Mathemadage: Rusty Bats

I have a problem. During the broadcast of Game 1 of the World Series, John Smoltz made an offhand comment that contact hitters do a better job of handling long layoffs between series than power hitters. “The eight to nine days off would… cause havoc on most offenses. But this offense is different, it’s not built on slug,” he said before quickly moving on. His partner in the booth, Joe Davis, didn’t even respond; he just pivoted back to the first inning’s action. Smart move – it’s the World Series, no one wants to debate truisms. But while Nick Martinez faced off against Jake Bauers, I was sitting there turning over that pearl of analyst wisdom in my head.

So do contact hitters handle rust better than power hitters? You could tell an intuitive story in the affirmative. They don’t need to connect perfectly with the ball to get to their good results, so they’re less affected by losing their timing thanks to a long gap between games. But you could tell the opposite story using intuition as well: Contact hitters rely on feel and placement. Tiny margins make the difference between flailing at bad pitches and punching them the other way, so being out of sorts might really hurt.

Some quick Googling didn’t settle things; AI mode told me that contact hitters really do suffer less from rust than power hitters. But when I asked to see the statistical evidence, the AI helpfully told me that it could find none and that it had relied on anecdotal evidence to reach its conclusions. Sounds like a job for Mathemadage, my column that investigates conventional wisdom using numbers.

I started by setting out to define the question I was going to answer. I didn’t use the eight-day-layoff cutoff because frankly, not a lot of teams get eight days off between games. I instead tried to answer this question: Do contact hitters and power hitters see different rust effects when they go a long time without playing a game? I then defined each of those terms. For contact and power, I used strikeout rate and home run rate. Hitters who were at least half a standard deviation above league average in both were power hitters. Hitters who were at least half a standard deviation below league average in both were contact hitters. Everyone else didn’t get a designation. For rust, I looked at playoff games where hitters had at least three days of rest, at least four days of rest, at least five days of rest, and six or more days of rest. I also separately measured hitters in the first game after the All-Star break, but more on that later.

That got us our two groups. I started by looking at the playoffs back to 2002, the farthest back our database goes and also a good source of long-layoff data thanks to all the playoff rounds we have now. I’ll level with you: There aren’t that many long-layoff playoff games, particularly after you break it down between contact and power hitters. Here’s how many plate appearances I had in each group:

Still, we can run the numbers on those, so it’s a good start. Next, I had to figure out how to measure rust. Luckily, I had a pretty good idea from previous investigations. First, I used an existing model that creates simple projections based on regressing a player’s regular season lines slightly based on playing time. I used that to get talent estimates for every pitcher and hitter in my sample, then used those plus a platoon adjustment to come up with expected wOBAs for each plate appearance. I’m not going to go into great detail on the specifics, but in broad strokes, here’s an example: facing Chris Sale lowers the expected outcomes of all hitters, and if two hitters of equal skill face him, a lefty projects to do worse than a righty.

I also created control groups for both power and contact hitters. In this case, the control group is easy: It’s just those same hitters, later in the series after the rust has worn off. For example, playoff hitters – all playoff hitters, regardless of profile – produce wOBAs about 15 points lower than expected based on their regular season lines. There are several causes here: pitchers are throwing harder and for shorter bursts, the weather is colder, the defenses are better, and so on. By comparing performance relative to expectation immediately after a layoff to performance relative to exception later in the series, I produced an estimate of rust effects for each group that hopefully strips out any general playoff effects.

Here’s an example: After five or more days of a layoff, power hitters produced a wOBA 19 points lower than my expectation. In the other games they subsequently played in those series, they produced a wOBA 15 points lower than my expectation. Thus, I estimated the rust effect at -4 points of wOBA. Contact hitters, by comparison, produced a wOBA 43 points lower than my expectation in their first game back from a gap, as compared to a wOBA 20 points lower than expectation the rest of the series. Thus, I estimated their rust effect at -23 points of wOBA. But as you’d expect with so few games, the results weren’t particularly stable across different cutoffs. Here’s the “rust effect” for each number of days off:

To be clear, that finding is what no effect looks like. The “pattern” – contact hitters show less rust than power hitters after layoffs of four-plus days, but underperform in the other slices – is almost certainly just noise. I tested that a few ways. First, I resampled with replacement, randomly making new groups of post-layoff games by picking from the existing population, to measure how much the wOBA gap could change based on sample size. I did that 2,000 times to get a plausible range. For example, after five or more days off, the standard deviation among those 2,000 samples was about 40 points of wOBA for power hitters, and 36 points of wOBA for contact hitters. The 95% confidence interval for the difference in layoff effects between contact hitters and power hitters was -138 points to +98 points of wOBA. In other words, our data tells us that either contact hitters do much worse after layoffs than power hitters, contact hitters do much better after layoffs than power hitters, or anywhere in between. Whoops.

I tried a different method to drive home how big the error bars are here. I randomly designated some completely normal playoff games – zero or one days of rest, mid-series – as “fake layoff games.” I ran the same tests that I did on the real layoff games. I made a bunch of fake samples of the same size as my real sample and looked to see how often they produced rust effects as big as the one I measured, even though there’s obviously no real effect here; I was grabbing games completely at random. For instance, let’s take our five-plus layoff days example from above. I found that 73% of my fake-layoff samples produced a gap as big as or bigger than the 20-point wOBA gap we observed, while 37% of my fake-layoff samples produced a wOBA difference between the contact and power groups of 50 points or more.

This makes logical sense to me. Why can’t we find any effects in playoff games? Because there haven’t been enough of them. Just look at the plate appearance numbers. Power hitters coming back from five or more days off have racked up 171 postseason plate appearances since 2002. You wouldn’t accept a broad conclusion about baseball based on 171 plate appearances. You’d barely accept a conclusion about a single hitter based on 171 plate appearances; that’s six weeks of everyday hitting, more or less. Sure, we could grab a few more playoff games by reaching deeper into history, but what would be the point? There’s just not enough data to say anything. So I turned to something more predictable: the All-Star break.

It’s perfect. Every year, baseball mandates that every hitter take five-ish days off from competitive games in the middle of the season. Want big sample sizes? By going back to 1974, I got 6,783 plate appearances worth of power hitters and 8,369 plate appearances worth of contact hitters. I performed the same test that I did for the playoff games: I looked at how each group performed relative to expectation in their first game back and compared that to how they did relative to expectation in the rest of the series. Maintaining a control group remains important: July is one of the hottest months of the year, so power hitters naturally do a bit better thanks to the ball traveling farther in air, which has to be stripped out.

After accounting for the control group, however, I found no effect. Power hitters beat the control group by just under three points of wOBA. Contact hitters beat the control group by just over one point of wOBA. The net difference (power hitter rust minus contact hitter rust) was one point of wOBA, with a 95% confidence interval of -15 to +17 points.

Just for kicks, I also tried different cutoffs for “power” and “contact.” Instead of half a standard deviation for each, I tried a quarter standard deviation; power hitters had a seven-point “rust advantage” in that cut. I tried a full standard deviation; this time, contact hitters had a seven-point rust advantage. At 0.75 standard deviations, the two sides had equal rust effects, just like at half a standard deviation.

With this larger sample, I tested some other effects too. I looked at strikeout rate first. Power hitters struck out meaningfully less than expected in their first game back; their strikeout rate relative to expectation was 1.2 percentage points lower than it was for the remainder of the series. Contact hitters actually struck out slightly more than they did the rest of the series. On the other hand, power hitters hit fewer home runs in the first game back than they did the rest of the series, while contact hitters narrowly outperformed their expected home run numbers in the first game back from a break. Both groups walked more – pitcher rust is surely a thing, albeit not one we’re measuring here.

But while it’s fun to find these little trinket effects, the overall takeaway seems clear. In a broad controlled sample of players returning after the All-Star break, there was no evidence that contact hitters and power hitters displayed different effects of rust. In the playoffs, there simply isn’t enough data to say, but the data we do have is contradictory and shows power hitters slightly outperforming contact hitters after layoffs in more samples than it shows the reverse.

More broadly, there isn’t much evidence of a rust effect at all. Forget the contact and power cutoffs; hitters perform pretty much the same, after accounting for who they are and who they’re facing, in their first game back after a layoff and in subsequent games in the same series. Across the entire sample of All-Star breaks, hitters were about two points of wOBA worse in their first game back, which is squarely in noise territory. As I keep saying, the playoff data is just not voluminous enough to say anything with certainty, but hitters have done better, by between two and 10 points of wOBA depending on your rest cutoff, in their first games back.

So next time you hear a claim about how one team’s days off might affect different hitters on the team differently, or how one squad has an advantage because they’re built to stay locked in, be skeptical. Nothing I did here today proves that there’s no effect. That’s not how statistics works. But despite looking deeply and broadly, I couldn’t even prove that rust produced meaningfully different results, never mind that different classes of hitter experienced that rust differently. Too much investigation for a tossed-off comment that I might have been the only person to register as potentially interesting? Most definitely. But that’s what Mathemadage is all about – and in my opinion, this was another good one.