13 April 2016

Why Chris Davis Is Not A Rally-Killer

Chris Davis 
Photo by Keith Allison

During last week’s Camden Highball podcast, I made the following statement (paraphrased):
I love you, Chris Davis. But I don’t want you batting in the bottom of the 9th when the team is down by two and there are two runners on base. One-third of the time you’re going to strike out (not advance the runner). These little moments are going to add up during the year.
Prior to recording the podcast I’d thought a lot about the relationship between swinging strike rate and WPA. My gut told me a high-strikeout player like Davis would hurt the team by failing to advance runners in close games.

It seemed true. It felt true. So I said it out loud.

After I listened to the recording, an embarrassed flush spread to my cheeks. Here I am, writing on a sabermetrics web site, and I just used my gut to make a statement. Ugh! We all say foolish things, but not many of us get the chance to say foolish things that strangers on the Internet hear and that live for eternity on Dropbox. I managed to do both at once.

In order to feel less foolish, I had to atone for my sins. Isn't that what this whole sabermetrics thing is about, backing up your beliefs with evidence? So I said "gut, I'm sorry, but I need to fact check you." My gut responded favorably, but that's probably because I'd just eaten a peanut butter creme Oreo.

I examined the relationship between a player's swinging strike rate and the following metrics:
  • Win Probability Added: Measures how much a player added to their team’s chance to win during the course of a season, taking into account both the leverages (inning, score, runners on base, number of outs) in which they batted and how well they did in the plate appearance.
  • Win Probability Added / Leverage Index (WPA/LI): WPA without the leverage component. Unlike WPA, WPA/LI doesn't punish players for appearing in lots of low-leverage situations, nor does it reward players to bat in a lot of high-leverage situations. Players can't control the leverage of the situations in which they bat.
I sampled non-pitchers from 2010-2015 who averaged at least 50 PA per season. This low threshold avoided survivor bias by looking at not only starters, but also role players and those who were injured.

My hypothesis: players with high swinging-strike rates will have a lower WPA than players with low or average swinging strike rates. For context, Davis’ swinging strike rate of 15.48% ranks 20th-highest out of 1,607 players in this sample.

Unfortunately for my gut, the research shows swinging strike rate doesn't correlate well to either WPA or WPA/LI:

Swinging strike rate explains only 0.07% of the variance in WPA, or about 0.002 wins per year. That's a tiny number of wins.

The relationship isn't much stronger when you remove leverage from the equation. The r^2 between swinging strike rate explains only 0.0198 wins of WPA/LI per year. No one will notice this change in a player's WAR.

But r^2 isn't everything. The regression lines slope upward, indicating that as swinging strike rate increases, WPA and WPA/LI also increase. If you followed this model you'd want a player to swing and miss as much as possible, because the model says their WPA would be very high. But no one wants a batter to swing and miss ever, let alone "as much as possible".

That's why the plots look different if you focus on players with medium-to-high swinging strike rates:

The r^2 values remain weak. More importantly, these trend lines slope downward. Now the model says: if you swing and miss a lot, you're starting from a deeper hole than your peers who make more contact. You can still make a positive contribution, but you'll have a harder time doing so. There's the logical sense we are looking for.

A 2nd-degree polynomial fit of the original data shows this effect better:

While Chris Davis' swinging strike rate doesn't explain his WPA or WPA/LI, he should be careful going forward. If he swings and misses much more than he does now, he'll have a harder time contributing to the team.

Fortunately, Davis is a more complete player than just swinging and missing. He possesses tremendous power and mixes in a pretty good walk rate. These factors boost his wOBA, which correlates much better with WPA and WPA/LI:

The r^2 between wOBA and WPA is 0.64 (2.1 wins), and between wOBA and WPA/LI it's a whopping 0.82 (2.3 wins). Overall offensive prowess, as measured by wOBA, explains variance in WPA and WPA/LI much better than than swinging strike rate does.

These relationships hold up well for hitters in Davis' class:

In both cases, the regression models make logical sense. Have a high wOBA and you'll contribute wins to your team. Chris Davis should have a high wOBA. All is right with the universe.

I'm sorry, Chris Davis. I take back what I said. I won't grimace in frustration anymore when I see you bat in a high-leverage spot. I'll remind myself that you're a very talented baseball player who whacks the ball all over the yard, no matter the game situation.

But please don't swing and miss any more than you already do.


Roger said...

LOL. Good article, Ryan. It really is emotionally painful watching some of Chris' swings and misses in crucial situation. I think that what the gut tells us is that he is such a productive player in a high leverage part of the lineup that our expectations are driven higher than they should be given the statistics involved. And we remember the disappointments more than the successes. But watching Davis Crush one to win a game is an extremely satisfying moment just as watching Trumbo exit the stadium over the Green Monster last night was epic, too.

Jon Shepherd said...

Yeah...I let you die on the vine there.

One note, which I think is minor, is that WPA is based on an average offense. It does not consider specifics of a situation player for player. In other words, striking out with Billy Hamilton at first is different than Wieters.

Matt Perez said...

Yeah, I think that SwStr is largely useless because it doesn't take fouls into account.

The real question is whether a high OBP or SLG is more valuable in this setting. Logic suggests that OBP is more important but the question is whether there's a relationship. For example is a guy with a .280/.360/.380 line a better option then a guy with a .260/.340/.500 line?

Roger said...

Matt, I'm not sure I agree. I watch the Braves as well as the O's and watching them get rally after rally getting one, two, or three men on base and still not being able to score, I'm not sure that having that one or more guys with the big SLG isn't better. Now the Braves may be a bad example, but, at the current time, they are somewhat opposite of the O's - decent OBA, no SLG. The O's might squander a few rallies by striking out but my gut tells me that one guy hitting it out of the park makes for better rallies than relying on three guys to hit it between 2nd and SS. I'd like to see a hypothetical analysis of having a lineup filled with .280/.360/.380 vs one filled with .260/.340/.500 (although, I think .240/.340/.500 might be more reasonable). Last night, the Nats beat the Braves because Bryce could hit a big double when needed and the Braves got the bases loaded with no outs and couldn't score. One superstar has more value than a bunch of good players. Just look at the O's corner OF situation.

Jon Shepherd said...

"When they needed it" is more about incidence rate and bundling. As I mentioned before WPA assumes all players outside of the batter are equal. In terms of generalities, a .360/.380 hitter is not equal to a .340/.500 hitter. It would be something more like a .290/.500 hitter. OBP is worth a lot, but .020 of it is not typically going to be equivalent to .12 of slugging.

Matt Perez said...

"I'm not sure that having that one or more guys with the big SLG isn't better"

Maybe. I'm sure someone has already done the analysis. Bryce has an excellent OBP and SLG.

The weights I threw out were just an example and not meant to mean anything per se.

Ryan Pollack said...

No worries Jon! I atoned for my sins ;-)