOBA is just focused on different things.
My own interest exists in roster construction
In the context of wOBA it seems safe to say that a player that had a higher wOBA over a certain sample performed better than a player with a lower figure. However this statement implies that it is a world where these players exist independent of other players.
What about the effect of the underlying skills as they relate to each other?
Lets just assume a team of 9 players all with a wOBA of .350
Would we be better off we a total mixing of the underlying components?
Or say would we be better if all the players wOBA is made up primarily due to walks? What about home runs? What about 7 guys that all they do is hit singles/walk and 2 guys that all they do is hit home runs? Or does it not matter at all?
Go Gators!!
Changing all that will matter, for sure.
Check out that markov link above. You can play around with different batting lines that all produce the same wOBA and compare the different runs per game.
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