Voros returns to BTF with a look at probability and the playoffs.
You often hear members of baseball’s underground intelligentsia (otherwise known as ‘stat drunk computer nerds’) describe baseball’s playoffs as a ‘crapshoot.’ Now despite the fact most of us subterranean baseball thinkers would likely soil ourselves if we ever found ourselves in the midst of a real back-alley craps game, in general we seem pretty damn confident we know what we are talking about when we use the term.
Not one likely to take these sorts of things on faith, I decided to take a cursory (please remember that word before someone starts chiming in with stuff you need a PHD just to get the introductory textbook to)…
…um, where was I—oh yes, I decided to take a cursory look at the issue and see if the statistical geekerati know what the hell they are talking about.
The experiment is simple. Estimate the winning chances in a game of two teams with given winning percentages and adjust for home field advantage. Then take those numbers and come up with the chances of winning a 5 or 7 game series.
The following tables list the chances of winning 5 or 7 game series for teams with differing everyday win percentages. The win percentages aligned vertically on the left side are the win percentages of the team with home field advantage, the winning percentages across the top are for the team with fewer home games in the series. The given resulting percentages are the chances of winning the series for the team with home field.
Home field advantage is set so that a .500 team would win at a .600 clip at home and a .400 clip on the road. Or, for our purposes, a series between two evenly matched teams would have the home team win on average 60.0% of the games. Why is that so much different than we see in the regular season?
(around .540) Well since the war, the home team has won roughly (very roughly but there are side issues at work that I don’t want to get into) about 60% of
the games in World Series play. Since there’s no inherent reason why a home team should be the better overall team in the World Series (until recently home field simply alternated leagues), this suggests that home field advantage is stronger in the postseason than in the regular season. I’ve decided to base the above on that assumption, since it’s quite reasonable to come up with reasons why that might be the case. (Insert gratuitous swipe at Eric Gregg here).
To come up with the winning percentage of a single game, the following formula was used:
A = Team A’s Win% (home team)
B = Team B’s Win%
((A*(1-B))/.5)/(((A*(1-B))/.5)+(((1-A)*B)/.5)) = Team A’s chance of winning
Then I raised that number by .737 to adjust for home field advantage in that game (an exponent works well here because you can’t go above 1 or below 0 with it). From there it’s easy to come up with full series winning percentages based on those numbers.
Anyway, what the table shows is that the geeks are, to an extent, correct. Any individual series can be a bit of a crapshoot. For example, if we assume the Cardinals face the Padres and their ‘true’ win percentages are .625 and .500 respectively, the Cardinals, even with home field advantage, expect to win the series only about 73.77% of the time. While that may seem like a lot, in actuality the Padres chances would be a little below the chances of rolling a ‘9’or higher in craps. In other words while the Padres are indeed underdogs, they certainly have a shooters chance.
Still, just like in craps, while any outcome can easily happen, some outcomes are more likely than others and the Cardinals do rank as clear favorites to win the series if we assume those win percentages are correct. Of course this is without adjusting for different starting pitchers and so forth, but remember this is just a cursory look to give us an idea of what level of crapshoot things are. Please do not use this info for wagering purposes, unless of course you win, in which case I’ll set up a pay pal site for you to send me my cut.
It’s also worth noting that even a favored team whose chances of winning each series it participates in is 70%, would still only win all three series about a third of the time.
So we geeks are essentially right. (And don’t we just love to announce it to the world when we are). The playoffs are, to a certain extent, a crapshoot. Baseball’s current playoff format ensures that even the very best teams are likely underdogs to win the World Series once they make the playoffs. There’s just not enough games against too strong of opposition to swing the balance too heavily in their favor. I’ll leave it to others to argue whether this be good or whether this be bad.
And while it’s unlikely the Padres will wind up winning World Series rings (or watches), their chances are not probably not too far from the chances of rolling snake eyes.
Which can happen, something we geeks know from many years of playing cutthroat games of
Posted: October 05, 2005 at 11:54 PM | 314 comment(s)
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