October 11, 2012

Manufactured Runs

Is the 2-3 Format Fair?

by Colin Wyers

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Today, the Oakland A’s and Detroit Tigers face off in an elimination game for both teams, with the winner advancing to the League Championship Series round. The A’s looked almost certain to be eliminated last night until they mustered some late-inning heroics, scraping together a three-run ninth against Tigers closer Jose Valverde.

On paper, the A’s were the higher seed coming into this series and thus were entitled to the greater home field advantage. But without last night’s miraculous win, the A’s were never going to see the benefit of their better record, due to the format of the five-game series. In order to cut down on travel days, MLB has switched to a 2-3 format—two games at home for the lower seed, then three games at home for the higher seed. In the 2-2-1 format it replaced, the team with the better record gets to take, well, advantage of their home field advantage if the series runs to three games or five games, with only a four-game series depriving them of that benefit. In the current setup, the series has to run five games for them to see the benefit of their higher seeding.

So in a different playoff series, would the A’s have needed those heroics to stay alive in the playoffs? Or would they have had an easier time dispatching the Tigers already if they hadn’t needed to force a four-game series just to see a second home game? Fans of the other higher seeds are probably wondering the same thing—of the higher seeds, the Yankees are the only team leading their series, and the Reds and Nationals are both facing elimination games today. Would those teams be in better shape right now if they’d been able to play under the old format instead of the new one?

In order to answer this question, I built a simulation that outputs the probabilities of a team winning given different sets of home and road games in a five-game series. For this purpose, I assumed that the higher seed and lower seed were evenly matched except in the matter of home field advantage. (In reality, the home seed should be a slight favorite most of the time, if home field advantage weren’t an issue.) This lets us see how the change in playoff formats affects a team’s odds of winning. Using historic data, I assumed that a home team would have a .540 winning percentage against a neutral opponent.

Let’s start by considering three-game series, which are the first possible outcome and the simplest to discuss. If either the higher seed or the lower seed sweeps those three games, the series is over. In the 2-3 format, the lower seed is actually the team with the home field advantage if the series goes to three games. So in this format, there is an 11.4 percent chance of the higher seed winning in three games, compared to 13.4 percent in the old 2-2-1 format—so, precisely a two-percent difference. Only about a quarter of these series will end in three games, and home field advantage plays a relatively small part in deciding which team sweeps. (When both teams are evenly matched, luck is the largest deciding factor—if you are uncomfortable with the word luck, what I really mean is randomness, or things unaccounted for in the simulation.) And more importantly, the chance of getting to game four is entirely unaltered by the change in playoff formats.

Going to four games is where things get more interesting. The saving grace of the format for the higher seeds is that they never face an elimination game on the road. Does that matter? It turns out that yes, in fact, it does. The benefit of being able to play game four at home means that the higher seed is more likely to win a four-game series than it would be under the old format, where two elimination games occur on the road. This format actually raises the odds of the higher seed winning the series in four games, from 17.8 percent to 19.7 percent, almost exactly what we saw above. (Actually, while the rounded figures show a slight difference, the raw figures show the same gains in the chance of winning in four games as they show a lowering of the odds of winning in three games.) And then in five games, the odds of winning the series are exactly the same as they were before.

So the new format isn’t to blame for the showing of the higher seeds in this year’s playoffs. All of them managed to avoid being swept, thus forcing terms at least as favorable to them as what they would have seen under the old playoff format. Major League Baseball is still planning to switch back to the old format for next year, but the owner’s interest in this probably has more to do with finances than fairness. (While playoff teams split ticket revenue equally, there are likely ancillary financial benefits to hosting a home playoff game that make it desirable to host them yourself rather than simply getting your cut of the gate from a road playoff game.) The simple truth is that teams haven’t been cheated out of wins by the 2-3 format.

​A version of this story originally appeared on ESPN Insider .

Colin Wyers is an author of Baseball Prospectus. Follow @cwyers
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