Postseason Rotations and Matching Up Aces

Last year Clayton Kershaw had an absolutely dominating season, which culminated in him winning both the NL Cy Young and MVP awards. When the playoffs started, I remember feeling a little bad for the Cardinals, who were facing the possibility of having to face Kershaw twice within the five-game NLDS. Of course, the Cardinals defied the odds by defeating Kershaw twice en route to winning the series, showing that anything is possible in a short series. I wonder, though, if they couldn’t have improved their odds of winning the series had they matched up their starters a bit differently.

In a five-game Division Series, most managers start their ace in Game 1, assuming that he is available to pitch on regular rest. That will optimize a club’s chances of winning Game 1. However, I’ve wondered if that does not necessarily optimize that same club’s chances of winning the series. Would a team be able to, under some circumstances, optimize its chances of winning the series by using their #2 starter in Game 1, and starting the ace in Game 2?

Regardless of what strategy you choose, you always want your ace to start twice in the LDS. Thanks to the schedule format, it is possible to start your ace in Game 2, and have him come back on normal four-day rest to pitch a potential Game 5. In that sense, by starting your ace in Game 2 instead of Game 1, you are in no worse position for the remaining games. My thinking was that Clayton Kershaw was so good in 2014, that even if you start your own ace against him in Game 1, you are still likely to lose that particular game. Therefore, it may make more sense to save your ace for Game 2, in order to maximize your odds of winning Game 2, and the series overall.

The idea isn’t entirely novel. Writing for The Hardball Times last October, Dan Meyer proposed the use of a staggered division-series rotation. The key difference is that Meyer proposes staggering all the pitching match-ups, and does not factor in bringing the ace back to pitch again in Game 5, after pitching Game 2.

Let me outline my model and analysis, along with assumptions that I make:

  • Assume a typical five-game ALDS or NLDS schedule spread over 7 days:

ALDS/NLDS Schedule
Day Scenario
1 Play Game 1
2 Play Game 2
3 Travel day
4 Play Game 3
5 Play Game 4 (if necessary)
6 Travel day (if necessary)
7 Play Game 5 (if necessary)
  • Focus only on the starting pitching assignments for Games 1 and 2. The starters for Games 3, 4, and 5 remain the same as they would have been before.
  • Assume the opposing team’s manager will start his team’s ace in Game 1, and his number-two in Game 2.
  • Assume that both team’s aces will start a potential Game 5.

Now, there are three possible outcomes for Games 1 and 2 combined:

  • Your team wins both games
  • Your team splits the two games
  • Your team loses both games

Ideally you want your team to win both games, but if that does not happen, you at least want to split the games. You definitely want to avoid losing both games.

The probability of each outcome and expected wins follows:

P(win both games) = P(win Game 1) * P(win Game 2)

P(split) = P(win Game 1) * P(lose Game 2) + P(lose Game 1) * P(win Game 2)

P(lose both games) = P(lose Game 1) * P(lose Game 2)

Expected wins = 2*P(win both games) + P(split)

Similarly to Meyer’s effort in The Hardball Times, we will define the probability of winning and losing a game in terms of the regular season ERA- of the one team’s starting pitcher and the other team’s starting pitcher, and using the Pythagorean expectation formula with the 1.83 exponent. There are certainly many other factors in play, but we are choosing to do this in order to keep the model simple.

P(win) = (Opponent starting pitcher’s ERA-) ^ 1.83 / [(Your starting pitcher’s ERA-) ^ 1.83 + (Opponent starting pitcher’s ERA-) ^ 1.83]

P(lose) = (Your starting pitcher’s ERA-) ^ 1.83 / [(Your starting pitcher’s ERA-) ^ 1.83 + (Opponent starting pitcher’s ERA-) ^ 1.83]

Now let’s put some numbers into context. These are the 2014 regular season stats of Clayton Kershaw (Dodgers’ ace), Zack Greinke (Dodgers’ number-two), Adam Wainwright (Cardinals’ ace), and Lance Lynn (Cardinals’ number-two):

2014 Regular Season Stats
Clayton Kershaw 21-3 50
Zack Greinke 17-8 77
Adam Wainwright 20-9 66
Lance Lynn 15-10 76

Here are the calculated probabilities and expected wins under the conventional strategy (start Wainwright in Game 1), and the alternative “save the ace” strategy (save Wainwright for Game 2):

Calculated Probabilities and Expected Wins
Win Game 1 Win Game 2 Win both games Split Lose both games Expected Wins
Conventional 37.6% 50.6% 19.0% 50.1% 30.9% .881
Alternative 31.7% 57.0% 18.1% 52.6% 29.3% .888
Delta -5.9% +6.4% -0.9% +2.5% -1.6% +.007

Ultimately, the Cardinals would be increasing their expected wins by .007 over the first two games. This is a nice improvement, although it is safe to say that this difference is likely not statistically significant.

Of course, that’s just based on the assumption that single season ERA is a good proxy for a pitcher’s true talent level. Given what we know about sample sizes and the variances of ERA, that’s not a great assumption, so let’s look at the same calculations, but using three years of data instead of just one, which will help smooth out some of the noise.

2012-2014 Regular Season Stats
Clayton Kershaw 51-21 56
Zack Greinke 47-17 80
Adam Wainwright 53-31 82
Lance Lynn 48-27 94

Calculated Probabilities and Expected Wins
Win Game 1 Win Game 2 Win both games Split Lose both games Expected Wins
Conventional 33.2%
42.7% 14.2% 47.5% 38.3% .759
Alternative 27.9%
48.9% 13.6% 49.6% 36.8% .768
Delta  -5.3%
+6.2% -0.6% +2.1% -1.5% +.009

In this set of data, the Cardinals’ pitchers score a lot lower, while the Dodgers’ pitchers score only slightly lower, thus resulting in lower expected wins for the Cardinals.  However, the change in expected wins is about the same at .009.

Let’s do another analysis. In 2011, the Yankees faced Justin Verlander and the Tigers in the ALDS. Like Kershaw in 2014, Verlander had a dominant season in 2011, winning both the AL Cy Young and MVP. Here are the stats for Justin Verlander (Tigers’ ace), Doug Fister (Tigers’ number-two), CC Sabathia (Yankees’ ace), and Ivan Nova (Yankees’ number-two).  In the actual series, there was a rain suspension in the second inning of Game 1, which reshuffled the rotation for both teams. Here, we are assuming that there was no suspension and the starters all made their planned starts.

 2014 Regular Season Stats
Justin Verlander 24-5 58
Doug Fister 11-13 73
CC Sabathia 19-8 71
Ivan Nova 16-4 88

Calculated Probabilities and Expected Wins
Win Game 1 Win Game 2 Win both games Split Lose both games Expected Wins
Conventional 40.9% 41.5% 17.0% 48.5% 34.5% .825
Alternative 31.8% 51.3% 16.3% 50.4% 33.3% .830
Delta -9.1% +9.8% -.7% +1.9% -1.2% +.005

2012-2014 Regular Season Stats
Justin Verlander 61-23 71
Doug Fister 20-31 89
CC Sabathia 59-23 73
Ivan Nova 17-6 92

Calculated Probabilities and Expected Wins
Win Game 1 Win Game 2 Win both games Split Lose both games Expected Wins
Conventional 48.7%
48.4 23.6% 49.9% 26.5% .971
Alternative 38.4%
59.0% 22.7% 52.1% 25.2% .975
Delta -10.3%
+10.6% -0.9% +2.2% -1.3% +.004

Under both metrics, we see smaller changes in expected wins compared to the previous case. Like the previous case, these changes do not seem to be statistically significant.

One interesting consequence of using the “save the ace” strategy is that had the Yankees started Ivan Nova in Game 1, then CC Sabathia would have come on in relief after the game resumed the next day, thus becoming the de facto starter since he would presumably have pitched the majority of the game. Then Sabathia would have been able to come back on normal rest to start Game 5, thus giving the Yankees the maximum utilization of their ace.

How might this strategy apply in this year’s playoffs? If the regular season ended today, the Mets would draw the Dodgers in the NLDS. While Clayton Kershaw is having a very good season, this year it is Zack Greinke that is having the more dominating season, and assuming the title of ace. The top Mets’ pitchers are Jacob deGrom and Matt Harvey. Here are the stats for the relevant pitchers, with the evaluation of the strategies. For the single-season analysis, we treat Greinke as the Dodgers’ ace, while for the three-season analysis, we treat Kershaw as the Dodgers’ ace.

 2015 Regular Season Stats (as of 9/18/15)
Zack Greinke 18-3 43
Clayton Kershaw 14-6 57
Jacob deGrom 13-8 71
Matt Harvey 12-7 78

 Calculated Probabilities and Expected Wins
Win Game 1 Win Game 2 Win both games Split Lose both games Expected Wins
Conventional 28.5% 36.0% 10.3% 44.0% 45.7% .646
Alternative 25.2% 40.1% 10.1% 45.1% 44.8% .653
Delta -3.3% +4.1% -0.2% +1.1% -0.9% +.007

2013-2015 Regular Season Stats (as of 9/18/15)
Zack Greinke 49-15 64
Clayton Kershaw 51-18 53
Jacob deGrom 22-14 74
Matt Harvey 21-12 71

Calculated Probabilities and Expected Wins
Win Game 1 Win Game 2 Win both games Split Lose both games Expected Wins
Conventional 36.9%
43.4% 16.0% 48.3% 35.7% .803
Alternative 35.2%
45.3% 15.9% 48.7% 35.4% .805
Delta -1.7%
+1.9% -0.1% +0.4% -0.3% +.002

Perhaps not surprisingly, we once again get slight increases in expected wins, but results that are probably not statistically significant.

In the end, it looks like playing the match-ups doesn’t really end up mattering that much; you give up roughly the same probability of winning Game 1 as you gain in Game 2, and there isn’t a big advantage to be gained by holding back your ace so that he doesn’t face the other team’s ace in the opening game. Add in the potential for a rain delay or some other cancellation forcing Game 2 to be pushed back a day and eliminating the chance for your ace to pitch on normal rest in Game 5, and it appears that this strategy probably isn’t worth pursuing. Throw your ace in Game 1 and hope you can beat the other team’s best pitcher.


(Note: Post was edited to fix a mathematical error in the Tigers vs. Yankees analysis)

Roger works as a software engineer by day, writes for The Hardball Times and FanGraphs by night, and has also worked for a Major League club.

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Aaron (UK)
6 years ago

It’s not really a question of statistical significance: given your model, the gains are real, if small.

One additional minor factor would be in working out how this might affect the rotation in the next round.

L. Ron Hoyabembe
6 years ago
Reply to  Aaron (UK)

The gains might not be statistically significant if they are smaller than the error associated with the Pythagorean expectation formula.