Sunday, December 21, 2008

NFL Playoffs: a probability lesson

Bucs and Falcons have two games left. One of them has to lose one of their two remaining games in order to give the Cowboys or Eagles a chance to sneak in as the last wildcard. I have said that I expect the Eagles to win today against the Redskins and win next week at home against the Cowboys and therefore sneak into the playoffs. But that would require the Bucs or Falcons to lose one of their last two remaining games. My contention is that probability favors one of those two teams losing one of their last two games. Here's why.

The probability of the Falcons and Buccaneers winning all four of those games is the product of the probability of them winning each one of their games. For example, suppose I flip a coin that has a 50% chance of coming up heads (or tails). The probability of getting 4 heads in a row is 1/2 raised to the fourth power, or 1/16. Bucs have two weaker opponents and Falcons have one tough game and one easy game. So suppose their chances of winning each of these games is 50% for the one tough game and 65% for the easier games. The chances of those teams winning all 4 games is .5 X .65 X .65 X .65 = 13.7% Obviously, the chance that they will not win all four of these games and lose at least 1 of these games, is 100% - 13.7% = 86.3%

So the Eagles have a 86.3% chance of getting into the playoffs if they win their last two games. That's a big if, of course, because the Eagles may not win both of their last games. I'm just saying that, by this logic, there will be a likelihood of 86.3% that the door will be opened for them. If they can win both games, they can walk right through.

If you give the Falcons and Bucs a slightly better chance of winning their games and say the Falcons have a 55% chance of winning their tough game and they both have a 75% chance of winning the other three games, it lowers the Eagles chances, but still gives them a good shot. In this case, the likelihood of the Bucs and Falcons winning their last four games is 23.2%, which means the Eagles have a 76.8% chance of making the playoffs if they win their last two games.

Go Giants.

1 comment:

wolfman said...

I hope I didn't totally bore you guys with my mathematics / probability lesson, but I just wanted to revisit this and point out that I was accurate in my prediction: Bucs already lost, so my assertion that the Bucs and Falcons had only a small chance of winning their remaining 2 games (4 games in total) proved accurate.

Of course, the Eagles also lost, so they blew their chance of controlling their own fate. But the door was open for them, as I predicted.