Who is playing the percentages? What are the percentages?by Max Marchi
October 11, 2011
- You! Strawberry! Good effort today. Take a lap and hit the showers. I'm putting in a right-handed batter.
- Pinch-hitting for me?
- Yes. You're a left hander, and so is the pitcher. If I send up a right-handed batter, it's called playing the percentages. It's what smart managers do to win ball games.
- I've got nine home runs.
- You should be very proud. Sit down. Simpson! You're batting for Strawberry.
(Mr. Montgomery Burns and Darryl Strawberry, manager and right fielder, respectively, of the Springfield Nuclear Power Plant softball team.)
This article was inspired by this thread at The Book Blog, in which Mitchell Lichtman criticizes Tony La Russa's managerial choices—well, actually "criticizes" is quite an euphemism.
The question is: Your starter has breezed through eight innings and is due to bat. Your team is leading by one run. Do you pinch hit for him?
Tony La Russa did not. It was the do-or-die fifth game of the National League Division Series, Chris Carpenter had blanked the Phillies lineup and was going to lead off the bottom of the eighth.
According to Lichtman, a.k.a. MGL, going to a better hitter was a no-brainer according to the numbers. You can read his arguments and his own words in the original thread, but the following summary should be a reasonable approximation of his position.
You pinch hit because:
1. You get a better chance of producing in your offensive inning.
2. Since every pitcher gets worse as he goes through the opposing lineup time after time, a fresh closer is a better option than a starter going to face the same batters for the fourth time.
Here we'll expand a bit on point number two. Full disclosure: If I were managing in a deciding game and that situation occurred, I would NOT substitute for my starter.
Let's suppose we can visualize the distribution of baseball talent among people. It would probably be something like this.
The guys who actually play baseball should all be on the right end of the curve, with the major leaguers being on the extreme right part of the chart. Let's zoom in on that part of the chart and focus on pitching talent. Something like the following might be reasonable.
No deep analysis has been performed to place those names on the talent spectrum, thus the positions are absolutely debatable. However, let's suppose they're placed appropriately.
We have Justin Verlander and CC Sabathia as the elite pitchers; Carpenter as a good-to-great player (if we were to consider the 2005/2006 seasons, his name would have been more to the right). Ted Lilly, who according to FanGraphs is one win over replacement level, can be considered a legitimate major leaguer. Finally, Dontrelle Willis, who has been attempting comebacks year after year, has to stay in the baseball limbo where the so-called Quad-A players have to live.
Starter versus closer
Let's now try to visualize Carpenter's effectiveness as the game progresses and compare it with Jason Motte's effectiveness. Again, the placement of labels on the chart is complete (though a bit educated) guesswork on my part and might not reflect the real values.
1. Why is Motte's name in the above chart marked with an asterisk?
2. And why is Carpenter's effectiveness the fourth time through the lineup marked with the "§" sign?
If you compare Carpenter's and Motte's ERAs (3.45 and 2.25 in 2011, respectively), or their batting averages allowed, or other more or less advanced metrics, you might be tempted to say Motte is the better pitcher, but we all know that's not the case.
Motte enters the game in the ninth, so he does not face batters a second, third and fourth time through the game, when he is tired and the opponents have had the opportunity to time his pitches. Also, you have to consider that while Motte can put everything he has on every pitch, Carpenter has to pace himself if he wants to throw multiple innings.
Thus, the asterisk means: Yeah, Motte's average effectiveness (that is, his ability to prevent opponents from scoring runs) looks better than Carpenter's average effectiveness, but that's because he pitches in a different setting. So, in the second chart, Motte's name would be to the left of Carpenter's name, not to its right.
Also, if you look at OPS allowed, you would think Carpenter has some kind of resurgence late in the game.
situation OPS First time through the lineup .676 Second time through the lineup .745 Third time through the lineup .732 Fourth time through the lineup .682
Several pitchers show those kind of numbers. Does it mean that pitchers get some kind of energy injection when they see the finish line? No, you know better.
Starters are allowed to pitch deep into games on nights when they are performing well, but get the quick hook when they show "they don't have it." If you forced managers to leave pitchers on the mound until they have completed their fourth time through the lineup no matter of the score, you would not see those "resurgences."
(One can look at old-timers' numbers—back when pitchers were supposed to complete their games—to prove this. Don Newcombe is a good example (Baseball-Reference time-through-the-order stats). I have done a cursory look and found similar patterns for Bob Feller, Robin Roberts and Whitey Ford.)
Thus, the "§" means: We have taken care of the selection bias issue.
Summarizing this section: If we suppose I have correctly laid down the labels in the chart, it's better to have a fresh Motte out to the bullpen than having Carpenter facing the opposing team for the fourth time.
Good and bad days
The sentence closing the previous section is true on average, or if the players are robots always performing at the same level (same performance, same decline each time through the order, and so on).
But players, fortunately, are human beings—if you had some question about Verlander not being human, the postseason games played so far should have convinced you of the contrary—and human beings have good and bad days.
The chart above shows Carpenter's Game Scores throughout his career. Though we should expect Game Scores variation for robots as well (due to luck), it's safe to assume a significant portion of the variation in the chart is caused by Carpenter having good and bad days (due to health issues, psychological factors, luck...whatever).
Even in 2005 (shaded on the chart), his Cy Young season, Carpenter had a couple of extremely bad outings. It's very possible that on those occasions he threw as well as in any other start and simply had bad luck, but it's quite likely that he was not 100 percent: he might have not slept well the previous night, some minor ailment could have been affecting him, or he simply "didn't have it" that night.
The chart below should not be too unreasonable.
On his best days, Carpenter can be the best pitcher in the game, while on an awful night he will resemble a back-of-the-rotation pitcher.
What kind of Carpenter was on the mound in the NLDS Game Five?
That question is why teams can not be run by computers.
The average Motte facing the opposing lineup for the first time in the game is better than the average Carpenter facing that lineup for the fourth time.
I'm pretty sure La Russa knows this; otherwise, he would not have relievers in his bullpen. If La Russa decides to leave his ace on the mound for the ninth inning, it's because he believes Carpenter is having one of his best days. Thus, the chart in La Russa's mind should look like the following.
Note: Carpenter's first and second time through the lineup, in this scenario, are literally off the charts.
Carpenter on his best night is probably better the fourth time through the lineup than the average Motte coming out of the pen. Yeah, Motte might also be having the best night of his life, but there's a difference.
For Carpenter we have eight innings of blanking the mighty Phillies. Sure, it can be the usual Carpenter with a lot of luck on his side, but with eight goose eggs against a powerful lineup we are entitled to shift (if ever slightly) our a priori idea of Carpenter's effectiveness for the night. With Motte we don't have any clue, except what he and the bullpen catcher can tell us.
La Russa bets Carpenter is blessed with an inordinately great condition and that Motte is his usual self. Is that bet ill-advised?
Okay, time for some numbers.
I looked at games played in the past 20 years, thanks to the invaluable Retrosheet data. I selected all the instances in which the starting pitcher has completed eight innings giving up one run at most. These should be the circumstances when the manager can believe his starter "has it" and can complete the game.
I removed the games in which the offense had provided the pitcher more than three runs. Thus, we are dealing with situations in which the game is still on the line, and the manager should be trying to maximize his chances. (In a blowout the skipper's choices could be dictated by having to rest the bullpen or wanting to try a young arm.)
The games were then split in two groups: Games with the starter beginning the ninth (STARTER) and games with a reliever beginning the ninth (CLOSER).
Here's how the two groups fared, with more than 1,000 games represented in each group.
runs percentage allowed CLOSER STARTER 0 76 74 1 14 16 2 7 5 3 2 3 4+ 0 1
Looking at the numbers above, the decision on whether leaving the starter in or removing him appears as a coin flip. However, the above table can suffer from selection bias, with three possible sources of bias coming to my mind.
It's not a given that the quality of opposing lineups does not influence the choice of going (or not going) to the bullpen. I believe the quality of offense faced is equal between the two groups, but a check should be done.
On the contrary, I'm pretty sure that the talent of both the closer and of the starter play a role in the decision. If you have Mariano Rivera, you are more likely to give him the ball even when the starter has thrown eight frames of shutout ball, which has the effect of deflating the CLOSER numbers in the table above. But if the starter is a top-notch player (and this is true in many of the games we are analyzing) and the bullpen is not dependable, the manager will lean toward the slow hook, which should deflate the numbers in the STARTER column above.
So what are the percentages?
I would say you could flip a coin and make your decision. Tom Tango, performing different analyses, has arrived at a similar conclusion. And this is noteworthy. Many of us (I, for one) would have believed that leaving the starter is the only choice. Instead, calling in the closer is an equally sensible choice. And when you factor in the pitcher being due to the plate in the National League, it becomes even more sensible.
Giving Lichtman's post the title Worst managing ever surely attracts some extra clicks, but it also overstates reality, even when you add to the mix the highly-questionable bunt calls not analyzed in this article.
References and Resources
The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at 20 Sunset Road, Newark, DE 19711.
During the past few days, a lot has been said (and calculated) on this subject at The Book Blog and Baseball Think Factory . I must admit that, while I tried to follow all the relevant threads, I might have missed significant parts of the discussions while writing this article.
After creating a baseball rendition of The Beatles' Sgt. Pepper cover, Max began his baseball writing because he needed an excuse to show the picture. He wrote for an Italian audience for six years before making the jump to The Hardball Times. You can contact him by e-mail.