If instead of the outcome of the games being decided by who scores more runs in nine innings, it was based on a simple coin flip, we can build a simple model to see what the probability of winning a Series at any given point would be. And luckily it involves VERY simple math that is easy to understand. For example, the odds of flipping heads two times in a row are 1 in 4 (50% x 50% or 1 in 2 x 1 in 2). So, if a team is down 3-2 in a Series, the probability of them winning both games and taking the Series is 25%.
Now, we all know the games aren’t based on coin flips, but I believe using a coin flip model helps to get at least a rough idea of what can be expected. I first mentioned this in 2004. Down 3-0 to the Yankees, the odds of the Red Sox coming back to win didn’t look good. Using a coin flip model, it was easy to see that the odds of winning 4 games in a row (or flipping a coin heads 4 times in a row), was 1 in 16 or about 6%. Now, this doesn’t sound very promising, but it’s not the 1 in a million that people made it sound like. (For comparison purposes, the odds of being dealt pocket aces are 1 in 221. Also not likely, but everybody has had this happen to them, several times if you play poker often enough). Sure, it had never happened in the history of baseball, but only 24 times previously had a team been up 3-0. The Red Sox coming back and winning and making it 1 time in 25, is pretty consistent with what would happen if every game was a coin flip*. It should happen about 1 and half times out of every 25. Once is slightly less than expected, twice is slightly more.
Anyhow, without even needing to use any math, it’s obvious that any time the same number of heads and tails have been flipped, the probability of getting a certain number of heads before the same number of tails is the same as tails reaching first (In other words… if teams are tied 1-1, or 2-2, the odds of either team winning a 3 of 5 or 4 of 7 are the same). Going through all the permutations of heads/tails out of 5 or 7 flips, you end up with this chart showing the probability of the leading or trailing team winning, depending on the current Series score:
(*) Note: I’m NOT saying that the outcome of each game is the same as a coin flip. Obviously some teams are better than others, pitching matchups, home field, injuries etc., all need to be taken into account. But when you get to the World Series, more often than not both teams are at least closely matched up. Even a 100 win talent team is only going to beat a 90 win talent team about 55% of the time in a given game. If we assume that in the previous 24 times, on average, the leading team had a 55% probability of winning each game, the chances of the trailing team coming back are (0.45)4=4% which is one time in 25, matching EXACTLY what has happened.
No comments:
Post a Comment