November 3, 2015
How Much the DH Rule Matters
Every year during the World Series, we’re once again brought face-to-face with the strangest oddity in all of professional sports. The rules for the sport itself change based on where the game is being played. If the game is being played in one of the “American” League parks, the pitcher doesn’t have to bat, but is instead replaced by a player who is his “designated” replacement in the lineup. In one of the “National” League parks, the pitcher has to take his turn like any of his other eight friends. Oh sure, we all have our opinion on the #TeamDH vs. #TeamBadBaseball debate, but take a look back and consider how strange it would seem if the Eastern Conference in the NBA had a three-point line but the Western Conference did not. Can you even imagine #Team3Pointer vs. #AllCountTheSame Twitter wars?
But aside from which rule is better, there’s another question. There are several players on American League teams who are—how to put this?—“DH types.” Great bat. No glove. Seriously, some of them don’t actually own a glove. Take the Royals’ DH Kendrys Morales. Morales actually played nine games at first base in 2015, but he’s mostly there for his bat. He’s the type of player that an American League team can afford to roster (or, perhaps more accurately, is specifically incentivized to roster) because of the DH rule. But this past weekend, when the Royals played at Citi Field, Morales wasn’t in the starting lineup, because the Royals already had Eric Hosmer playing first base. It’s a big deal to take a bat like Morales’s out of the lineup. A lot of AL teams have to pay this penalty in the World Series (and during the regular season during interleague play).
On the other hand, when the National League champion New York Mets came to Kauffman Stadium, they started Kelly Johnson at DH in Game One and they moved Michael Conforto into the DH slot in Game Two, which allowed them to get Juan Legares’s glove into the lineup. In both cases, the “extra” bat that they pulled into the game hit ninth. The Mets didn’t have a classic DH type on their roster, but rather guys like Johnson who are reasonable pinch-hitting options, but who wouldn’t hold a candle to Morales’s production if given four plate appearances a night.
The AL team is hurt significantly in the NL park by the loss of its DH. The NL team just plays its usual lineup. The NL team is hurt by the DH rule in the sense that the AL team has a guy who is a hand-in-glove fit for the role already on their roster, while the NL team can only match it by playing a bench guy. We can see that there’s a penalty to be paid for playing under the other league’s rules, but that those penalties are ever-so-slightly different. Who gets the shorter end of the stick on this one?
Warning! Gory Mathematical Details Ahead!
This ends up being a much more difficult question than you might imagine. For starters, we need to remember that a team playing by the “other” league’s rules is, by definition, the road team, and one thing that we know for sure is that there is a home-field advantage in baseball. Using data from 2010-2014, we see that home teams scored and average of 4.30 runs per game while visitors scored 4.19. We also know that home teams win about 54 percent of the games played (In 2010-2014, 53.7 percent of games ended with the home fans cheering their conquering laundry) so we need to tiptoe a bit around that issue.
The other issue is that we can’t assume that American League and National League teams (as two giant undifferentiated masses) are equal to each other in their talent, and that makes things more difficult. If a National League team goes to an American League park, gains the DH, and scores 6 bazillion runs, was that the presence of the DH or was it the fact that the AL team didn’t have a good pitching staff?
Thankfully, we have a nice database of interleague games from which to draw to investigate the question. We do have a way of looking at the differences between the two league’s pitching staffs on even footing. I looked at all games in which an American League team was the home team, meaning that they were always using their comfortable DH-included lineup. I then looked at the number of runs they scored based on whether they were having a National League or an American League team over for dinner. I did the same for National League teams at home, who in that case were always using their #TeamBadBaseball lineup.
For now, we’re going to average those two effects and say that we expect AL offenses in this data set to do .195 runs better against NL pitching than we expect them to do against AL pitching.
When we look at American League teams playing on the road, when they go to an American League park, they score an average of 4.36 runs per game. So, we assume that if they went to an NL park, but there was a DH for some reason—such as common sense finally taking over—they would score 4.555 runs per game. In fact, without the DH, they actually score 4.10 runs per game, suggesting that the penalty of an American League team playing without the DH in its lineup is on the order of .455 runs(!) per game.
When a National League team goes on the road, but plays in a National League park, they score 4.06 runs per game playing without the DH. If they visited an American League park, but for some reason they weren’t using the DH that day, we would expect them to score 3.865 runs per game based on the league-to-league adjustment. But with the DH rule in place, because it’s an AL park, they score 3.97 runs, meaning that they clear an extra benefit of .105 runs. The DH is worth about three times more to the AL than to the NL, on average.
But let’s put some perspective on how big of an effect that is. The net swing in value is between the two DH effects is .35 runs, with the benefit going to the home team. We saw above that the difference between home and road teams in runs scored was .11 runs. The change in rules because of the DH is more than three times more important than home-field advantage.
So in an interleague game like the World Series (or just during the regular season, when we do geographical puns like the Marlins playing the Rays because—get it? They’re both from Florida!)—the home team not only has the home-field advantage, but the home-rules advantage. Sure enough, in games between teams from the same league in 2010-2014, the home team won 53.5 percent of the time. In interleague games, that number jumps to 55.5 percent.
It All Goes Back to the All-Star Game
None of this should surprise anyone. An AL team likely has to sacrifice one of its better hitters when it takes a walk in an NL park and give three of the four plate appearances that he would have gotten to a pitcher and one of the other guys on their bench. The NL gets to “upgrade” from a pitcher to a competent major-league hitter—but still a bench player—for the whole game (figure the stand-in “DH” would have gotten a pinch hitting appearance anyway). We should expect the effect to be greater for the AL.
Even if the numbers for the DH effect seem a bit on the high side, cut the effect in half and it still trumps home-field advantage. At the All-Star game, when they say that “It Counts” for home-field advantage, the actual advantage being conferred in the World Series is not the ability to use your home ballpark but to use the rules that you’ve designed your roster around, although teams get both.
Last year, I calculated that the team that, assuming two World Series teams of equal strength, the team that held the home-field advantage would win the series 52 percent of the time. When I calculated those odds, I was assuming just a standard (54 percent) home-field advantage. It seems that interleague games are even more tilted than I had assumed, making home-field advantage even more valuable. So next year when Ned Yost and Terry Collins meet again in PETCO Park for the 2016 All-Star game, they may do more to determine the outcome of the 2016 World Series than they might imagine, even if neither of their teams manages to get there.