I was reading one of Baseball Prospectus’s collections this morning and came across an interesting story. It’s a part of baseball lore that Willie Mays started his career on a brutal cold streak (though one punctuated by a long home run off Warren Spahn). Apparently, manager Leo Durocher told Mays toward the end of the slump that he needed to pull his pants up because the pant knees were below Mays’s actual knees, which was costing him strikes. Mays got two hits the day after the change and never looked back.

To me, this is a pretty great story and (to the extent it’s true) a nice example of the attention to detail that experienced athletes and managers are capable of. However, it prompted another question: do uniform details actually affect the way that umpires call the game?

Assessing where a player belts his pants is hard, however, so at this point I’ll have to leave that question on the shelf. What is slightly easier is looking at which hitters wear their socks high and which cover their socks with their baseball pants. The idea is that by clearly delineating the strike zone, the batter will get fairer calls on balls near the bottom of the strike zone than he might otherwise. This isn’t a novel idea—besides the similarity to what Durocher said, it’s also been suggested here, here, and in the comments here—but I wasn’t able to find any studies looking at this. (Two minor league teams in the 1950s did try this with their whole uniforms instead of just the socks, however. The experiments appear to have been short-lived.)

There are basically two ways of looking at the hypothesis: the first is that it will be a straightforward benefit/detriment to the player to hike his socks because the umpire will change his definition of the bottom of the zone; this is what most of the links I cited above would suggest, though they didn’t agree on which direction. I’m somewhat skeptical of this, unless we think that the umpires have a persistent bias for or against certain players and that that bias would be resolved by the player changing how he wears his socks. The second interpretation is that it will make the umpire’s calls more precise, meaning simply that borderline pitches are called more consistently, but that it won’t actually affect where the umpire thinks the bottom of the zone is.

At first blush, this seems like the sort of thing that Pitch F/X would be perfectly suited to, as it gives oodles of information about nearly every pitch thrown in the majors in the last several years. However, it doesn’t include a variable for the hosiery of the batter, so to do a broader study we need additional data. After doing some research and asking around, I wasn’t able to find a good database of players that consistently wear high socks, much less a game-by-game list, which basically ruled out a large-scale Pitch F/X study.

However, I got a very useful suggestion from Paul Lukas, who runs the excellent Uni Watch site. He pointed out that a number of organizations require their minor leaguers to wear high socks and only give the option of covered hose to the major leaguers, providing a natural means of comparison between the two types of players. This will allow us to very broadly test the hypothesis that there is a single direction change in how low strikes are called.

I say very broadly because minor league Pitch F/X data aren’t publicly available, so we’re left with extremely aggregate data. I used data from Minor League Central, which has called strikes and balls for each batter. In theory, if the socks lead to more or fewer calls for the batter at the bottom of the zone, that will show up in the aggregate data and the four high-socked teams (Omaha, Durham, Indianapolis, and Scranton/Wilkes-Barre) will have a different percentage of pitches taken go for strikes. (I found those teams by looking at a sample of clips from the 2013 season; their AA affiliates also require high socks.)  Now, there are a lot of things that could be confounding factors in this analysis:

1. Players on other teams are allowed to wear their socks high, so this isn’t a straight high socks/no high socks comparison, but rather an all high socks/some high socks comparison. (There’s also a very limited amount of non-compliance on the all socks side, as based on the clips I could find it appears that major leaguers on rehab aren’t bound by the same rules; look at some Derek Jeter highlights with Scranton if you’re curious.)
2. AAA umpires are prone to more or different errors than major league umpires.
3. Which pitches are taken is a function of the team makeup and these teams might take more or fewer balls for reasons unrelated to their hose.
4. This only affects borderline low pitches, and so it will only make up a small fraction of the overall numbers we observe and the impact will be smothered.

I’m inclined to downplay the first and last issues, because if those are enough to suppress the entire difference over the course of a whole season then the practical significance of the change is pretty small. (Furthermore, for #1, from my research it didn’t look like there were many teams with a substantial number of optional socks-showers. Please take that with a grain of salt.)

I don’t really have anything to say about the second point, because it has to do with extrapolation, and for now I’d be fine just looking at AAA. I don’t have even have that level of brushoff response for the third point except to wave my hands and say that I hope it doesn’t matter given that these reflect pitches thrown by the rest of the league, so they will hopefully converge around league average.

So, having substantially caveated my results…what are they? As it turns out, the percentage of pitches the stylish high sock teams took that went for strikes was 30.83% and the equivalent figure for the sartorially challenged was…30.83%. With more than 300,000 pitches thrown in AAA last year, you need to go to the seventh decimal place of the fraction to see a difference. (If this near equality seems off to you, it does to me as well. I checked my figures a couple of ways, but I (obviously) can’t rule out an error here.)

What this says to me is that it’s pretty unlikely that this ends up mattering, unless there is an effect and it’s exactly cancelled out by the confounding factors listed above (or others I failed to consider). That can’t be ruled out as a possibility, nor can data quality issues, but I’m comfortable saying that the likeliest possibility by a decent margin is that socks don’t lead to more or fewer strikes being called against the batter. (Regardless, I’m open to suggestions for why the effect might be suppressed or analysis based on more granular data I either don’t have access to or couldn’t find.)

What about the accuracy question, i.e. is the bottom of the strike zone called more consistently or correctly for higher-socked players? Due to the lack of nicely collected data, I couldn’t take a broad approach to answering this, but I do want to record an attempt I made regardless. David Wright is known for wearing high socks in day games but covering his hosiery at night, which gives us a natural experiment we can look at for results.

I spent some amount of time looking at the 2013 Pitch F/X data for his day/night splits on taken low pitches and comparing those to the same splits for the Mets as a whole, trying a few different logistic regression models as well as just looking at the contingency tables to see if anything jumped out, and nothing really did in terms of either greater accuracy or precision. I didn’t find any cuts of the data that yielded a sufficiently clean comparison or sample size that I was confident in the results. Since this is a messy use of these data in the first place (it relies on unreliable estimates of the lower edge of a given batter’s strike zone, for instance), I’m going to characterize the analysis as incomplete for now. Given a more rigorous list of which players wear high socks and when, though, I’d love to redo this with more data.

Overall, though, there isn’t any clear evidence that the socks do influence the strike zone. I will say, though, that this seems like something that a curious team could test by randomly having players (presumably on their minor league teams) wear the socks high and doing this analysis with cleaner data. It might be so silly as to not be worth a shot, but if this is something that can affect the strike zone at all then it could be worthwhile to implement in the long run—if it can partially negate pitch framing, for instance, then that could be quite a big deal.