Plate Discipline, in One Number

How do you describe a batter’s plate discipline? I sometimes struggle with it. I might describe their walk rate and strikeout rate, maybe add in something about how often they swing. I’m never sure how much to weight walk rate and how much to care about strikeouts. How does someone with a 25% strikeout rate and 10% walk rate compare to someone with a 20% strikeout rate and a 7% walk rate?

What about Anthony Rizzo? He gets on base without swinging the bat fairly often, but it doesn’t show up in his walk rate, only in bags of ice and bruises. Getting hit by a pitch is marginally more valuable than a walk if you listen to our linear weights (because walks happen more often when there are bases open, while HBP tend to be random), but it doesn’t show up in the “plate discipline” numbers we’re used to looking at.

I’ve danced around this concept a few times here at FanGraphs. When I wrote about Joey Gallo’s new approach, I touched on how his strikeout and walk rates related to how good he needed to be on contact to succeed. When I wrote about Luis Arraez’s unique talents, I framed his walks and strikeouts in terms of what it meant for the rest of his contact. Behind the scenes, I’ve been using a standardized version of this calculation for quite a while. Today, with no baseball coming to save us, it’s time to explain my method.

Imagine a perfectly average hitter. Not someone with a 100 wRC+; that’s a hitter whose results are average. No, I’m talking about a hitter who does everything at the exact major league average rate. He walks 8.5% of the time, strikes out 23% of the time, and bats .252/.323/.435. He puts the ball in play exactly as often as the league as a whole, and when he does, gets perfectly ordinary results.

Next, let’s start varying things. We’ll add 1% of walk rate into the mix while holding strikeouts constant. Now our hitter has a wRC+ higher than 100. To lower his overall output to league average, we’d have to make our hitter worse when he puts the ball in play. If we did the opposite, adding strikeout rate while keeping walks constant, we’d have to make the hitter better than average on balls in play to create an average overall hitter. In fact, we can express how good a hitter is when he doesn’t put the ball in play in terms of how good he has to be when he does put the ball in play to create an average batting line overall.

Let’s use a real-world example to make this clearer. Consider Mike Trout. Excluding intentional walks, he came to the plate 586 times last year. He walked in 96 of those plate appearances (16.4%), struck out in 120 (20.5%), and was hit by a pitch 16 times (2.7%). Put it all together, and Trout ends a trip to the plate without putting the ball in play 39.6% of the time.

Next, let’s work out the wOBA value of these non-contact plate appearances. Our Guts page helpfully lists the wOBA value of each event. Plugging in the value of a walk (.690), a strikeout (0), and an HBP (.719), we can work out Trout’s wOBA when he walks, strikes out, or gets hit. It comes out to .335.

Next, we’re going to make Trout average. That’s not perfectly accurate, actually; we’re going to figure out how good Trout would need to be when he puts the ball in play to be an average batter overall. Recall, if you will, that the ball ends up in play on 60.4% of his plate appearances. Average wOBA for baseball as a whole last year was .324. Trout produces a .335 wOBA in 39.6% of his plate appearances. We can calculate how well he’d need to do on those 60.4% in-play trips to be average overall. I found that he’d need to produce a wOBA of roughly .317 on those: (.604 * .317 + .396 * .335) = .324.

When batters make contact, they do better than that. Significantly better than that, in fact: batted balls produced a .384 wOBA in 2019. A hitter with Trout’s exact non-contact results could be only 82.5% as good as the average hitter when he puts the ball in play (.317/.384) and still be average overall.

That, in essence, is the entire ball of yarn. Want to know how valuable a batter’s work with walks and strikeouts is? You can express it in terms of how good they would have to be on contact to make the whole thing work. One quick mathematical flourish is worthwhile; we like to think of all-in measures like this as plus stats. Scaling everything to a percentage of league average, with higher being better, is the most intuitive way to think of these. So instead of 82.5%, let’s express it as a plus stat in the same way ERA+ is calculated: 2-(.317/.384), or 117.5.

What are we going to call this statistic? I’ve had this idea bouncing around in my head for a while, and when I’ve explained it before, I’ve called it NOC+, or Non-Contact Management +. The name isn’t great, but the all-in-one nature is. Want to compare unlike players? This stat has your back. For example, Rizzo (120.3 NOC+) is amazing. He does it with 4.4% HBPs and a low strikeout rate. Willians Astudillo (117.3 NOC+) is also amazing — he could create contact 17% worse than league average and still be an average hitter. He does it by never striking out; balls in play are more valuable on average than non-contact outcomes, and Astudillo simply puts everything in play.

The list goes on. Josh Donaldson (108.3 NOC+) is above average despite his 23.6% strikeout rate. That’s because he walks a lot (14.9%) and takes a few balls to the lower extremities (1.2% HBP rate). His NOC+ is higher than Nicky Lopez (108.1 NOC+), whose numbers look better offhand; a bargain-basement 12.7% strikeout rate is awesome, and he walks 4.5% of the time. Still, Donaldson could get by with worse results on contact than Lopez, because those walks are valuable.

On the bottom end, it’s basically what you’d expect. How do you create a player who needs extremely loud contact to create average overall value. Find someone who strikes out a lot and doesn’t walk much, like Keon Broxton (50 NOC+!) or Gallo (78.1 NOC+). Gallo needs to produce contact 21.9% better than league average to get to a 100 wRC+. He does, and does so easily, but it’s a good numerical representation of the uphill battle he faces.

For now, I’ve provided a list of every batter’s 2019 NOC+ here. Also, here’s a top 10 board for you if you don’t feel like clicking the link:

How useful is this statistic? I’d say marginally. It’s mostly for fun, and while it’s nice to see everything collapsed down to one number, the statistic doesn’t cover things like “Do batters who walk more tend to hit the ball harder?” And “Are all strikeouts created equal?”

Those questions are beyond the scope of this analysis. This is simply one number you can look at to put everything in perspective. To reuse an earlier example, Astudillo and Mookie Betts have nearly identical NOC+ numbers. That means that if they produced equally loud contact, they’d be equally good hitters, despite the fact that Mookie walks 13% of the time and Astudillo walks only 2.5%.

Should NOC+ account for stadium? Is it stable year-to-year? Is being contact-quality agnostic reasonable? Those are great questions I plan on answering in the coming weeks. For now, it’s just a toy; one number that can tell you whether what a hitter does without putting the ball in play is helpful or harmful, and to what extent.