September 21, 2012

Baseball Therapy

Wild-Card Game Theory

by Russell A. Carleton

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Let's play poker. With wild cards.

It's the time of year when the races to the top start to tighten, and for lovers of chaos and mayhem (like me!), we can start dreaming of scenarios that involve ties and one-game playoffs. And this year, as an added bonus, we're guaranteed to get two games of win-or-you’re-out thanks to the new wild-card play-in game. My favorite scenario—far-fetched at this point, but it could happen—is one in which the Orioles, Rays, and Yankees finish tied atop the AL East, with the same record as the Angels and Tigers, and all one game behind Oakland for the second wild-card spot. Texas wins the AL West, and the White Sox win the AL Central. Just for giggles, we can have the Rangers tie the A's so that they can battle to decide who wins the AL West and who gets the first wild card.

From my understanding, the Orioles, Rays, and Yankees would have to go through a three-team mini-tournament to hash out the AL East. The two losers would then still have to fight with the Angels and the Tigers for the last wild-card spot and would engage in a four-team tournament for the right to play a one-off with the A's/Rangers loser. In theory, one of those AL East teams could end up playing four(!) extra games—against a different team every day—and that's before getting to the actual wild-card one-off with the Rangers/A's loser. While everyone else is blowing out their bullpens, the White Sox could conceivably sit back, rest, and watch some really compelling baseball from the comfort of their clubhouse for most of a week.

As wonderful as that would be, let's instead shift to a more realistic scenario. Baltimore, despite the extensive amount of rain that I and others have attempted to pour on their parade, manages to finish tied with the Yankees for the AL East crown, and with both teams having a good enough record that the loser of the one-game playoff would still make the wild-card game, likely against Oakland. What should the Orioles do? They face a showdown with the Yankees, likely with CC Sabathia on the mound. If the Orioles win, great for them!  If they lose, it's not the end of the world. They play Oakland the next day in the wild-card game. They have to win only one of the two, and if they do, they're into the ALDS. It's not a bad spot to be in, really. 

Let's focus on the Orioles for a moment in this win-one-of-two scenario and think strategically. To get to this point, the Orioles have probably been sprinting for the last week or so, asking hitters to forego off-days, asking relievers to go an extra out or two past their usual quota, and perhaps throwing a starter on short rest here or there. Guys are tired. Baseball is a game of attrition, after all. The standard refrain will be that you can rest in November, but maybe it might be the right strategic decision to take a little break—by punting the one-game playoff for the division crown.

The usual strategy for the one-game division playoff would be to start your ace, if available, even on short rest, prepare your high-leverage relievers to go two innings, and generally max out all available resources to win this game. If you win, you end up in the ALDS (and can claim in 20 years that you won your division. Woohoo!) If you lose, your ace is unavailable for the wild-card game. Your high leverage relievers all have tired arms. Your hitters have to fly across the country to Oakland to face a bunch of guys who watched your game on TV yesterday. You maxed everything out yesterday and are going to face a team that had an off-day. Good luck.

What if, instead, the Orioles sent a skeleton crew of backups to face the Yankees? The divisional playoff counts as a regular-season game, so the expanded September rosters are still available. Cobble together some bench guys, those Triple-A callups at whom you’ve wanted to take a look, your fifth starter, a couple of "arms" to cover any relief innings, and send them out—on national TV—to get humiliated. (If they magically win, that's pure frosting.)

The "real" team spends the day golfing and catches an early flight out to California. The next day, everyone's on full rest and ready to go for the biggest game of the season. And if you win that one, you still end up in the ALDS. Sure, the O's get only one chance instead of two, but the way the schedule works, they might be able to marshal their full resources for only one game anyway. Why not pick the one when everyone can be a little better rested?

And then there's the issue of whom you would rather face with everything on the line: the Yankees or the A's? There comes a point where this might actually make sense. It's like playing two sequential hands of poker, only knowing in advance what your cards will be on the second hand. If you don't have a lot of chips, doesn't it make sense to bet harder on the better hand? September makes things that look silly in July seem sensible.

(Credit where due: I was inspired by the article by Max Marchi linked directly above. Also, I believe that BP alums Joe Sheehan and Rany Jazayerli had a discussion of these types of possibilities where teams might actually have an incentive to lose, in a slightly different context, on their podcast.)

Okay, fantasy over. Here's why this would never actually happen, even if it should.

First off, even if I could make the case that punting the game makes sense, this would (correctly?) be viewed as the Orioles ducking the Yankees, and masculine pride has a thing about not backing down, even when it's the correct course of action. Second off, we're talking about a team semi-intentionally trying to lose a game that decides a playoff participant. The commissioner's office might take an interest in that not actually happening. Third, if the plan backfired, it would create a backlash on an order that has never been seen before. Come to think of it, even if it works...

Even throwing those objections away, there's another more logical reason why a team would never actually do this. Suppose the Orioles telegraphed their intentions, most likely through announcing their starting pitcher. Suddenly, the Yankees are looking at "wasting" Sabathia's start on a game where the other team is clearly not even trying and the game is not really a must-win. The Yankees might figure that they can get by with some other starter, hold Sabathia back a day, and get him some extra rest. In some sense, the Yankees might be seen as punting here. But now, if the O's play their "real" team, the game looks a lot more winnable—maybe a better bet than going to Oakland, even with the extra rest. But, if the Orioles are going to play their real lineup, the Yankees might go back to Sabathia. Which could lead the Orioles to go back to their Triple-A lineup. This turns into a bizarre cat-and-mouse game really quickly. We've entered the land of game theory.

There's probably a master's thesis in the calculus that would dictate what the actual best decision would be for both sides. The reality is that even if two teams got to the point where they were entertaining such thoughts, the tie-breaker in this ambiguity would be the cultural expectation that no one backs down. And a call from the commissioner's office. Both teams would probably max out for this game and let tomorrow come as it may. 

The odd denoument to this thought exercise is this: suppose that the Yankees and Orioles get into the game, and by the fourth inning, someone is winning 11-0. The logical thing to do for the losing team would be to fold up, not use any important bullpen resources to try to chase the game, and maybe get the regulars off the field for an earlier flight (and arrival time) to the next game. And either Joe Girardi or Buck Showalter would be recognized for the wisdom of not throwing good money after bad. No one would consider it a punt because the situation is essentially hopeless for this game. But what if those calculations had happened a day earlier?

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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