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You want your ace on the mound when all the marbles are in the fire. When the stakes are high, the big cheese needs to have his hands on the wheel. Are those real metaphors? No, but I bet you knew what I was talking about in each case, because the playoffs are a perfect time to discuss the importance of star pitchers. But do you want to deploy them as early in the series as possible? Or do you want them for the decisive game? Does it even matter?

In our game chats and article comments — across the internet really — it’s hard to find a consensus. When I wrote about Chris Sale earlier this week, there were comments to the effect of “It’s a bummer he pitched out of the ‘pen in the Wild Card, now he won’t get to pitch in NLDS Game 5,” as well as “Don’t save Sale for Game 7 of the NLCS, there might not be a Game 7!” Those are exact opposite opinions, and yet they both make a lot of sense when I hear them. But they can’t both be right, so let’s do some math. Even though there’s no real adage to prove or disprove here, this feels like a job for Mathemadage.

Here’s the question, as I see it: For a given set of pitchers making postseason starts, which way would you like those starts arranged in a seven-game series? In other words, if you have an ace, a second banana, and some bullpen games, would you prefer to have your ace for Games 1 and 5 or Games 3 and 7? There are good intuitive reasons to prefer either. Games 1 and 5 happen in almost every seven-game series; Game 7 is a much less frequent occurrence. More innings for my best guy, please! But the stakes can also never be higher than they are in a decisive game. In a big spot? Why wouldn’t I want my best guy in?