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Let’s have a debate about the DH. No, not that debate. The debate that a few American League teams are having as they gather around to eat turkey and cranberries. Should we sign (or trade for) a guy to be our full-time designated hitter?

In the past few years, there’s been a new strain in the philosophy of how teams approach the position. What was once a refuge for an older hitter who was now even beyond “defensive liability,” but who could still smack 30 home runs, is now seen as something different. Teams now speak of having the DH be something of a shelter for players to rotate through in order to get a “partial day off.” For example, teams might have four outfielders whom they plan to start on a regular basis. Three of them can start in the outfield and the fourth can be a DH. The theory goes that it keeps those four guys a little more fresh. When it comes time to play those pesky interleague games, a team isn’t carrying a guy who can’t really play in the field. They can also keep the DH spot open for a guy who gets hurt, but who can still hit, rather than have someone just kinda stuck in that lineup spot.

Is this a smart strategy? Should teams refrain from signing a full-time DH and go with some alternate plan?

Warning! Gory Mathematical Details Ahead!

So, obviously, the answer is going to start with “It depends.” If a team has a bunch of relatively healthy hitters and a fielding-impaired DH who takes the H part of his title seriously and is a threat to hit 50 home runs with a 1.100 OPS then, yeah, that’s just fine. We want to know what possible benefits there might be from using the DH as a timeshare.

First, we look at what the possible benefits are of hitters being able to take a “half day” off, serving only as the DH, rather than playing in the field. To test that, I looked for all plate appearances (2009-2013) in which a hitter started a game two days earlier in the field and was starting again today in the field. There were three possibilities for that intervening day. He could have started in the field (no day off scenario), he could have started at DH, or he could have had the day off (whether because he didn’t play or his team just had an off-day).

Per usual, I used the log-odds ratio method to control for the batter-pitcher matchup and calculated the expected odds of various events. Compared to players who played in the field on all three days, only the batters who had the day completely off (didn’t play) the day before showed a significant increase in their OBP the next day. The effect size was also rather small. There was evidence that hitters who DH the day before are more likely to single (and almost reaching significance at .073 were extra-base hits) than we might otherwise expect out of them, but this comes at the expense of walks. The singles and doubles are more valuable than the walks, but we’re talking about an effect size in the two-tenths of a percent range. One extra-base hit that otherwise would have been a walk every 500 PA, which is something like once a season. The singles show roughly the same effect size. If we say that using the timeshare DH method is worth upgrading two walks, one to a single, one to a double, for a team over the course of a season, then that might be worth half a run. Not half a win. Half a run. By the second day, there were no further significant effects.

OK, if rotating the DH occupant isn’t a big deal, then maybe there’s some other reason to use it? One possibility is that a team can use the DH spot to create a jerry-rigged mixed-position platoon. For example, a team might have a right-hand hitting third baseman and a left-hand hitting outfielder, whom they want to platoon and who both have some defensive chops. The team’s regular third baseman can DH on days when a lefty plays (and the platoon third baseman is in the lineup) and go back to third against righties. I’ve previously estimated that such a platoon is worth about half a win under ideal circumstances. Not bad, but certainly not the sort of thing to be making big strategic decisions about.

Some teams say they don’t want to clog up the DH spot with a dedicated DH (or if they have a regular DH, insist that he must be able to play the field in a pinch) because they fear that a hitter might get injured in such a way that he can’t field, but he could hit, and the team would like to have a spot available for just that occasion. I don’t know that there’s a way to estimate how likely this is, but let’s play it out.

Let’s say a team has a full-time DH who is not capable of playing in the field, and one of its regular position players sustains an injury that leaves him incapable of playing in the field, but does not affect his hitting. The team then decides which of the two men (the injured position player or the regular DH) is the better hitter and writes him in as the DH and sends a (presumed replacement level) backup out to play the injured guy’s defensive position. The net result after the injury is that a team is forced to downgrade from its DH to replacement level production. Let’s say that our injured regular is the better hitting option, but it really stings to lose the DH because he’s a 3-win DH!

But then, let’s say that a team has no full-time DH. They just rotate it around and everyone has a fielding position that they are capable of playing, so there’s some positional redundancy. One of the regulars gets hurt. In that case, if the ninth guy can play that position, then he goes out there, and the team plugs its next-best bench guy into the DH spot. If the ninth guy can’t play that spot (or play some other spot and push someone else around the diamond) then the team is faced with the same situation as above. They have to decide who the better hitter is at this moment, make him the DH, and then send some replacement level backup out there. The amount of risk that the floating DH role covers with respect to injury is going to be a function of how much positional flexibility the team really has.

And if you’re not careful here, you might miss the forest for the trees. The team with no full-time DH really is in a (slighty) better position in case of an injury to a regular; instead of sending out the best player it has at the injured player’s position, it might be able to get away with just promoting its best bench hitter to the DH spot. Might. Even over the course of a season, that might be worth a couple of runs. So, is structuring a roster around the thought that a specific type of injury might occur and hedging that to save a couple of runs worth it if it means forgoing a 3-win DH who will, more likely than not, be able to play all season? A 2-win DH? What he has to overcome to make up the difference in expected value for this very strange set of circumstances is not huge.

So, the fact that the DH spot in a manager’s lineup resembles a carousel actually has limited value. It’s not zero, but in terms of expected return, it’s very limited. Sure, it might make sense given a particular set of players on the roster, but it’s not worth choosing for its own sake.

The Real Reason Not To Have a Full-Time DH
If there’s very little value to the “No regular DH” approach in terms of value, then why do it? The answer, as it is with almost everything, is “follow the money.” Research by Matt Swartz shows that teams seem to pay more per win for a designated hitter than just about any position on the field. (Left field is the exception.) If a team wants to invest in a player, it’s likely that they can get a bigger bang for their buck by signing an actual position player. Designated hitters tend to specialize in talents that are still overvalued by the market (read: home runs), and are often older players who are a high risk to suffer a big injury. Even if not, they are, somewhat by definition, players with only one skill. If that skill starts to deteriorate, then what do they have left? DH’s are really bad bets when you think about it.

When a team announces that they are going with no regular DH, what they are likely saying is that they figure that they can better spend the money elsewhere. As an added bonus, they can pick up a couple of runs, if they are clever, from using the carousel DH. At that point, you might as well. But we need to see the carousel DH not as some strategic master-stroke, but as a passive response prompted by the fact that DHs have, in general, become bad bets in the market.

Thank you for reading

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Thanks. With the Blue Jays trading Adam Lind and having no obvious replacement, I was wondering if Alex Anthopoulos had some slick strategy we should know about.
While you analyzed the daily advantage of the "partial rest" advantage, you didn't analyze the seasonal effect of playing 140 games in the field plus 15 at DH vs. 155 in the field. I would be interested in knowing whether there is a positive effect overall to the occasional partial day off. Does it improve one's seasonal performance? Does it avoid the "Ripken effect", where the wear and tear of everyday play hurts you in August and September? Does it diminish the risk of injury by enabling key players to stay in the lineup when not 100% because they don't have to play the field? Some of these aren't really quantifiable - injuries that either didn't happen or are irrelevant to the activity are tricky to deal with. Still, there are multiple reasons why the ability to rest a regular while not also losing a high end bat could be useful.
Obviously, if you have David Ortiz, none of this is meaningful, but there are very few of his ilk.
Another thing that would interest me is the overall batting performance as DHs for these "irregular" DHs. Are their DH numbers worse than their numbers when in the field? What percentage of them are better or worse as DHs? That also has a part in the discussion.
I actually ran (but didn't report) the regular vs. irregular DHs. The small effect that a player gets from DHing yesterday is mostly driven by guys who play positions regularly.

The wear-and-tear/injuries question is harder to get at. A good reason to move someone to DH for a day or two is because he's hurt, but that also means that he's a bigger injury risk going forward. We might see that DHing once in a while is associated with a greater risk of serious injury, when the DHing is just an indicator, not the cause.