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During the September stretch drive and the playoffs, when the good players play every day and the good pitchers pitch more innings than they’re used to, there’s a saying that “you can sleep in November.” Hopefully, some major leaguers are taking a well-deserved nap right about now. But baseball never really sleeps. There are general managers getting ready to call agents to make offers to free agents and calling each other to propose crazy deals. In December, they’ll throw a big sleepover in National Harbor, Maryland during the Winter Meetings and make a bunch of those deals.

Hopefully, they have a pillow fight at some point.

(OK, fine. I’ll pause while you picture Theo and Jed bouncing on one of the beds in the Cubs suite, hitting each other with pillows while the World Series trophy sits on the nightstand.)

Not that kind of pillow fight. I want them to discuss pillows. The kind that you sleep on at night. If they’re going to obsess about how they’ll sign a player who might make them a win better, they might as well obsess over something else that might make them a win better: pillows.

(And toothbrushes.)

Warning! Gory Mathematical Details Ahead!

There aren’t any magical hitting pillows out there, but there is something magical about getting a good night of sleep. Not only do you feel better, but it’s a quick proof to show that it makes for a better baseball player. What might surprise you is by how much. When we talk about a complete lack of sleep, I don’t mean people who are forced to stay up all night without going to sleep at all. That would be cruel. I’m talking about what sleep scientists call “partial sleep deprivation” and you call “just one more episode of Full House.”

It’s getting sleep, but not quite getting the recommended 7-8 hours. There’s plenty of that in baseball. Some of it is the travel schedule. Some of it is probably living out of hotels and not being able to have your favorite blankie around. Some of it might be what we call “behavioral.” Let’s just say that sometimes the reason a player isn’t asleep by 1:00 a.m. has to do with choices that he makes about where to spend his time.

One of the primary effects of a lack of sleep is a dulling of reaction times. This intuitively makes sense, but we have laboratory data on how much of a difference it can make and it’s a big deal. But let’s start with a quick primer on reaction times. It takes the human brain about 200 milliseconds (ms), minimum, to respond to anything at all. There are neurons that need to fire, but 200 ms (two-tenths of a second) is pretty quick, when you think about it. Human beings are amazing.

Response time also varies within a person. Sometimes responding to whatever it is takes 300 ms, sometimes you get a quick reaction in 150 ms. Sometimes you have a little brain cramp and it takes 500 ms. Those extra 300 ms are the sort of thing that you might pick up on with the naked eye if you were watching a fielder specifically, but you might not if you were relying on TV. Most of the time in life, the extra three-tenths of a second doesn’t make a difference. Baseball isn’t most jobs.

Consider that 300 ms gap in baseball terms. Three-tenths of a second from home to first is the difference between an 80-grade runner, say Billy Hamilton, and a 50-grade runner, which is “league average." (There are those of you who understand why I just used “scare quotes.” The rest of you can move along.) The act of running to first is so ingrained in the swinging process by muscle memory that it’s not likely that someone can have the kind of brain cramp needed to make them actually stop and say “wait a minute … what am I supposed to do here? Oh right, run to first!” before running down the line.

But let’s take that into the field. An outfielder, when he perceives that there is a fly ball coming toward his assigned area, must react, run over to where the ball will land, and catch it. How difficult that job will be depends on how much hang time the ball has and where the ball is scheduled to land. There are some catches that any competent MLB outfielder can make. There are some that no human on earth could make. But then there are the marginal cases. Those are the ones where the good fielders get there and the bad ones don’t.

I’ve previously made the case that, for an outfielder (singular), we are talking somewhere around 60-80 balls per year that are in the zone where an elite runner probably gets to them, but a “league-average” runner (who would likely be below average for a center fielder) does not, ceteris paribus. That’s out of about 600 balls that an average center fielder fields annually, whether catching on the fly or picking it up after it bounces. That’s back-of-the-envelope math, but we’re in the right neighborhood.

Now let’s say our fielder has one of these reaction time lapses as he has to react to a ball being hit toward him. Even if he’s an 80 runner, that lapse now effectively turns him into a 50 runner. It’s possible that this one particular fly ball might not have been affected. Maybe it was one of those he’d never get to anyway. Maybe it was hit right at him so that as long as he wakes up at some point in the next three seconds, he’s fine. But what if it’s in that marginal zone? That brain cramp just turned an out into a hit.

Now, we return to talking about sleep deprivation. I mentioned that sleep deprivation slows down reaction time. In the lab, there’s a test known as the Psychomotor Vigilance Task (PVT), which is a commonly used gauge of reactions over a sustained interval. The test itself runs for 10 minutes and when a person sees a letter on the screen they push a button. The response times are recorded by the computer. Most people react when they see the letters, but we’re most interested in how long it takes them. Researchers commonly use that 500 ms threshold as a definition for an elongated response time. Everyone has one every once in a while, but sleep deprived people have them more often.

Researchers tested volunteer research participants who were “sleep restricted” during this time (they were allowed only four hours of sleep per night). The researchers tested the participants over the course of five consecutive nights of sleep deprivation. Even after one night, the participants showed a 1.2 percent increase in their rate of making these 300 ms lapses over their baseline rate (which was tested before their sleep restriction began). After two nights, it was 2.4 percent of the time that they were having reaction time lapses. The numbers climbed to 7.8 percent after five nights.

But let’s just focus on two nights of not-quite-enough sleep. At that point, we assume that a fielder has a 2.4 percent greater chance of having a lapse than if he were fully rested. He’s not always going to be in that sort of state. There will be nights where he’s gotten good sleep over the past few days. There will be that one road trip where he just can’t get comfortable at the team hotel. His sleep debt will fluctuate over the course of the season. But there will be sleep interruptions. Baseball is a grindy game.

Of the 60-ish balls (let’s just say 60 out of 600) that are hit into that magical area where an 80 runner gets to it and a 50 runner does not, an extra 2.4 percent chance of suffering a mental lapse (which effectively turns an 80 runner into a 50 runner) means an extra ball-and-a-half that drops over the course of a year. A ball that drops when it should have been caught is an out turned into a hit, which is worth about three-quarters of a run if it’s a single. So, the difference between being well-rested and being somewhat sleep deprived is worth a little more than one run … for one outfielder.

And that under-sells it a little bit. The researchers only “counted” cases in which the respondent had a response time lapse that was 500 ms or more. If a fielder were to have a response time of 400 ms, it’s the same as taking him from a 70 runner to a 50 runner, and those would be additional “lapses” that we’re not even considering. (The evidence shows that mean response time in general goes up). Perhaps we might say the average effect is around 1.5 or 2.0 runs runs for the center fielder (and perhaps a little less for the less-busy left and right fielders).

Across three outfielders, perhaps that’s four or five runs that a team loses from the effects of sleep deprivation all year compared to playing while well-rested. That’s just the outfield. Reaction time is something that infielders need to think about as well. It’s harder to quantify that because we don’t have good public data on how fast an infielder would have to move to get to a ground ball, but we know that impairing his reaction time isn’t going to help. But really, if sleep issues let a few extra balls bleed through, then that’s a few extra hits that teams will allow. That adds up.

Then there are the effects that are harder to pin down. Sleep deprivation-induced lapses in reaction time (and concentration) aren’t limited to the field of play. They’ll be there in the pre-game meeting where teams go over all the strategy for the night’s game. Maybe someone misses something during the meeting. Maybe it makes a difference. We can’t put a solid number on that, but it’s hard to believe that it would be anything other than negative.

It’s not a stretch to assume that the effects of sleep deprivation, compared to a baseline fully-rested state, are somewhere in the neighborhood of 10 runs. It’s hard to pin an exact number on it, but the effect is not trivial. We all know what one-win players go for on the open market. It’s not likely that we’ll ever get most players to a fully rested state on a regular basis. There’s a lot of travel in baseball and it’s hard to sleep on planes and in hotels, but if we can claw back even some of those 10 runs, that’s nearly free value.

Now, how to do that …

Zen and the Art of Bicycle Maintenance

I was recently listening to an episode of the Freakonomics podcast in which they interviewed the head of the British cycling team. He talked about an interesting challenge faced by a couple of British cyclers as they did long races such as the Tour de France. Because those races take riders to a different town every day, sleeping accommodations are in whatever hotel the organizers book for the riders. More importantly, it meant a new mattress every night for the riders, and in a sport where physical recovery and rest are important, having to adjust to a new mattress meant not getting as much sleep as they could.

The solution: there was an advance team that carted the team’s personal mattresses from one town to the next and made sure that they were waiting for the riders at the hotel that night. That way, the riders could sleep in the same posture each night on a familiar mattress. That might not be scalable to baseball, but I love the innovative thinking. And the focus on sleep.

Perhaps the most scalable solution that’s been tried is good old caffeine. Red Bulls are cheaper than better infielders. And there is evidence that caffeine can attenuate some of the effects of sleep deprivation (again, measured by that same Psychomotor Vigilance Test), though the effects are relatively short-lived (caffeine has a short half-life in the body) and it doesn’t completely restore alertness to well-rested levels. In a strange way, that makes the clubhouse pop machine the 26th man on the roster. On Day 6 of a West Coast trip, it might be the most popular member of the roster.

But here’s a question: In the same way that we can always ask whether we can find a better backup catcher, we can also ask whether we can find someone else who can do the pop machine’s job better. Another solution that’s been tried to fight baseball fatigue is allowing players to nap when they can. If you can’t get seven hours at night, maybe you can catch a power nap during the day and repay some of that sleep debt. (Parents who have done the newborn thing know exactly what I’m talking about.) We even saw the Cubs earlier this year eschew batting practice in favor of letting their players rest up a bit more. Napping might seem intuitive (fighting sleep debt with sleep), but here’s one you might not have thought of: meditation.

In a small study (and as a good researcher, I should say twice that this was a very small study), a group of research participants did one of three activities: a 40-minute nap, 40 minutes of meditation, or 40 minutes of some other distractor activity. All of the volunteers participated in all three activities (on different days). What the researchers found was that when the volunteers took the PVT after meditating, their performance improved greatly, while after a nap it got worse.

Even more, the researchers did a second study in which they looked specifically at a separate group of people who practiced meditation (all of whom lived in India, where religions which incorporate meditation are much more prevalent than in the United States much in the same way religions which incorporate caffeine consumption are more prevalent in the United States) versus those who did not meditate, the group that meditated actually had PVT scores that were pretty good and they actually seemed to require less sleep at night.

Maybe teams should fire their pop machines and install meditation coaches in their place. Maybe if teams can’t do the mattress thing, they can have an employee whose entire job is to make sure that players all have their own pillows delivered to their rooms. I’ll make the case for one more crazy plan: the cult of the toothbrush. Telling a bunch of 20- and 30-something guys they need to go to bed on time might go over as well as when I tell my 7-year-old daughter that it’s time for bed. There does come a point where you have to allow that these people are adults. Especially my daughter.

But how to encourage them to get a good night of sleep, both in terms of getting them to decide to call it a night and in terms of helping them deal with the fact that it’s hard living on hotel mattresses. Classic social marketing techniques will tell you to always re-phrase something that you are telling someone they can’t do (“you can’t stay up any later”) into something that they should do. In this case, I’d encourage a team to encourage its players to brush their teeth. Aside from the obvious dental benefits, consider that brushing your teeth is also the first step in a cultural script.

Most people have a pre-bedtime ritual, and while different people have different things that make up that ritual (hey, no judgments), I’ll bet that yours includes brushing your teeth at some point. It might be the leadoff or the (ahem) cleanup hitter of your lineup, but it’s probably in there. Psychologists who specialize in sleep problems often speak of a concept called “sleep hygiene.” Sleep doesn’t just begin when your head hits the pillow. It really begins in the half hour before you even lay down. That’s why people should (and do) have those pre-bed rituals. It’s a signal to the body to start shutting things down in preparation for sleep.

Encouraging players to brush their teeth is a bit of a nudge. There’s no sane way to enforce it and not everyone will actually do it, but it does prompt people to develop a pre-sleep ritual (or more likely, to retain the sleep routine that they have from home). Even if the bed isn’t the same, the steps that the body goes through prior to sleep can be the same, and that calming familiarity is one more clue for the body that it’s time to fall asleep. It might mean a little better sleep and a little better sleep means better players. And it has virtually no cost.

***

We are used to a sabermetrics in which we use increasingly exotic numerical models to discern some nugget of wisdom about which players have hidden value that no one knows about. But the end recommendation always boils down to “hope that the next Mike Trout happens to fall in your lap” or “sign players who [insert statistical oddity here].” The action piece is always something to do with swapping out players. Like we’re playing fantasy baseball. Or like we’re trading stocks. There’s always going to be a place for all that, but it’s not the only thing out there.

Here, I’d like to make an argument for a different approach. The math I did above is slap-dash at best. Maybe with the application of a little more StatCast data, I could make it stick a little better, but I’m not interested in third-decimal-place accuracy on this one. Lack of sleep is an issue in baseball, and the effects are non-trivial. If I can get to that point with some amount of confidence, I don’t care what the actual numbers are. When you’re researching behavioral and cultural questions, the interventions that usually go along with them have costs that are negligible and a lot of times there’s already research on the topic to fall back on. The rest is just figuring out how to implement it in a baseball team setting.

I’d propose that the trade of the Winter Meetings, the one that might have the biggest impact on a team, would be the trade of one pop machine for a meditation coach, a guy who looks after everyone’s pillow, and 25 toothbrushes to be named later. Maybe some of that works, maybe it doesn’t, but I’d argue it has about the same chance of “working” as any of the other trades that might be made in National Harbor.

So, I hope you all have a fun pillow fight. And please brush your teeth.

Thank you for reading

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LlarryA
11/08
The British cycling team you mention has got to by Team Sky, and I can really see them doing that. Now, it's a lot easier lugging 9 mattresses (fewer for some events) around than 25, but 25-50 pillows might be feasible. When I'm traveling, the pillows can be as much an effect as the mattress on getting comfortable (and could help someone who hasn't yet realized he marginally allergic to feather pillows...). Russell, I gotta say I love the way you look at these seemingly irrelevant conditions to see if they might be a way for a team to squeeze out that extra win or two.
brucegilsen
11/11
Another thing to consider that the effect of naps (and other tools) vary from person to person. For me, a nap is a lifesaver, and has been for the past 10 years. I go from feeling like someone has sucked the life out of me with a giant straw to being reinvigorated for hours. But I talk to people about this, and some people say a nap helps but others say they're useless for the rest of the day if they take one.