## Sabermetrics 101: wOBA

Jake Roth-US PRESSWIRE

The first installment of Sabermetrics 101, an offseason series in which we will cover the basics of advanced statistics. In this post, we explore wOBA -- Weighted On-Base Average.

Sabermetric principles have begun to rapidly permeate the baseball blogosphere and our own community. In an attempt to bring a little more color to sabermetrics, this will be the first in the Sabermetrics 101 series that will run this offseason. I will try and include as much detail as I can while also painting the bigger picture whenever I can. Hopefully the explanation will be thorough enough for those who enjoy the details, and concise enough for those who prefer understanding the main idea.

Introduction

Traditional offensive metrics -- Batting Average (BA), On-Base Percentage (OBP), and Slugging Percentage (SLG) -- all have certain deficiencies: Batting Average does not incorporate walks, On-Base Percentage does not differentiate among the numerous offensive outcomes, and Slugging Percentage does not incorporate walks nor does it correctly weight the different offensive outcomes.

Furthermore, it would be much easier to evaluate players based on one catchall number. The following is an exercise demonstrating why. Let's take two different players:

Player A: .295/.330/.410

Player B: .265/.310/.450

If we look solely at the players' BAs, we would conclude that Player A is the better player. If we looked at OBPs, we would conclude that Player A is the better player. If we look at SLG, we would conclude that Player B is the better player. So which one is the better player? Well, if we look at all three statistics, we're still left wondering.

In order to incorporate walks and differentiate between offensive outcomes, statisticians created OPS, On-Base Plus Slugging, which is simply the sum of On-Base Percentage and Slugging Percentage. However, one major problem remains: OPS still incorrectly weights the offensive outcomes. According to Slugging Percentage, a component of OPS, a double is worth two singles, a triple is worth three singles, and a home run is worth four singles. In actuality, here are the run values of common offensive outcomes:

Home Run: 1.39 | Triple: 1.09 | Double: 0.77 | Single: 0.47 | Walk: 0.32

Figure 1

Run values represent the change in the expected number of runs scored over the rest of the inning as a result of the event. So, if a player hits a home run, the expected number of runs scored in that inning increases by 1.39, (the difference between expected number of runs scored before and after the event is 1.39).

We can now index the run values of these common offensive outcomes relative to a single and compare them to the Slugging Percentage weights to see how invalid Slugging Percentage is.

Home Run: 2.957x | Triple: 2.319x | Double: 1.638x | Single: 1.000x

Figure 2

While Slugging Percentage states that a home run is worth four singles, run values show us that a home run is actually worth approximately 3 singles, a triple is worth 2.3 singles, and a double is worth 1.6 singles.

Weighted On-Base Average solves this problem by placing the correct value on every offensive outcome. It attempts to package a player's entire offensive output into one statistic using a form of the run values from Figure 1.

Constructing wOBA

Figure 1 showed the run value of each event above the result of an average plate appearance. Below is a modified version of Figure 1, Figure 3, that shows the run value of each event above the run value of an out, which is approximately -.3. Figure 3 essentially adds .3 to each run value in Figure 1:

Home Run: 1.70 | Triple: 1.37 | Double: 1.08 | Single: 0.77 | Walk: 0.62

Figure 3

wOBA could be calculated with the run values from Figure 3, but sabermetricians scaled wOBA to make it similar to OBP values. This way, they could use a scale familiar to them when comparing wOBAs. Similar to a player's OBP, a wOBA below .290 is poor, a wOBA of .320 is average, and a wOBA above .400 is exceptional. In order to scale the wOBA to OBP-like levels, we must increase the run values by 15 percent, resulting in the adjusted run values depicted in Figure 4:

Home Run: 1.95 | Triple: 1.56 | Double: 1.24 | Single: 0.90 | Walk: 0.72

Figure 4

By using the run values that we derived in Figure 4 as the coefficients of common offensive outcomes, we can derive the formula for wOBA:

(0.72 * NIBB + 0.75 * HBP + 0.90 * 1B + 0.92 * RBOE + 1.24 * 2B + 1.56 * 3B + 1.95 * HR) / PA

Now, instead of having to look at a player's BA, OBP, and SLG, you can look at just one number -- wOBA -- in order to evaluate a player's offensive ability.

Conclusion

Let's look back at our two players to finally determine which one is the better player.

Scenario 1 (the same scenario as the one at the beginning of this piece)

wOBA tells us Player B is slightly better, but so does OPS, so one may begin to doubt the value of wOBA. Aside from the fact that is a more theoretically accurate evaluation of a hitter's offensive contribution, it is also practical as we see in the following scenario.

Scenario 2 (the only difference is that Player B has one fewer walk)

wOBA tells us Player A is better, but OPS tells us that the two players are essentially equivalent. This is because Player B benefits from the fact that SLG inflates the values of doubles, triples, and home runs as we found in the discussion of Figure 2. Once we accurately weight these extra-base outcomes, we come to realize that Player A is the better player.

wOBA essentially distills the three numbers down to one easily comparable number, and a number that is more accurate than OPS. So the next time you're trying to evaluate a hitter or compare two hitters, look no further than wOBA -- it's arguably the best tool we currently have at our disposal.

Footnotes

All run values come from The Book.

NIBB stands for non-intentional walk | HBP stands for hit-by-pitch | 1B stands for single | RBOE stands for reached base on error | 2B stands for double | 3B stands for triple | HR stands for home run | PA stands for plate appearances

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