## Thursday, September 29, 2011

### Playoff Meanderings

I always like to put down some of my thoughts about the playoffs each year, but it’s a challenge to say anything even remotely close to being meaningful. Predicting the outcome of short series is folly (although I’ll engage in a little of this folly later), and you can read that anywhere. So I always try to come up with a different angle to illustrate why the playoffs are subject to such uncertainty.

I’ve certainly had some more interesting illustrations in the past; this one is pretty lame, but for some reason when it crossed my mind in August I thought it was a lot more interesting than I do now. What is the value of each playoff game or series in terms of a regular season game? In asking this, I’m not talking about the weight that should be applied to playoff performance for evaluating individual value, or any such thing...I’m just asking what the implied value is, given the assumption that the regular season standings carry over to the playoffs.

Of course, that’s not how it works--it's a cliché, but every team starts every series out at 0-0. However, I’ll assume that regular season standings carry over (resetting with the start of each additional round to keep things manageable) and the playoff games are weighted in a manner such that at the end of the series, the team that wins the series has a better overall record than its opponent.

There are at least two different ways to approach this increasingly silly scenario, which will be best illustrated by example--treating the series outcome as a binary, or considering the games individually. Suppose that the Alphas enter a five-game division series with a record of 92-70 while their opponents the Betas are 90-72.

First, from the series outcome perspective, if the Alphas win, the series was unnecessary since the Alphas already led in the standings. If the Betas win, however, the series must be given a weight of a number of games such that adding that many wins to the Betas and losses to the Alphas give the Betas a better record. Leaving things in terms of whole games, the answer in this case is three. Giving the Betas three additional wins leaves them at 93-72; three additional losses for the Alphas would make them 92-73. The series could have gone three, four, or five games, making the effective value of those games equal to either 1, .75, or .6 regular season games.

You can also consider this from the game perspective, that is actually looking at the outcome of each game in the series rather than treating the series as a binary win or loss. If the Betas win the above series 3-0, this is pretty straightforward given the two game margin--treating playoff games as equivalent to regular season games leaves the Alphas 92-73 and the Betas 93-72. Suppose the Betas had been 88-74 instead of 90-72, though. In order to bring the Betas ahead of the Alphas (on a whole wins basis), they need five, so each win (and thus each game has to be worth) 5/3 = 1.67 times a regular season game. Now the Alphas have 3*1.67 + 70 = 75 losses and the Betas have 3*1.67 + 88 = 93 wins, so that the Alphas record is 92-75 and the Betas 93-74.

You can see that if the final margin of the series is 3-2 in favor of the Betas, the weight on each playoff game would have to be roughly four times that of a regular season game since the Betas only pick up one win when the playoff series is considered. A 4x weight brings the Alphas and Betas together at 100-82.

This is all just a silly digression, but given the assumptions it is a simple way to think about how the implied value of a playoff game compares to that of a regular season game.

Getting to the 2011 playoffs, let me offer some quick thoughts. I’ll leave the detailed handicapping to those who are better suited for it and also like quixotic quests. The marginal value of more in-depth analysis is limited, but if that’s what you seek, you won’t find it here.

The probabilities that follow assume nothing about home field advantage or pitching matchups, or even true talent for that matter. They are simply based on my crude team rankings, fueled by 25% actual W%, 25% expected W% (from R/RA), 25% predicted W% (from RC/RCA), and 25% from .500.

That formula is also arbitrary. The results should be fairly reasonable, but I’m also eager to disown at the same time, as something of a commentary on the futileness of the exercise...and most especially the bloviating that is done without any logic at all. I’m sure that there are many scribes across the country furiously writing about how certain teams have no chance, never learning the lesson that the differences between major league teams simply aren’t that great, especially after eight of the best have been selected from a 162 game sample.

This method considers all of the playoff teams to be in the top ten in MLB; only Boston (#3) and the Angeles (#8) are on the outside looking in. The Yankees, Phillies, and Rangers are near co-favorites to win it all; NYA and TEX are ranked about evenly, while PHI benefits from the weaker NL field and has the highest odds of winning a first round series and the pennant. Overall, the AL has an estimated 57% chance of winning the World Series. The most likely matchup in the Series is NYA/PHI (11%); the least likely is DET/STL (4%). The rankings imply that the worst playoff team (ARI) would beat the best playoff team (NYA) 43% of the time, which over 162 games is seventy wins. Strictly equating true probability to actual 2011 record, consider the odds that the Padres could win a seven game series against the Indians, and there is roughly the same likelihood of the Diamondbacks winning a seven game series against the Yankees.

As far as my personal rooting interests go, New York and Tampa Bay are my top two choices, followed by Milwaukee and St. Louis. I would be happy to see any of those teams win, have no particularly strong feelings about Arizona or Detroit, and be mildly disappointed if it’s Philadelphia or Texas. But there are no White Sox in this group.