Why Did Dave Roberts Let Yu Darvish Hit?

A little later today, Jeff will have a post about the most amazing play we’ve seen all postseason: Yu Darvish drawing a bases-loaded walk — on four pitches — from Carl Edwards Jr. last night. How did a quality reliever throw four consecutive balls to a career AL pitcher who had zero intention of ever swinging? In the NLCS? For the defending champs?

But in this post, I’m going to ask a different question about that at-bat: why did we ever see it in the first place?

To set the stage: the Dodgers led 3-1 in the top of the sixth inning. The bases were loaded. There were two outs. The pitcher’s spot was due up. A base hit in that situation would almost certainly score two runs, giving the Dodgers a four-run lead with just four innings to go. A home run basically ends the game then and there.

But instead of sending Curtis Granderson up to face Edwards and attempt to build the lead, Roberts chose to stay with Darvish, who then drew the most improbable walk you’ll ever see against a pitcher with a 15% walk rate. The Dodgers’ rally continued.

It was a rally whose end Roberts had effectively conceded, though. Darvish is a career .129 hitter. AL pitchers — of which Darvish was an example until a few months ago — hit .116/.152/141 this year. The odds of a hit were minimal. In his postgame press conference, when asked about the decision, Roberts admitted that, even after seeing Darvish draw a walk to somewhat validate the decision, he had “to go into that at-bat not expecting to come away with a run right there.”

Roberts said he thought Darvish, who had thrown only 70 pitches to that point, could give him “more than an inning,” and he preferred the value of those extra outs to the increased probability of scoring. Is that a reasonable belief?

Bases loaded with two outs has a run expectancy of about .77 runs, a figure which is based on the types of batters who usually bat in those situations. Pitchers generally do not hit in those situations, so obviously, the run expectancy with a pitcher batting would be much lower. It’s not zero, as Darvish showed. A walk, hit batter, or wild pitch/passed ball can occur without any real input from the hitter. And Edwards isn’t exactly a guy with elite command, so those bad-pitch scenarios are more likely with him on the mound than the average pitcher.

And then there’s the chance of Darvish getting a hit or reaching on an error. Given that he does have one double and one home run in 34 career plate appearances, the chances of a bases-clearing extra-base hit have to be calculated in, as well. So even with something like an expected .150 OBP, the run expectancy with Darvish batting was probably somewhere in the range of .25 runs, or about half a run lower than what we’d think it might have been with Granderson at the plate.

How much better would Darvish have to be to trade half a run for a few extra outs? Well, Darvish has a career ERA of 3.42, which translates to giving up 0.38 runs per inning pitched. Adjusting for the third-time-through-the-order penalty, Darvish is closer to 0.45 runs per inning pitched for that sixth inning, but for this exercise, decimal-point precision isn’t that important. To get an equal run expectancy trade-off in the bottom of the sixth inning, Roberts would have had to replace Darvish with a pitcher who had a true-talent ERA of something like 8.00 to 8.50, which works out to 0.89 to 0.94 runs per inning.

The difference between the best and worst pitchers in baseball over an inning of work is still nowhere near the run-expectancy gap between even a decent major-league hitter and a pitcher batting in that situation. And, obviously, Roberts wasn’t choosing between the best and worst pitchers in the game; the guys he’s using as lower-leverage relievers in this series are Josh Fields, Ross Stripling, and Tony Watson. Those are solid bullpen arms, and it’s not even clear that they would have been likely to give up any more runs in the sixth or seventh inning than Darvish was facing the Cubs for a third time in the game.

So, strictly from a run-expectancy standpoint, the decision is pretty indefensible. The team gave up significantly more in expected offense than they gained in expected defense. It’s not even close.

But run expectancy isn’t really what Roberts was considering when he made that call, and we do have to account for the factors that may have driven his decision. The fact that the Dodgers already had a 2-0 series lead and had roughly a 75% chance of winning Game 3 even if Darvish made an out, meant that the Dodgers chances of winning the NLCS were already above 90% at that point. Roberts isn’t just managing that situation to maximize his chances of winning this particular game. He has to consider what bullpen usage now might mean for his team the next two games and, potentially, in the World Series.

Given that it was a 3-1 game when he made the decision, he likely expected to close out the game with some combination of Brandon Morrow, Kenta Maeda, and Kenley Jansen. If he pinch-hit for Darvish, one of those guys would be working multiple innings and might have very limited availability in Game 4. By letting Darvish pitch the sixth and get the first out of the seventh, he was only asking his bullpen for eight outs. That could have significant benefits for the remainder of the series.

And, again, the series win probability was already over 90% at that point. Roberts has the luxury of managing a bit conservatively, knowing that his team is in a good position to advance to the World Series already, and that there’s some reward for saving some of these October pitches for the next round.

But all those defenses of letting Darvish hit pretty much went out the window by the way Roberts handled the bullpen for the final two innings. After Darvish and Watson combined to get the team through seven, the Dodgers added on two more runs to take a 6-1 lead to the bottom of the eighth inning. Their win probability, at that point, was 98%. Letting Darvish hit had worked, and now the Dodgers could save their best bullpen arms for the next two games.

Except Roberts handed the ball to Brandon Morrow to start the eighth inning, then warmed up Kenta Maeda behind him. With a five-run lead and six outs to go, Roberts still felt the game was too close to lean on his second-tier relievers. Morrow threw 22 pitches to get through a scoreless eighth, pushing the team’s win expectancy up to 99.4%.

So Roberts went to Ross Stripling for the ninth. Five-run lead, only need three outs. Yeah, these comebacks can happen, but the game was pretty safely in the bag for the Dodgers at that point. But Roberts still didn’t really think so, and had Kenley Jansen warming up behind Stripling. Two base hits later and Jansen was called on to get the final three outs and put the Dodgers up 3-0 in the series.

Despite getting the best of both worlds — pushing Darvish into the seventh inning and adding on three additional insurance runs — Roberts still asked Morrow and Jansen to throw 34 pitches between them, and warmed up Maeda to boot. He saved a few pitches for his best arms, but in the end, not really that many, and certainly not as many as they might have saved had Granderson put one in the gap and put them up 6-1 in the sixth inning.

If Roberts knew he was probably going to pitch Morrow and perhaps Jansen even if the team was already in a 99% win-probability situation, then almost the entire argument about saving the bullpen goes by the wayside. Maybe you got Jansen to throw 12 pitches instead of 20, but there wasn’t a lot gained here by having Darvish get those four extra outs.

Up 3-0 in the NLCS and still undefeated in the postseason, this isn’t something Roberts will spend any time second-guessing, most likely. Darvish showed that you can get a run even without pinch-hitting, and then he cruised through the next four outs with ease, putting the team in a situation where they are likely to wrap up the NLCS with plenty of time to rest all their relievers for the World Series.

But in case this situation comes up again, it might behoove one of the Dodgers’ horde of analysts to show Roberts the math on that decision, and point out that the team is far more likely to come out ahead long-term if he pinch-hits with the bases loaded than if he tries to squeak out a few extra outs from his starter.