The Math on Letting Lance Lynn Hit

There were a bunch of turning points in Game 2 of the NLCS, including three late-game home runs that allowed the Cardinals to walk-off as winners. Yadier Molina‘s exit, due to a strained oblique, also looked like a big moment, especially when backup catcher Tony Cruz couldn’t handle Trevor Rosenthal’s game-tying wild pitch in the ninth inning. But, given the change in expected outcome, the biggest moment of the game might have actually occurred way back in the bottom of the fourth inning.

Already up 1-0, the Cardinals mounted a rally against Jake Peavy, with Matt Adams drawing a leadoff walk and Jhonny Peralta following with a single. Yadier Molina then laid down a bunt, which wouldn’t have made any sense if he was healthy, but it seems like he very well may not have been, which would help explain why he gave himself up to move the runners over. With first base open, the Royals easily decided to walk Kolten Wong, but then Randall Grichuk singled to drive in a run while also keeping the bases loaded.

At this point, the Cardinals had a 2-0 lead and three runners on with only one out. Their win probability had ballooned to 86%, in part because the run expectancy of a bases loaded/1 out situation is 1.5 runs, so while the Cardinals led only 2-0 at that point, the WPA graph was assuming that the inning would end with them either having a 3-0 or 4-0 lead, most likely. And that would make them overwhelming favorites to hang on and win.

However, Win Probability doesn’t know about which hitters are due up, or in this case, which pitcher is due up. Becasue Grichuk was hitting 8th, Lance Lynn was the next batter, and Lance Lynn is not a good hitter, even by the standards of a normal pitcher. 31 pitchers have hit at least 200 times over the last four years; of that group, Lynn’s .102 wOBA ranks 29th. His 49% strikeout rate is the highest of any of those 31 pitchers, and his .006 ISO is second worst. The only decent thing he can do at the plate is draw walks, as he’s somehow managed 11 of them despite a complete inability to do any damage with the bat. In the 195 plate appearances he’s had where he wasn’t walked, he reached just 11 times, an .056 OBP.

In other words, as long as Jake Peavy threw strikes, Lance Lynn was almost certainly going to make an out. And probably not even a run-scoring out. With the force play at home and the double play in order, any ground ball would probably lead to, at best, an out at home, and at worst, an inning-ending double play. Of the 59 non-bunt ball in plays he’s managed in his career, 39 of them — or 68% — have been hit on the ground. Of the 20 balls he’s managed to get in the air in his career, two of them didn’t even leave the infield. The odds of Lynn driving a fly ball deep enough to score a run were extremely thin, and the overwhelming likelihood was that either he was going to strike out or he was going to make an out that either forced all the runners to hold or hit into a double play.

As mentioned, the run expectancy in that situation was 1.5 runs; making one out cost the team 0.77 runs, while a double play would have erased the second half of that total as well. Of course, the out wasn’t actually guaranteed, so we have to calculate some probability that Lynn could have unexpectedly come through in order to find out the expected run value of letting him hit in that situation.

First, let’s deal with the walks. Lynn’s career 5.3% walk rate is actually not so bad, as mentioned, while Peavy has a career 7.3% walk rate, virtually tied with what he did this year. However, those are average walk rates in all situations, and with the bases loaded, Peavy’s career walk rate is just 4%. Not surprisingly, none of those six bases-loaded walks came with a pitcher at the plate. While it’s not impossible that Peavy would have lost the strike zone and issued four pitches out of the zone to Lynn, there isn’t much in the way of historical precedent for it. I think we can probably set the chance of a walk in that situation at somewhere around 1-2%, and given how rarely Peavy hits batters (just 74 out of 8,870), that doesn’t move the needle much either.

Now, for the chances of a hit. Lynn’s career average is .065, a little lower than the .096 mark pitchers have put up against Peavy over his career, which makes sense because Lynn is a terrible hitter even for a pitcher. But we probably shouldn’t even assume overall average production, since this is the situation where Peavy is least likely to just groove one to Lynn in order to keep his pitch count down.

In his career, Peavy had faced pitchers with the bases loaded 15 times; he gave up just one hit, recording 14 outs, seven of them by strikeout. Only one of the eight pitchers who put the bat on the ball managed to lift it into the outfield — Travis Wood, last year, when he hit a grand slam off Peavy — as Peavy was basically all strikeouts and groundballs in these situations. So, given Peavy’s extra incentive to get Lynn out, and Lynn’s own futility as a hitter, let’s assume a 5-6% chance of a hit.

We also have to account for the chances of an error by the Cardinals defense, since that would also get the run in. On the whole, the Giants defense had a .984 fielding percentage this year, exactly equal to the league average. In just over 4,000 bases loaded plate appearances in MLB this year, there were 43 reached on errors, so using a 1% chance of an error seems about right.

Finally, there’s the chance of a sacrifice fly. Lynn has hit one in his career, and Peavy has allowed one to a pitcher, so it’s not a zero probability outcome. It’s probably pretty close, though, given Lynn’s extreme K/GB tendencies. Again, Lynn has hit 18 air balls to the outfield in his 205 career plate appearances, and we’re already accounting for most of this in the probability of him getting a base hit, so there’s not much left here. But let’s give him another 2% chance of hitting a deep enough fly ball to score the runner from third.

Add it all up, and you’ve got about a 10% chance of scoring a run with Lynn at the plate in that situation, and of that 10%, some of the time the team would score multiple runs, either because Lynn shoots a gap or the Giants defense really screws up and boots the ball around. So, let’s estimate the run expectancy of Lynn hitting in that situation at around .15, and in situations where he manages to only make one out, the Cardinals still have Matt Carpenter hitting with a .73 run expectancy. That puts the net loss of having Lynn hit, versus having an average hitter at the plate, about .6 runs, and that’s without including the possibility of the double play. Add that in, and we’re closer to a .7 or .8 run difference in letting Lynn hit versus an average hitter.

Of course, one could argue that the Cardinals didn’t have any average hitters available to pinch-hit at that point. Oscar Taveras was the only pinch-hitter Mike Matheny used yesterday, and he was atrocious at the plate for the Cardinals this year, batting .239/.278/.312 in 248 plate appearances. The 2015 Steamer forecast — which includes his much better minor league numbers — for Taveras’ has him doing much better, but still only posting a 102 wRC+, and that’s without factoring in the pinch-hitting penalty. So, let’s assume that a pinch-hitting Taveras is a below average hitter, which pushes the net difference between he and Lynn back down to closer to .5 or .6 runs. Just to give Matheny the full benefit of the doubt, let’s call it .5 runs, since that makes the math easier too.

How much worse would the Cardinals relievers have to be relative to Lynn to justify punting a half run of offensive potential by letting him hit there? Well, it depends on much longer you’d expect Lynn to pitch, but let’s say that the goal was to get two more innings out of him, which would leave just three innings for the bullpen. Lynn had a great year this year, posting a 2.74 ERA, though his career mark is a less great 3.46. Let’s split the difference and say that Lynn is a true talent 3.10 ERA pitcher right now — dramatically better than Steamer’s 3.77 ERA projection, but that projection seems a little odd and is maybe a topic for another post — so he’d be expected to give up 0.7 runs over two innings pitched.

To balance out the half run loss of letting Lynn hit versus using Taveras, the Cardinals relievers would have to project to give up 1.2 runs over those two innings, which translates to a 5.40 ERA. That’s a far below replacement level performance, and is the kind of pitcher that no playoff team actually carries on their October roster. The Cardinals have plenty of good relief arms, and almost certainly could have increased their odds of winning yesterday’s game by pinch-hitting for Lynn and using their bullpen to cover the final five innings.

However, there’s a bit of a catch here. The two most likely pitchers to handle the 5th and 6th innings would have been Marco Gonzalez and Seth Maneess, but both were used fairly extensively the day before, with Gonzalez throwing 30 pitches and Maness throwing 19. With Michael Wacha being relegated to extra-inning duty, the Cardinals really only four relievers available for significant work last night, and one of them is an extreme platoon-split LOOGY. Is it fair to suggest that the Cardinals should have asked Carlos Martinez, Pat Neshek, and Trevor Rosenthal to get 12-15 outs between them in order to get Taveras at the plate in the bottom of the fourth inning?

Maybe. The math says it would have been a better option from the standpoint of winning Game 2. The potential for big hit there that could have essentially ended the game outweighs the marginal value of Lynn getting a half dozen more outs. And down 1-0 in the series, one could easily argue that Matheny’s sole focus should have been on winning yesterday’s game, and then he could figure out his bullpen usage for the rest of the series once that was accomplished.

But I don’t think we can shrug off the Cardinals relief situation entirely. Having just four relievers, one a specialist, to cover five innings isn’t a great situation, even with a significant lead, even with Wacha in reserve. The math strongly suggests hitting for your pitcher in that situation, but there is some value to be gained from not having to push Martinez, Neshek, and Rosenthal too hard in Game 2 of a seven game series. How much value we put on keeping their workload reduced is a matter of opinion, and it’s very difficult to think that the benefit is large enough to justify letting Lynn hit, but it’s at least another factor in the process.

Matheny, of course, would point to the fact that Lynn was pitching extremely well at the time, and very few -(if any) managers would remove a starter after four shutout innings. Of course, Lynn went on to show just how predictive being “on a roll” is, as he faced nine batters after hitting in the fourth inning, and gave up hits to four of them, recording just five outs and surrendering the lead in the process. But you’ve heard the times-through-the-order lecture from me enough lately, so I won’t say much more about this part of the decision.

Bottom line? Letting a pitcher hit with the bases loaded in a playoff game is almost never going to be a good idea. The best way to preserve a 2-0 lead is to make it a 3-0, 4-0, 5-0, or 6-0 lead, and managers put too much emphasis on trying to preserve small leads rather than being aggressive in situations that could make them much larger. Sending Taveras up to hit for Lynn would have likely improved the Cardinals chances of winning the game. But the team’s bullpen usage the day before was a legitimate extenuating factor, and Taveras was available to pinch-hit for the pitcher later in the game, so the gap is not as large as the simple run expectancy calculations might suggest.

Still, though, if that scenario comes up again, pinch-hitting is probably the better call. You’re better off protecting a bigger lead with even overworked relievers than you are trying to protect a small lead with a tiring starter.