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.
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.