Should the Nationals Duck Gerrit Cole?

It will come as no surprise to you that the Nationals are underdogs in the World Series. Projection systems might vary in their exact view of the series (ZiPS has the Astros as around 60% favorites, while our top-down model has them closer to 70% and betting odds tab them somewhere in between), but every system agrees that Houston is out in front.

It’s simple logic, when you’re an underdog, that increased variance is good for you. You probably can’t beat Magnus Carlsen at chess; he’s the best player in the world, and you’re someone reading this baseball blog. You have a far better chance of beating whoever the best poker player in the world is in a single hand — there’s far more variance involved.

So to maximize their chances of winning the World Series, the Nationals should be looking for ways to increase variance. Some of that will be straightforward — they should be more willing to play the infield in to prevent runs, more willing to issue intentional walks that risk a big inning but come with a higher chance of escaping unscathed, and more willing to play for the win in the ninth inning, even if it means increasing the chances of losing on the spot.

For the most part, baseball doesn’t offer many ways to increase variance. You can’t tell your pitcher to go out there and throw in a way that will either allow six or zero runs, and you can’t tell your batters to either score in bunches or not at all. While I was brainstorming variance-increasing ideas, though, a friend suggested something interesting. What if the Nationals could tinker with their projected starters to create more lopsided matchups?

Off the top of my head, this didn’t sound like a variance-increasing strategy so much as a way of rearranging the deck chairs. After all, you’re decreasing your odds of beating Gerrit Cole by throwing, say, Aníbal Sánchez out against him at the same time that you increase your odds of winning another game by downshifting, Max Scherzer to face Zack Greinke.

But if I was skeptical, I was also curious. There’s something behind the logic; it sounds intuitively correct that if your team is going to have an off day, you’d prefer to have it when you’re already unlikely to win. What better way to control which days your team is best than by choosing the starting pitching matchups?

I decided to simulate two different ways of thinking about this problem. First, I created a team with two aces and two average pitchers. This doesn’t exactly represent the Nationals, but bear with me. For my first method, I approximated their win percentage against a .500 opponent with each pitcher on the mound, like so:

Then I created an opponent, with an absolute stud pitching Game 1 and a step down from there:

From here, the plan was simple. I ran a million simulations of these teams playing each other in a seven game series, inclusive of home field advantage. The winning percentages are conveniently selected so that if the pitchers simply face off down the list — best against best in Game 1, second-best against second-best in Game 2, and so on — the “Nationals” will win the series 40.2% of the time, which roughly matches ZiPS.

This scenario isn’t reality; the Nationals don’t have two pitchers of equal skill as their third and fourth starters. If I make the third starter better than the fourth starter, however, the ideal strategy is to just play your best people, and that’s uninteresting for our purposes. So instead, let’s assume that the Nationals are using Corbin in Game 4 no matter what and using him in relief intermittently the rest of the time.

Okay, so we have our setup, and right now the underdogs win 40.2% of the time. Next, let’s enact our strategy. We’re going to duck the Game 1 matchup with Cole by pitching our third starter, hoping to make it up in Game 3. This bumps the “Nationals” odds of winning the series up — all the way to 40.35%. Switching the starters barely matters, but it matters in the right direction.

Why is this? It comes down to a quirk of the true talent method I’m using to approximate the series. The better one team is, the less impact the other team’s starter has on determining the outcome of the game. Using one of the two co-aces rather than a back-of-the-rotation starter to face my Gerrit Cole simulacrum only raises your odds of winning, even at a neutral site, from 34.4% to 41.7%, a 7.3% increase. On the other hand, using a co-ace to face simulated Greinke bumps the odds of winning from 48% to 55.7%, a 7.7% increase. In other words, extra skill matters more in closer contests, so the “Nats” can pick up marginal edge by matching up that way.

This was a pretty unsatisfying answer — 0.15% edges aren’t usable edges, even if they’re higher than the margin of error over a million trials — so I moved on to a second way of modeling the games. In this method, I built a distribution of runs allowed for each pitcher. For example, nine innings of a Cole start look like this, inclusive of bullpen:

From there, I simply simulated each game by sampling the distribution randomly to determine how many runs each team allowed. In the case of a tie, the game goes into “extra innings,” a weighted coin flip where the Astros are 54% to win due to their bullpen. I ignored home field advantage and instead attempted to bake it into the run distributions.

This is all extremely arbitrary, of course, but I’m aided by one key factor: I know what I want the eventual outcome to be. I’m not trying to work out who will win the series from first principles: I’m taking Dan’s numbers as my central tendency, which means that if I can find a set of run distributions that produces a 59.8%-ish chance of the Astros winning, I’m most of the way there.

In any case, I built a set of run distributions that gives the “Astros” that 59.8% chance of winning the World Series. Then, like before, I switched up Washington’s (err “Washington”‘s) pitching rotation, throwing Sánchez Game 1 and Scherzer Game 3. This time, it worked slightly better: the “Nationals” win the World Series 40.7% of the time by using this strategy, picking up 0.5% of equity.

Of course, none of this really works if you think Corbin is better than Sánchez (and to be clear, I do). The edges you can pick up from this strategy are so narrow that they’re dwarfed by just throwing your best pitchers in Games 1 through 3 in some order. If you account for that by adjusting my pitcher talent estimates, there’s still a benefit to having Corbin face Cole, but it’s minuscule: less than 0.1% by my first method, and 0.25% by my second method.

In essence, we’ve established a narrow but relevant rule. In a seven game series, you should always throw your best three pitchers in the first three games to allow for multiple starts. From there, the team with the best pitcher should seek to match up ace-to-ace, while the other should try to hide their worst multiple-game starter against the opponent’s best. It’s a small advantage. It might be overwhelmed by something else you care about — pitching your best pitcher in the first game so that he can throw a few innings of relief in Game 7, for example.

But it’s measurable. There’s a benefit, however small, to ducking the best starter your opponent has if you don’t have the best pitcher in the series. This is a case where the intuition my friend had is right: at some point, it really is worth just giving in against Gerrit Cole. I don’t think this World Series calls for it, and indeed the Nationals are starting Scherzer in Game 1. If you think Cole is a little better than my forecasts, or even a lot better, it could be worth it. Don’t read too much into this though: you need very particular circumstances, and a particularly dominant opposing starter, to make it worth considering.