The big story of the Nationals' season so far (other than that guy who got a save the other day) has been the resuscitation of Ryan Zimmerman. Zimmerman, who has battled injuries for the past few years, reached double digits in home runs for the month of April. According to a story that should probably be called “apocryphal,” Zimmerman’s renaissance can be credited to deep, late-night conversations with teammate Daniel Murphy. Murphy had one weird trick that he suggested Zimmerman might try this year: swing up. Apparently, it worked.

It’s entirely possible that Zimmerman and Murphy were talking shop in the Nationals' clubhouse. Maybe that is the reason that Zimmerman once again looks like an All-Star. It’s also possible that Zimmerman is finally healed of his injuries from the past few seasons and, while he was always trying to swing up, he’s now healthy enough to do so. Maybe it’s a little of both.

Here’s a more interesting question: Is this sort of peer-to-peer learning effect common? Do players change based on who is surrounding them? If a player goes from a team of free-swingers to a team of patient people, does he become more patient as a result? Most projection systems effectively say “No.” They tend to use a player’s stats and only a player’s stats when making a guess on what he might become in the coming season. Sure, talent is going to have something to do with it, but maybe there’s more.

Warning! Gory Mathematical Details Ahead!

Let’s pull a few tricks off the shelf. First off, we need a good measure of year-to-year change. If a batter’s strikeout rate in 2015 was 15 percent and in 2016 it was 16.6 percent, he changed in absolute terms by 1.6 percentage points. Except, well …

Player A, 2015: 3 strikeouts in 20 PA
Player A, 2016: 1 strikeout in 6 PA

Player B, 2015: 90 strikeouts in 600 PA
Player B, 2016: 100 strikeouts in 600 PA

The conceit here is that, mathematically, those are the same percentages, but Player A was a bit player who got a couple cups of coffee while Player B was a regular starter. I feel pretty good about saying that Player B actually was, somehow, more prone to strikeouts in 2016 than 2015. Player A, despite having identical strikeout rates, has such a small sample size that I’m not sure if that’s the real him. We need something better than that.

Fortunately, we have a way to standardize these things, known as the reliable change index. The method adjusts for the fact that different statistics have different levels of reliability at different sampling frames, as well as adjusting for the population spread (i.e., standard deviation). What results is something that maps onto a Z-distribution. We can report how much a player has changed in standardized units.

Because we are modeling change (his strikeout rate increased by 1.6 percent), rather than absolute strikeout rate (we predict he will strike out 16.6 percent of the time), we have one thing that we need to watch out for, or perhaps two somewhat related things that can be controlled in roughly the same way. One of the problems is a ceiling/floor effect. The idea there is that if you have a particularly low strikeout rate, there’s really only room to go up (floor effect) and if you have a higher rate, it’s likely to go down (ceiling effect) for the same reason.

The other problem is simple regression toward the mean. We know that extreme strikeout rates (or rates of anything, really) tend to shrink toward the mean, whether coming from well below the mean or well above it. So, in the regressions that we are about to put together, I used the previous year’s strikeout rate as a control. Someone who is well above (or below) the mean is likely to see a specific type of effect on their change score based on these principles. (Spoiler: This bore out in all of the analyses that I did.)

OK, now that we have a way of checking on how players change over time, what is correlated with that change score? If we’re looking into teammate effects, we need some information about the guys with whom our player was hanging around most often. I started off by looking at strikeouts. I looked at what percentage of a player’s teammates who played regularly (defined as having 250 PA on the season; I used data from 2012-2016), were one standard deviation above the league-average strikeout rate and what percentage were one standard deviation below.

It turns out that the more teammates you have who strike out at an above-average rate, the more likely you are to strike out more than you did last year. It doesn’t work the other way around for strikeouts with low-strikeout teammates leading to a lower strikeout rate. I re-ran the same analyses, this time with walks instead of strikeouts. In that case, having teammates who are low-walk guys predicted that a player would see a decrease in his walk rate as well, although that effect was only marginally significant (p = .09).

The effects of having an additional hitter on the team who was overly fond of the letter K wasn’t a giant, even if we buy that it’s real. It was worth about three quarters of a strikeout over 600 PA, but in theory, everyone on the team would see this effect and that can add up.

Let’s Chat

It’s important to make a distinction about what we’ve learned here today. It is entirely possible that players teach each other things. In fact, I guarantee that someone out there this season is having a breakout because of something he learned from a friend on the team. Here we’re discussing whether those effects are individual or systemic. Can there be something about a clubhouse that turns hitters into a massive, flailing ball of strikeout? Here we see some evidence that the answer is yes, even if it’s weak evidence.

We don’t know what the cause is here. It might be that the players are talking to each other and, in this case, spreading bad habits around the clubhouse. It’s possible that since they all have the same hitting coach and manager, this actually reflects a team-wide approach. It’s possible that a team with a couple of free-swingers is more likely to go out and get guys who are trending that way anyway, because they don’t see a problem with it. Or maybe strikeouts spread.

It’s possible that team chemistry is also happening on an interpersonal level as well. The Murphy-Zimmerman story, assuming it’s true, is a pretty good example of how it might work. The most important factor there isn’t that “the Nats have a good clubhouse” but that “Murphy and Zimmerman were talking.”

It doesn’t mean that the two ideas are exclusive. If a team has a clubhouse culture that encourages this sort of collaboration, all the better, but the atomic unit, the one that we really want to zoom in on to figure out what’s going on, might be that one-to-one relationship. As of right now, FriendCast doesn’t exist. But this is a first step in figuring out how the group affects the individual. The answer to that question is not “zero” even if we don’t know how it all works or if it’s big enough to be important. There’s at least something going on.

Thank you for reading

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Did you take park effects into account? K and BB rates can change with park by: 1) smaller foul areas reduce foul outs, thereby lengthening counts, 2)Changes in batter and pitcher strategies
Not directly, though K and BB park effects tend to be small, and I did test (and left on the cutting room floor) whether the effects were there specifically for team switchers and the results came out the same.
Are these the same teammates? It might be your GM likes (or doesn't mind) guys who strike out more.
They are the same teammates, but we're looking at year-to-year change. So, if a GM likes guys who strikeout a lot, they probably already were K-hogs, and therefore, their change scores aren't going to be that big.