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:
| 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):
| W-L | ERA- | |
| 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):
| 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.
| W-L | ERA- | |
| Clayton Kershaw | 51-21 | 56 |
| Zack Greinke | 47-17 | 80 |
| Adam Wainwright | 53-31 | 82 |
| Lance Lynn | 48-27 | 94 |
| 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.
| W-L | ERA- | |
| Justin Verlander | 24-5 | 58 |
| Doug Fister | 11-13 | 73 |
| CC Sabathia | 19-8 | 71 |
| Ivan Nova | 16-4 | 88 |
| 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 |
| W-L | ERA- | |
| Justin Verlander | 61-23 | 71 |
| Doug Fister | 20-31 | 89 |
| CC Sabathia | 59-23 | 73 |
| Ivan Nova | 17-6 | 92 |
| 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.
| W-L | ERA- | |
| Zack Greinke | 18-3 | 43 |
| Clayton Kershaw | 14-6 | 57 |
| Jacob deGrom | 13-8 | 71 |
| Matt Harvey | 12-7 | 78 |
| 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 |
| W-L | ERA- | |
| Zack Greinke | 49-15 | 64 |
| Clayton Kershaw | 51-18 | 53 |
| Jacob deGrom | 22-14 | 74 |
| Matt Harvey | 21-12 | 71 |
| 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.
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.
The gains might not be statistically significant if they are smaller than the error associated with the Pythagorean expectation formula.
This is all very cool and interesting. As mentioned, it may be a small gain, but an advantage is an advantage.
I’m a little hesitant to trust the data from 13-15 when comparing the Dodgers’ starters to the Mets’ starters. We’re looking at three years of data for both Greinke and Kershaw and comparing that to the same time period for Harvey (did not pitch last year due to Tommy John) and deGrom (did not pitch in 2013 as last year was his rookie year). So, to me, those numbers are not exactly apples to apples.
Final note: Congrats on the first article, Roger!
Thanks Phillies113! I thought of the same point as you regarding less data for Harvey and deGrom. Coincidentally, if you use the 2012-2015 stats for Harvey (three seasons for him), his ERA- is exactly the same.
It’s also relevant that pitching your ace game 1 allows him to pitch game 4, which you would sometimes need to win to force game 5.
He can pitch Game 4, but he’s on 3 days’ rest (unless Game 3 is rained out).
The history of starters on 3 days rest in recent years suggests that an ace on short rest may not be a better option than a #4 starter.
You have the wrong set of NL East pitchers represented. It should read Scherzer and Strasburg.
Ah ok, so now I know you’re just troll.
A fun exercise but I feel 100% of managers would reject this. It’s hard to quantify the damage this could do to your chances.
1) MENTALITY – A team must believe they can beat anyone on the mound. If you’re sitting your ace for game 1 it is because their ace is better. You’re telling your team you don’t like your chances.
2) MOMENTUM/MORAL – Game 1 is likely the most important game in a series. It can shape the trajectory. Similar to the first run being most important in baseball or the first quarter/score being most important in football.
3) Shorter rest for your ace if he goes 2 and 5.
I would hate it if I was on the team. This exercise is way to SABER for me. The baseball games are played on the field, not on paper.
“The baseball games are played on the field, not on paper.”
+100 Internet Points for originality.
Why are you Drew7 and not simply Drew?
It’s J.D.!
*Most* managers would reject this.
It’s possible that if the benefit was greater than schedule-related risks (weather, etc.) a savvy manager (Joe Maddon?) might start a “No. 1” in Game 1 (Jon Lester) instead of “No. 1!” (Jake Arrieta) using a red-herring rationale of experience that would resonate with at least some percentage of fans.
A lot of assumptions in that scenario, but it shows there is a logical possible path that maximizes win opportunity while also creating less backlash than might be expected.
If you pitch games 2&5 in a division series, you’re on full rest. There’s an extra travel day after game four, compared to a 7 game series.
No, you’re telling your team you think your #2 is so good he matches up well with the other team’s #1. You — if you are, you know, the kind of hairy-chested, steely-eyed leader who plays the games on the field and not on paper — are telling them you’re convinced your team is so much better, they can beat the other team’s ace even without your own on the mound.
WHAT about ME?
I think that in this case ERA is more appropriate. ERA allows for fluctuations from team defense and ballpark, which do matter. Basically, a fielding-independent statistic is not relevant here because RUNS are what matter and they are fielding-dependent.
Of course ERA is not perfect either and maybe wOBA or OPS would be better still.
So you want to inflate the projected win pct. of pitchers who pitch in low run-scoring parks? Why? Using ERA makes little sense; using 3-year ERA makes arguably even less sense.
Well, since about half of the games are going to played in that low run-scoring park, why not?
Interesting analysis. Looks like there’s a small error in the last table of the Tigers-Yankees matchup; the alternate appears to increase winning by .004, not decrease.
The difference is likely larger, and perhaps significant, depending on the strength of the top two pitchers. When the Dodgers have two guys with an ERA- of ~60, it doesn’t matter how you match up.
I suspect that even if there is a real edge, no team would do so for fear of public criticism. It’s just like using the Wild Card game as a bullpen day rather than throwing your #1 starter.
Meant to post my above reply here. Sub most managers for most teams.
Thanks Adam for pointing out the error! The post is now fixed.
What can’t be measured how this would impact player confidence, both the SP being moved to game 2 and the rest of the team during game 1.
There are a few reasons it wouldn’t really work in this case. As Adam S writes above, you have to consider the strength of the top two pitchers. If they didn’t have Greinke and the drop-off was from Kershaw to a mid-rotation type, then it would have much more of an impact.
The same goes for the Mets’ duo. There’s not a whole lot separating deGrom and Harvey, especially when you look at a single start. So for both teams, the pitchers in question are pretty interchangeable. Factor in that Harvey can probably only pitch once per series due to the innings limit, and it doesn’t make sense to start him in game 1. It might not even make sense to pitch him in game 2, if he’d be unavailable in a potential game 5.
How much does bullpen affect this? If I have the Royals bullpen, I’m less likely to leave my ace in too long. If I have an inferior pitcher, his 5 innings +2 bullpen innings might be better than their Ace’s 7 innings.
I agree with the sentiment above. You’re more likely to participate in a game 4 than a game 5 (by definition, game 4 happens 100% of the time before game 5).
So you run the risk of throwing your ace once rather than twice, which would heavily pile on the criticism from the media.
If you view the coaching aspect of the game as the idea that coach are solely into self-preservation of their jobs, then losing by your ace is far better than risking it for a chance to minimally increase your overall series chances.
It’s the same idea as playing for a game tying field goal in the NFL when you’re the underdog, especially getting conservative when you get to the fringes of field goal range.
I don’t think this necessarily holds water. I’d argue that most (all?) teams these days are avoiding starting guys on three days rest. So the odds are you won’t have your game 1 starter pitching game 4 regardless of the situation. Your ace only goes twice if the series goes to 5 games.
For some reason I expected to read David Price’s name in this piece. Not sure why since he has only been talked about twice on this site in the past year.
This is how the Hitless Wonder White Sox beat the 116 win Cubs in the 1906 World Series. The White Sox avoided pitching their best in Game 1 against Three Finger Brown, managed to steal the game anyway, saved their best pitchers and won the Series. More teams should use this strategy.
Hmm, it’s an interesting theory, although I agree with your ultimate conclusion that the risk of a Game 2 rainout is of more importance than the slight edge a team might get otherwise.
Then again, it will be interesting in itself to see how the Cardinals use their rotation in the playoffs this year, as they’ve got as balanced a starting rotation as I’ve ever seen for a playoff team with no real ace among them compared to the others. In fact, there’s a good chance they’ll send a 14-7, 3.01 ERA (currently) All-Star starter to the bullpen for the playoffs. They may be more willing to look at factors like the opposing starter, opposing lineup, and home/road splits than the usual playoff team when making those decision.
By the way, while 3-year compilations are generally more effective in portraying true talent level, such an analysis is unfair to the Cardinals in your first example. Lynn was a young, still developing starter in 2012-13 before breaking out in 2014, while the first half of Wainwright’s 2012 season wasn’t his usual dominating work with him just returning from TJS.
If you are trying to win the series and get to the AL/NLCS you have to consider the schedule of your pitchers for the next round too.
If your ace pitches in games 2/5 of the Division series, on regular rest they would start Game 3 of the League Championship series on regular rest, then only available for game 7 on their regular rest schedule. Starting Game 1/4 of the Division series would have them starting Game 2 on regular rest and then available again for game 6.
He still wouldn’t start Game 4 unless on short rest. The point is that whether the ace starts Game 1 or Game 2, the next time he’ll be available on regular rest is Game 5 either way thanks to the scheduling quirk of the (N/A)LDS.