The Math Behind Pulling Nathan Eovaldi

Nathan Eovaldi had it all working. Through his first five innings of work, he had a spectacular game brewing: seven strikeouts, two hits, no walks, and no runs. The Red Sox were already ahead 3–0. Everything was coming up Boston.

After a strikeout to begin the sixth inning, Eovaldi faced the top of the Yankees’ order. Suddenly, things got tough. Anthony Rizzo clobbered a home run. Aaron Judge followed with an infield single, narrowly beating out a throw from Xander Bogaerts. Suddenly, the tying run was at the plate — and it was freaking Giancarlo Stanton, who had already doinked a ball off of the Green Monster earlier in the night.

Ten years ago, that would be the introduction to an article about one of two things: either Eovaldi’s heroic stand where he faced down his doom and retired Stanton and Joey Gallo, or the Yankees’ dramatic comeback from a 3-0 deficit. But last night, Alex Cora went to the bullpen.

It wasn’t a pitch count issue, to say the least. Eovaldi had thrown only 71 pitches, carving through the New York lineup with great speed. It wasn’t a handedness issue; Cora went with a righty to replace him. It wasn’t even a homer-proneness issue, a handy thing to keep an eye on when the tying run stands at the plate: Eovaldi induces more grounders than does Ryan Brasier, the pitcher who replaced him, and has allowed fewer home runs per inning pitched, both in 2021 and his career.

This substitution was squarely in the times-through-the-order camp. Rizzo and Judge were the first two Yankees that Eovaldi faced a third time, and the stakes had gone up since those at-bats. When Rizzo strode to the plate, the game’s leverage index stood at 0.66; the results of that plate appearance, on average, would change the two teams’ odds of prevailing by less than a random plate appearance. After the home run, Judge stepped up with a 0.89 LI — again, less impactful than a random plate appearance. After he reached base, though, Stanton’s at-bat ballooned to 1.65, nearly twice as important as the average batter-pitcher confrontation.

In other words, this one really mattered. Against Rizzo, the payoff to choosing the best possible pitcher for the spot was low. Against Judge, that was still mostly true. Raise the stakes, and Cora suddenly made a move. Given that backdrop, it’s reasonable to speculate that he thought Brasier was a better bet to get the next out all along but wanted to give Eovaldi some extra rope, with an eye on preserving the bullpen, if the lead wasn’t huge.

Was Brasier actually a better bet? It comes down to how much of a penalty you think Eovaldi faced. There’s essentially no dispute that the penalty exists: Rob Mains tracked it through time earlier this year and found that it’s always been there, and potentially to a greater magnitude than today. What magnitude, exactly? The most authoritative look at the subject puts that penalty at roughly eight points of wOBA. Conveniently, it also splits pitchers into high-pitch-count and low-pitch-count groups and finds no difference, which means we can mostly ignore the fact that Eovaldi had been efficient through his first five innings.

That gives us a first pass at the stakes of the move: Eovaldi allowed a .298 wOBA to all batters this year; Brasier checked in at .319. This suggests that Eovaldi would still be the better choice. Cut and dry, right?

Unsurprisingly, I don’t think it quite works that way. A few factors combine to make the decision tougher. First, one that might have mattered, though I don’t think it should: Eovaldi has displayed a large times-through-the-order penalty in 2021 — 41 points of wOBA the third time through. That’s exaggerated by facing the toughest part of lineups disproportionately often in that context, but still, that’s a big gap, and it’s cavernous over the course of his career: 65 points of wOBA.

I’m skeptical how much that matters. Splits like this take a notoriously long time to become reliable. For example, hitters have a .359 BABIP their third time facing Eovaldi, compared to .300 and .288 the first two times through. They’ve turned 8% of their infield grounders into hits, as compared to 4.6% the first time and 6.9% the second time. Maybe he’s been worse, but it’s far from clear that you should expect this extra-large gap to continue.

Another point in favor of Eovaldi: he throws five pitches and varies his timing, as you no doubt heard on the broadcast last night. To the extent that the TTOP is about familiarity, you’d expect those factors to give him an edge. I haven’t seen much evidence that a broad pitch mix alleviates a pitcher’s disadvantage, but to the extent that it matters for Eovaldi, it’s to his credit, not detriment.

The reason to remove him comes down to one of two things: the identity of the next batter, and a specific home run penalty based on times through the order. Stanton is a great fastball hitter, but more than that, he’s a low fastball hitter. Eovaldi locates his fastball all around the zone; Brasier is a four-seam, top-of-the-zone type pitcher. Could this matter?

I’m again skeptical for several reasons. First, while Stanton is a good low-ball hitter by repute, he’s also just a good hitter. Since 2015, he has a .551 wOBA when he puts a low fastball into play, but also .548 on mid-height fastballs and .450 on high ones. He’s simply a punishing slugger to any part of the zone. Second, Brasier isn’t better than Eovaldi at avoiding the dangerous parts; 26.4% of the pitches he’s thrown this year have been fastballs in the lower two-thirds of the strike zone, Stanton’s launching pad, compared to  21.5% for Eovaldi. If we’re worried about batter identity in particular, that probably favors Eovaldi rather than the other way around.

One last look: Do starters give up extra home runs their third time through? To check, I looked at home run rates for starting pitchers each time through the order and calculated an expected home run rate for each plate appearance based on the pitcher’s and batter’s 2021 numbers and regressed platoon splits. Then I looked to see how many home runs were actually hit in those appearances:

If you want to get very granular, I suppose you could point to this. A huge chunk of that third-time penalty comes in the form of extra home runs; if an extra 0.4% of random plate appearances turned into home runs, average wOBA would go up by seven points, close to the eight-point penalty cited above. In a spot where a home run is the worst possible outcome and one of the best home run hitters in the game is at the plate, I can see why the Red Sox opted to fight that penalty.

I wouldn’t have done it with Brasier, though. The Red Sox have other, better relievers. He’s more middle reliever than high-leverage arm, and I think that any of the other relievers Boston used in the game would have been a better option. I also think leaving Eovaldi in would have been a better option; even the third time through, I like his odds of suppressing hard contact better than Brasier’s.

In the end, Brasier got an out, albeit when Stanton smashed a laser beam so hard off of the Monster that Judge was thrown out at the plate. It was a 115-mph, 400-foot missile, and it more or less sealed the game.

Was Cora right or wrong? I don’t think it’s so cut and dry. Leaving Eovaldi in or removing him was a move that would only fractionally change their odds of winning. Cora pulled him; were I managing the Sox, I’d have left him in. Neither of us, though, would have wanted Stanton to make the hardest contact of the game, and elevate it no less. That’s why arguing about managerial moves is so fun and yet so inconsequential in the final accounting of things: we’re arguing over single-digit moves in wOBA or fractions of a percentage point of home run rate, while baseball is played on the field and strange outcomes happen all the time.

Was it a good move? I think not. But it was pretty close to a neutral move, and it’s notable that baseball has moved so far toward pulling starters early that teams now might be doing it too often.