Why the "Tigers in 3" commentary was over the top, and why Sox in 4 would be...

A lot of talk has gone into the discussion regarding how random chance affects team's success (or lack thereof) in the playoffs.  I thought that I'd dedicate today to showing how much it actually is a factor.  My analysis is a bit crude, but it has the advantage of using pretty simple mathematical rules, and showing off results that are easy enough to understand.  Just to review a bit of that high school math, if I flip a coin, half of the time, I get heads, and the other half of the time, I get tails.  That means that I have a .5 chance of either result.

Now, each successive throw does not depend on the previous throw.  So, if I flip a coin again, after getting heads, I have half a chance of heads or tails.  Same thing if I get tails.  That means, if I flip a coin twice, I have a .25 chance of getting heads twice, a .5 chance of getting heads once and tails once, and a .25 chance of getting tails twice.

What does this have to do with baseball, do you ask?  Well, I can take the number of games a team won and lost in the regular season and convert into their probability of winning another game.  One can do the same with a given matchup.  We can then run the math through the logic of a five or seven game series--if you get to three or four wins, the series ends, but otherwise, you keep on playing.  We can then take all of this, and generate the probabilities that teams with a given regular season record, independent of matchup, or anything else, will win or lose a playoff series.  The results for two .500 teams are shown below:


Obviously, neither team has an edge--both have a 50% chance of winning either a five or seven game series.  Also note that in one out of four runs of this sort of problem, you will get a series sweep in a five game series, and even in a four game series, there is a 12.5% chance that the end result will be a series sweep by one of the two teams.  Also note that there is an equal chance that the winner wins by two games or wins by one game.  Now, let's look at the same table, but applied to the matchup of the 2006 Cardinals and the 2006 Tigers:


Note that, for all the pre-series discussion regarding the absurd dominance of the Tigers over the Cardinals, before you even factor in regular season injuries to the Cardinals, or the absence of jason Marquis, you still have a 42% chance that the Cardinals would win the series against the Tigers.  The probability of a Detroit sweep was only 8%--one fifth as likely as a Cardinals win.  

Similarly, perhaps we shouldn't have been quite as heartbroken about the 2004 Cardinals:


The Cards win probability was only at 54%, based on regular season record.  Still, it was kind of hard to expect an actual sweep.  But it's still pretty crazy to see how little nine extra wins in the standings actually buys you.  So, that brings us to the rockies and the indians, assuming the latter hold on, and keep Manny cheering as his team loses:


This looks like a pretty fun series.  The teams are pretty easily matched.  Looking at that, I'll take the Rockies in seven.

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