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The Cardinals and Phillies are playing the last game of their Division Series tomorrow, with each team’s ace (Chris Carpenter and Roy Halladay) taking the mound. The game—and thus the series—may very well be settled by which team’s ace pitches better. But it might just come down to which team’s manager has the audacity to sit his ace down on the bench.

One game this series has already been strongly influenced by a decision to pinch-hit (or not) by each manager—Cardinals starter Jaime Garcia struck out with runners on first and second to end the sixth inning in Game Three, then stayed in to allow a three-run homer to Phillies pinch-hitter Ben Francisco in the seventh.

The trouble with pinch-hitting for your starter is that it forces you to go to your relievers early, and often that means bringing in the middle- or back-end of your bullpen rather than your top relievers. But this is an elimination game, meaning that both managers should be managing to win this one game without worrying about tomorrow. A team’s best relief options (including starters from earlier in the series) should be available if necessary, so a creative and determined manager should be able to find more quality bullpen innings than he would in an ordinary game.

So how can we identify situations in which a manager should be most willing to turn to a pinch-hitter? We can look at something called run expectancy, which examines the average number of runs scored in the rest of the inning, given how many runners are on base, which bases they occupy, and how many outs there are. I’ve provided two run expectancy tables side-by-side—one in which a pitcher bats in that plate appearance, and one in which a pinch-hitter bats in that plate appearance. Looking at historic data from 1993 through 2011:

RUNNERS

OUTS

RE_PIT

RE_PH

DIFF

___

0

0.50

0.49

0.00

___

1

0.21

0.25

0.04

___

2

0.05

0.09

0.04

1__

0

0.79

0.84

0.05

1__

1

0.38

0.50

0.12

1__

2

0.12

0.19

0.07

_2_

0

1.02

1.13

0.11

_2_

1

0.56

0.64

0.08

_2_

2

0.18

0.28

0.09

12_

0

1.46

1.40

-0.06

12_

1

0.69

0.87

0.18

12_

2

0.24

0.43

0.19

__3

0

1.34

1.39

0.06

__3

1

0.75

0.93

0.18

__3

2

0.22

0.35

0.14

1_3

0

1.57

1.74

0.17

1_3

1

0.86

1.10

0.24

1_3

2

0.26

0.44

0.18

_23

0

1.77

1.96

0.19

_23

1

1.10

1.34

0.24

_23

2

0.28

0.57

0.29

123

0

2.04

2.32

0.28

123

1

1.20

1.51

0.32

123

2

0.42

0.79

0.3

Speaking broadly, the situations where a pinch-hitter offers the most bang for the buck come with multiple runners on and at least one out. Especially with two outs, a key offensive weapon for the pitcher (the sacrifice bunt, or any other out in play that would advance the runners) has been removed, making the pitcher even more offensively challenged than he would be normally. In the situation that led to the Garcia strikeout earlier in the series, a typical pinch-hitter would be expected to score .19 more runs on average than the pitcher would if allowed to bat, basically doubling the expected number of runs.

Another way we can look at it is to assess a team’s chances of scoring at least one run. In the situation Garcia faced, a team scores at least one run 13 percent of the time when the pitcher bats, compared to 22 percent when the team utilizes a pinch-hitter.

How does that compare to what we would expect from the starter who stays in to pitch the following inning, relative to a reliever? When the starting pitcher goes out to pitch the seventh inning, his team will allow at least one run 29 percent of the time, while if the inning is started by a reliever the team will allow at least one run 28 percent of the time. It can be noted that Garcia is an above-average pitcher and had been pitching well so far, but that’s going to be true of starters who reach the seventh inning far more often than if we simply looked at all innings. Moreover, even when looking at starters who are pitching well enough to make it to the seventh inning, we see that a fresh reliever has a slightly better chance of having a scoreless inning than a starter who has already worked his way through the lineup two-three times.

It was unlikely that the Cardinals would push a run across in that situation no matter what Tony La Russa did, but it was nearly twice as likely had he put in a pinch-hitter instead of letting Garcia bat for himself. In addition to robbing the Cardinals of an extra chance to score runs, it’s possible that he may have increased his team’s odds of surrendering more runs the following inning as well. It would be unfair to assume that La Russa cost his team the game by leaving Garcia in—it doesn’t always work out the way it did there. But it is an advantage that a manager can’t afford to deny his team in a must-win game, even with his ace on the mound.

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ahaning17
10/06
The game is tomorrow (October 7th).
cwyers
10/06
I didn't realize which day this piece was running, so I screwed that up. Sorry, it's fixed now.
Ogremace
10/06
I can't wait till a manager has a run expectancy chart in the dugout. I mean, aside from split stats and scouting reports, I can't imagine information i'd rather have.
BillJohnson
10/06
In the dugout? TLR has it in his head. Problem is, he treats it just like he treats the voices.
bflaff1
10/06
Hard to see CM pulling Halladay from Game 5 unless the squirrel chews his right arm off.
kmbart
10/07
If the St. Louie squirrel shows up tomorrow at the Bank Park, MLB should investigate the Cardinal organization for transporting feral rodents across state lines for immoral purposes. Old Chollie should have his shootin' iron at the ready though, with some buckshot wadded up in the barrel.
mdangelfan
10/07
If the game is tied or the Phillies are losing 6th inning or later, Halladay should be PH for. Phillies have another ace who is rested, Lee. Halladay for 5-6, Lee for 1-2, and Madson for 1-2 ensures that Phillies will have a top notch starter on the mound throughout, and allows them two pinch hitters.
doctawojo
10/07
Cliff Lee is shaking his fist at you, Colin: "I'll show you who the ace is."
lichtman
10/07
Colin, great stuff. Minor point: The numbers are apples and oranges, of course, because the pool of pitchers faced, and other "environmental" factors, are going to be different (e.g., when the pitcher bats, he is likely facing the opponent pitcher early in the game, whereas when a pinch hitter bats, he is likely facing a reliever late in the game), but your point is well taken and clearly explained. The two points are, one, you give up a substantial RE/WE letting your pitcher bat late in (or even in the middle of) a game in a high leverage situation (the LI was 2.51 in this game), and two, you likely don't even save/gain anything by allowing your starter to remain in the game, especially when you have lots of good reliever options (as in the post-season) and you don't have to worry about taxing your bullpen. My rule has always been this: Always pinch hit for your starter after the 5th inning in a high leverage situation (the high leverage takes care of the fact that the game is likely close and there are likely runners on base) unless your starter is elite (like a Halliday or Lee), and even then, still pinch hit if the inning is past the 6th or 7th, unless a sac bunt is a viable option, such as you are down a run, up a run, or the game is tied, and there is a runner on first or second with 0 out.
FredOwens
10/07
All of this assumes incorrectly that the pitcher in the bullpen is an equal or better option than the one in the game. If LaRussa had anyone he trusted more than Garcia down there that he was willing to insert that early old change pitcher every time you inhale Tony would have done that. Starters send to the pen for post season don't perform as their in year numbers indicate for many reasons. The relievers down Tony's pen have all failed him at one time or another all year. If instead he had a trusted cadre or arms that performed well in relief that plan works. But, Tony has too LOOGY's 2 closers he picks based on match up both short men, Boggs who has been wild as a march hare lately and Dotel. Tony obviously believed Garcia who had had Philly pretty well in his grasp to that point was a better option. In his mind the chance of scoring there was less that the chance the Phillies would get that back and more off a reliever. It's true that Garcia gave up the homer but hindsight is 20/20. If he Francisco's hit is simply a fly out, he pitches a scoreless 7th, Cards win 2-0 and Tony's a genius.
noonan
10/07
The top relief options in the Cardinals pen are certainly better than Garcia for a couple of reasons: 1) Starters are significantly worse each successive time through the order 2) The average pitcher shaves a run of his ERA when pitching in relief. The true talent level of the top Cardinals relievers is unlikely to be more than a run worse than Garcia.