Statistically Significant: wOBA

I'd like to take this week to continue my stat primer series I started last month (on FIP, here). This week, Weighted On Base Average (wOBA). I'll try to make it as painless as possible, but feel free to skip the math section if you want.

Why wOBA?

Before I can get to the actual stat, I'm going to need to go over what led to its creation.

The "triple slash" method of notation is an extremely common one, and it's one you've undoubtedly seen. It summarizes a player's offensive contribution by listing batting average, on base percentage, and slugging percentage, in order, separated by slashes. (For example, Eric Chavez finished 2004 with a great .276/.397/.501 line.) These are three good statistics, and together in combination, it's easy to eyeball the strengths and weaknesses of a particular hitter.

In fact, on base percentage and slugging percentage complement each other quite well. OBP measures the value of walks and singles well, but a power hitter who hit a lot of extra base hits would be more valuable than his OBP would otherwise indicate. And slugging percentage provides a great measure of power, but a batter with no power but great plate discipline would be more valuable than his SLG would otherwise indicate. And as such, OPS was created by simply adding the two together. For the most part, it works remarkably well. OPS is a very good all-around statistic that provides the total value of a batter.

But OPS suffers from a few problems of its own. You can add OBP to SLG, but are both statistics really worth equal amounts of offensive value? A walk is counted in OBP, but a single is counted in both OBP and SLG. Is a single really worth twice as much? And, for that matter, is a home run really worth two times as much as a double? All of these questions dull the accuracy of OPS considerably. A .900 OPS hitter is clearly more valuable than an .800 OPS player, but can you really say the same for a .750 OPS player over a .740 OPS one? Last year, Nick Johnson batted .291/.426/.405, for an OPS of .831. In the same year, Carlos Lee batted .300/.343/.489, also for an OPS of .831. Both batting lines have an identical OPS, but they were achieved in very different ways. Johnson was an on base machine with little power. Lee was rarely on base but boasted tremendous slugging ability. Which season was actually more valuable?

The Math

Clearly, OPS was lacking enough that a new offensive statistic needed to be made. The problem with OBP and SLG is that events are assigned whole number values in the formulas that look and play nice but are otherwise meaningless. Thankfully, with run values, we can assign numeric values to events that actually reflect real data.

I explained run values in the previous column, but as a quick refresher, a run value indicates the average amount of runs that the average team scored from the occurrence of the event until the end of the inning. The run values for all of the most common offensive events are listed below, in the blue row.

For example, the first column indicates that on average, a walk was worth 0.32 runs, while a hit by pitch scored 0.35. The numbers come from all games played between 1999 and 2002, a sample a few hundred shy of 10,000 games.

These run values give us the exact value of each offensive event. The creators of wOBA noticed this, and realized that if we took the weighted average of a player's offensive contributions with the run values as the weights, you'd have an airtight, all-purpose offensive statistic.

Notice the last column, which says that the average out penalizes a team by 0.3 runs. In an attempt to get rid of negative numbers (if you strike out on every pitch, you'd have a batting average of 0.000, not a negative number), the creators of wOBA added 0.3 to each value, which gives the run value of every event relative to an out. Furthermore, they multiplied every value by 1.15, which has the convenient effect of putting a league average hitter's wOBA close to the league average OBP. These values are in the green row.

And it's these green row values that make up wOBA. The formula looks bad, I know, but it's a lot easier to use than calculate.

In Practice

The league average wOBA moves around from year to year, but it tends to sit somewhere around .325-.330. Other than that, wOBA pretty much works like a more complete, more accurate, all-around better version of OPS, in that it measures total offensive value, rather than one or two facets of offense, like power or contact ability.

The best way to get a feel for what constitutes a good wOBA is to look up players on Fangraphs and compare it with OPS, but I'll include a few benchmarks here. The league leader in wOBA tends to be somewhere a little north of .420, which usually sits where a 1.000 OPS mark does. Last year, Albert Pujols batted .327/.443/.658 for a .449 wOBA. On the flip side, last year's league worst wOBA belonged to the inimitable Yuniesky Betancourt, who batted .245/.274/.351 for a .271 wOBA.

As for the Nick Johnson (.291/.426/.405) vs. Carlos Lee (.300/.343/.489) question I posed earlier? Johnson's wOBA was .373, while Lee's was a far smaller .355. They had the same OPS, but the actual difference between the two seasons? A little over 10 runs, or about one whole win.

The A's are on a road trip for much of the next two weeks. They kick off a three-game set at Baltimore as Dallas Braden faces Jeremy Guthrie at 4:05 PM.

Odds and Ends

• For a crazy legendary high-water mark, Barry Bonds' best season came in 2002, the year after his 73 HR season. He batted .370/.582/.799 for an absolutely insane .546 wOBA.
• That Yuniesky Betancourt season I mentioned? Eric Chavez is currently performing at that level (2009 Betancourt: .271, 2010 Chavez: .270). Imagine having that performance for a full season, coupled with the worst SS defense in the majors.
• It turns out that most of the problems with OPS stem from the fact that OBP is around twice as valuable as SLG. You can actually make a fairly close approximation of wOBA by multiplying OBP by 2, adding it to SLG, and dividing by 3.
• I know it seems odd that a hit by pitch is worth a little bit more than a walk, but that's how the run values worked out. The best explanation I can think of is that pitchers who hit batters were more wild and gave up more runs after the event than pitchers who walked guys.
• By the way, about the odd acronyms in the formula: NIBB stands for "non-intentional base on balls", and RBOE stands for "reached base on error".
• All values come from The Book: Playing the Percentages in Baseball, by Tango, Lichtman, and Dolphin.