Filed under:

# An Idiot’s Guide to Advanced Statistics: wOBA and wRC+

These two stats are at the core of much of our hitting analysis here at LL, but how do they work?

They say distance makes the heart grow fonder, so while it’s been a while since the last installment of our award-eligible series on advanced stats in baseball, an idiom says everyone is as excited as I am to be back. For those of you who checked out during the offseason, we’ve been working on a brief overview of some key sabermetric statistics that we utilize frequently here at Lookout Landing, with the intent of making sure our entire community is on the same page. Our first piece looked at Wins Above Replacement and Win Probability Added, and the second attempted to shed some light on the use (and dangers) of Pythagorean Win/Loss.

Today we get back on the horse, with the third part in the series, and it’s all offense. We’ll be looking at Weighted Runs Created Plus (wRC+), the most commonly referenced offensive metric here at LL. To do this, we’re going to have to work our way backwards and break down the simpler Weighted On-Base Average (wOBA), which is integral to the wRC+ formula. Both are pleasantly intuitive, and well-explained here and here, respectively, on Fangraphs, but I will do my best to minimize the math further still.

As a reminder: if you are already a sabermetric whiz this will likely be old hat for you. If there are questions or you see an opportunity to help curious neophytes expand their depth of knowledge, please jump in, preferably supportively. Now, let’s dig in.

### Weighted On-Base Average (wOBA)

Both wOBA and wRC+ attempt to comprehensively showcase a hitter’s overall productivity. The core idea behind each is that, while the familiar “Triple Slash” display of Batting Average/On-Base Percentage/Slugging Percentage is useful, it lacks detail. Why trust batting average so much when it values a bloop single the same as an upper deck home run? Why use slugging percentage, which simply measures total bases divided by at-bats and discredits the value of less powerful players, when we can combine all offensive production into useful, easy-to-use statistics? wOBA assigns multipliers to each type of offensive production, then plugs in a player’s production into one big, not-so-scary fraction, and viola: a more comprehensive look at offensive value.

For a long time, the closest that traditional statistics have come to showcasing this is through OPS, or On-Base Plus Slugging. Most of you are likely familiar with OPS, and while unrefined it is a decent baseline for evaluating players, and much more reliable than simply looking at their batting average. Just for a brief moment, let’s glance at an equation:

Every way that a hitter is credited with getting on base is accounted for on the top part of the equation, but unlike in OPS, there is some nuance to the values. Instead of treating a double as twice as valuable as a single, wOBA is a bit more tempered. Simply getting on base is extremely valuable, and so walks and HBP’s, while not quite as useful as singles can be, still receive a solid valuation. Having a metric where you can pit someone like Nelson Cruz against prime Ichiro Suzuki and evaluate their productivity fairly equally is the goal of wOBA.

Another way of looking at the value of wOBA and wRC+ is to consider the flaws of simply judging a player by their batting average. Ketel Marte hit .259 last year, or five points better than Troy Tulowitzki’s .254. Their OPS, however, values Tulo’s ability to draw a walk, ever, and also his penchant for extra-base hits, including 24 homers to Marte’s 1.

2016 Batting Average OPS wOBA wRC+
2016 Batting Average OPS wOBA wRC+
Ketel Marte 0.259 0.61 0.266 66
Troy Tulowitzki 0.254 0.761 0.327 102

Tulowitzki has a higher OPS, wOBA, and wRC+, but those numbers are somewhat meaningless without a scale. If your eyes glazed over all of this as soon as that equation appeared earlier, the only thing you need from this entire article to have a sense of what folks are talking about when these metrics get used is a scale. While this scale is an estimate, the league average fluctuates from year to year and can be tracked here. Again, I’ll borrow from Fangraphs:

My cousin once ate horse, unknowingly, for a month and a half in Italy, until her host sister suddenly realized it was not something she would be used to and informed her. She was nearly ill on the spot. I can’t imagine anyone needing a metric of any sort other than their eyes to see the misery that was Ketel Marte with a bat last year, but now that you know with absolute certainty you were eating horse, how about a scoop of sorbet to cleanse that palate?

2016 Batting Average OPS wOBA wRC+
2016 Batting Average OPS wOBA wRC+
Ketel Marte 0.259 0.61 0.266 66
Troy Tulowitzki 0.254 0.761 0.327 102
Jean Segura 0.353 0.867 0.371 126

2017 should be fun.

The limitations of wOBA are a trade-off of its relative simplicity. It may slightly undervalue speedier players, as someone who steals a lot of bases without getting caught frequently is essentially hitting a double instead of a single. It also does not adjust for position, so a wOBA of around .304 would be acceptable for a shortstop, but would be quite subpar for a first baseman. What’s that? You say that’s what Adam Lind’s wOBA was last year? What a strange coincidence.

The other limitation for wOBA is that it does not account for the environment in which the game was played. Red Sox players are liable to have a slightly higher wOBA as a result of playing in hitter-friendly Fenway, as well as Camden Yards and Yankee Stadium. Additionally, adjusting for the NL vs. AL, as well as from year to year, and the different offensive climates in each, demands a slight dabbling to achieve precision. That’s where Weighted Runs Created and Weighted Runs Created Plus come in.

### Weighted Runs Created Plus (wRC+)

Weighted Runs Created (wRC) is a metric that relies on a bit more math, but requires nothing more than what we’ve already gone through above to figure out. wRC is a rate counting stat, like RBI or WAR, which accumulates over the course of the season. As a result, while useful, it can be less helpful to look at in the middle of a season, or if a player has an injury and misses time. For this reason, and a few others, we tend towards its shiny big brother: wRC+

wRC+ looks a bit hairier, but is, at its core, simple: take a player’s wOBA, add it with what a league-average player would be expected to generate per plate appearance, combine that with constants that have been ascribed to the different parks the player has performed in, and then divide that by the AL or NL’s average wRC/PA. You end up with a tiny little number somewhere from 0-2, generally, and so it is multiplied by 100. This is valuable to know and understand, but not essential to effectively understanding and utilizing wRC+. What IS essential is this scale, and the beautiful simplicity of wRC+:

100 is average. Every number higher or lower than 100 is a percentage point better or worse than average. Ketel Marte had a wRC+ of 66 last year, so he was 34% worse than the average hitter. Again, like wOBA, wRC+ does NOT adjust for position, so he was only 28% worse than the league average SS, who had a wRC+ of 92.

The joy of wRC+ is that it can be implemented for comparisons of any sort. You want to see how Nelson Cruz stacks up against Edgar Martinez at the same age?

At age 35 Batting Average OPS wOBA wRC+
At age 35 Batting Average OPS wOBA wRC+
2016 Nelson Cruz 0.287 0.915 0.383 147
1998 Edgar Martinez 0.322 0.993 0.425 156

wOBA won’t tell the whole story, since Edgar benefited from the offensive playground of the Kingdome. wRC+ has you covered, reliably. Edgar was still spectacular, but not only was Nellie remarkable playing in Safeco, he shined in a time where the league has far less offense on average than in the hot-hitting 90’s.

It’s important to note that, like WAR, wOBA and wRC+ don’t tell us too much in the way of projection. They tell the story of what happened. If you dig into the guts of each they’ll tell you a bit more about HOW things occurred, but they are not any more predictive than other stats, only more thorough in their depiction of the past. Add them to your arsenal and be confident, though, in your ability to ascribe value and productivity. You’re ready to assess some hitters.