# Know Your Stats: Weighted On Base Average (wOBA)

An article by posted on July 15, 2013

For the next few days, I will be highlighting some of the most popular sabermetric stats available to the public. Earlier today, we began the series with OPS/OPS+. Now we continue with wOBA…

Batting Average, On-Base Percentage, and Slugging Percentage are all incomplete. Batting average doesn’t account for what type of hits a batter has. It also doesn’t account for walks. On-Base Percentage is better because it accounts for walks, but it doesn’t weigh how a runner gets on base correctly. Slugging Percentage attempts to weigh hits, but fails. A triple isn’t three times as valuable as a single. The reason we know that is because of linear weights, which is a very important sabermetric concept that weighs every action in a baseball game. Everything has a run value. We use the decades upon decades of baseball history to determine how valuable a certain action is.

Before we get to wOBA, it’s important to understand one very important thing about linear weights, which will clear up the somewhat confusing formula. Take a look at this excerpt from Fangraphs’ library:

There is nothing arbitrary in the exact weighting we have of a home run relative to a triple, or a ground ball to a line drive. Years upon years of data allow us to convert back and forth, or up and down with ease. A common complaint with modern sabremetrics is the bewildering array of fractional coefficients that dot the scene, but if you look at a formula that’s based on linear weight, don’t see them as confusing numbers. Instead, look at them as relative values, derived through years of baseball being played.

The goal of a team on offense is to score as many runs as possible and therefore make outs as infrequently as possible, so linear weights is put in terms of how it affects a team’s likelihood of scoring, and how many runs you can expect them to score.

When you look at the weights, they make sense without seeing how the run expectancy plays out. A walk is worth slightly less than a single because runners on second tend to score on a single, but they don’t move on a walk, making a single slightly better. However, just as eras change, the weights in wOBA vary slightly from year to year as well. Certain factors can make a single more or less valuable than it was thirty years earlier. Essentially, it adjusts for the run environment of the league, which was vastly different in 1900 than in 2000. Here is the formula from 2012:

wOBA = (0.691×uBB + 0.722×HBP + 0.884×1B + 1.257×2B + 1.593×3B +
2.058×HR) / (AB + BB – IBB + SF + HBP)