Basic wOBA Equation
Here at FanGraphs and RotoGraphs, I occasionally delve into articles that look at split-data, and have had to create a simplified version of our wOBA formula in order to generate some numbers where wOBA isn’t easily available.
wOBA is simply a rate-stat version of a linear-weights calculation, but because the relative values of events change according to the run environment, the value of the different types of outcomes that go into the formula change from season-to-season. This is why why we publish the guts of wOBA, so that you can see exactly how to calculate wOBA for any given year.
But if you’re looking at multiple years including different run environments, it can be helpful to have a basic wOBA formula that gets very close to the results for any individual year, but includes static values and a set formula. To that end, I’ve created what I call Basic wOBA, which does exactly that; follows the year-by-year wOBA shifts very closely without needing to update the variables for each season. We’re not rolling this out as an official version of wOBA, and it won’t appear on the site itself, but it will be referenced occasionally in articles, and so it is helpful to have the formula listed as a reference for when it is called upon.
After some testing, here is the equation we decided to use:
Basic wOBA = (.7* (BB + HBP) + .9*1B + 1.25*2B + 1.6*3B + 2*HR)/PA
Looking back at players with more than 200 plate appearances since 1980, the R-squared between the actual wOBA and Basic wOBA is 0.986, with a value of 1.0 being a perfect 1:1 relationship. So while not perfect, it will give a nearly equal value in almost every case.
If you see Basic wOBA referenced in an article, this is the formula that isbeing used.
Jeff, one of the authors of the fantasy baseball guide,The Process, writes for RotoGraphs, The Hardball Times, Rotowire, Baseball America, and BaseballHQ. He has been nominated for two SABR Analytics Research Award for Contemporary Analysis and won it in 2013 in tandem with Bill Petti. He has won four FSWA Awards including on for his Mining the News series. He's won Tout Wars three times, LABR twice, and got his first NFBC Main Event win in 2021. Follow him on Twitter @jeffwzimmerman.
I’m assuming that should be .725 for HBP? Otherwise, we’ve really been underrating Craig Biggio.
I think you meant .725*HBP
I think there may be a typo with HBP. I find it hard to believe getting hit by a pitch is worth 7.25 runs.
I hear about this stat a ton, but I’m honestly curious, what exactly is the point of this statistic? What does it accomplish that OBP does not?
Larry, which guy do you want on your team. The guy with a .350 OBP and a .350 SLG or the one with a .340 OBP and a .500 SLG?
OBP treats all hits and walks like their worth the same amount. They aren’t. wOBA weights each way of reaching base according to how much it factors in to actual run production.
http://www.fangraphs.com/library/offense/woba/
OBP counts a HR and a BB equally. This is more like OPS except the weights are more accurate than what you get from randomly adding two different stats.
Typo aside, can anyone explain why an HBP is worth more than a walk?
The coefficients are based on historical data, so HBP leads to slightly more runs historically, the why is a an educated guess. People on here have said it’s because it indicates “wildness” for a pitcher…or because sometimes walks are tactically defensive (an unintentional-intentional walk for e.g.), while HBP are random.
To find these values they’ve mined data to see the number of runs caused by the action. Pitchers hitting batters are more likely to be on the cusp of a nervous breakdown than those simply walking, and therefore more runners score, on average.
Thanks to everyone for the explanations. However, since it probably comes down to how the pitcher is doing rather than the hitter, wouldn’t grouping BB and HBP together for the purposes of the analysis make sense?
Well, ultimately that depends on what you’re trying to quantify. How well a player was or how good a player is.
Also HBP is a skill, thus players have widely differing rates so you do want to credit them for the extra HBPs earned.
wOBA is based on actual run values, so I’m guessing that historically speaking, a hit-by-pitch has been slightly more valuable than a walk. That’s possibly because walks include intentional walks, which might actually help limit runs in some situations, whereas you won’t have an intentional HBP (well, aside from beanings).
Well the formula doesn’t distinguish between BB and IBB and IBB usually occur at strategic intervals where the benefit is lessened. This would also apply to the the unintentional intentional walk. A HBP by comparison isn’t really ever a strategic maneuver.
That is the best guess I have at least.
Walks are slightly weighted to situations where they’re less impactful while HBPs (even including the payback ones) are more evenly distributed across base/out states. If the ratio of leadoff hitters in an inning walked to plunked is X, the ratio with 2 outs and 1b open is going to be more than X, and the ratio with 2 outs, a guy on 3rd, and a weaker hitter on deck is going to be higher still.
I think there is a typo there. It should be 725,000*HBP
Ron Hunt agrees
I dont know if anyone has pointed it out yet, but there is a typo in the equation. It should be .725*HBP
I think part of the reason the general public doesn’t trust sabermetrics is not just because they don’t understand the math behind them, but because they don’t understand what the metric represents. Batting average is the percentage of at-bats that has resulted in a hit. OBP is the percentage of PAs that have resulted in not making an out. Slugging Percentage is the average number of bases per plate appearance.
For something like wOBA, what does it represent? It’s calculated using Linear Weights, which in turn is (I believe) the expected run value of every possible outcome. Can you describe it as the run value per plate appearance that player has been worth? If a player has a .360 wOBA, would that mean they created .36 runs / plate appearance? If not, then .36 *what* exactly?
And also while on the topic, is the weight applied to each event the number of runs that event lead to in the instance of the event, or overall? i.e. if a player hits a double, and that player then later scores a run, would that run count toward the expected run value of a double? Or would that run count toward the expected value of the event that lead to him scoring? Or both?
From the glossary entry on wOBA here on FG: “Weighted On-Base Average combines all the different aspects of hitting into one metric, weighting each of them in proportion to their actual run value”. So I think, you can describe it the way you did. Plus, wOBA can be easily converted to metrics like WRAA or WRC+, which evaluate the actual number of runs the player contributed to the offense (with or without adjusting it for the park and league).
If I got your second question right, the run would actually count towards both. Let’s say, you have 0 outs, nobody on. Then a player hits a double. If the run is scored eventually, it will give us +1 double in the column which will represent the amount of doubles hit in the situation of 0 outs, empty bases and +1 run in the column of runs scored in the inning with a double happening in that situation. Then the following event (say, it was an RBI single in 0 outs 2B situation) will give us +1 single in the column which will display the actual number of singles hit during some period of time (say, 3 seasons) in that particular situation (0 outs, 2B) and +1 run in the column of runs scored in that inning with a single happening in that situation. If you are familiar with “The Book”, you can access that kind of breakdown for HRs for 24 base out/states in the introductory chapter. Hope my explanation helped a bit.
Jeff:
http://tangotiger.com/index.php/site/comments/standard-woba
I recommend collapsing the HBP into BB. You won’t find any difference for any player, rounding wOBA to three decimal places. And if you do, it will be .001 of a difference. So, no reason to make it uglier by having a separate item for HBP.
Among the 146 hitters with the most PA, the standard deviation of wOBA using .7 instead of .725 for HBP is one SD = .00015. The guy most affected was Starling Marte, who increased his wOBA by .00056 more than the group average. All the guys with 0 HBP decreased their OBP by .00022 relative to group average.
Thanks Tom
Interesting stuff. Do these coefficients remain the same for other levels — minors, college, etc.?
Apologies if I missed something obvious, but I thought the lw for HRs was historically determined to be ~1.402. Why is it ~2.00 here?