Thursday, April 28, 2011

Playoffs: Playing the odds

So my team is out of the playoffs.  Sigh.

This unfortunate turn of events has given me more time to think of other things though, and one of those things was the "fairness" of the playoff system.  In the NHL, sixteen teams compete in four rounds of playoffs, with each round being a best of seven elimination.  All things being equal, every team would have a one in sixteen chance of winning the Stanley Cup... but of course, things are never equal.

But what would happen if one of the teams was, say, twice as good as every other team in the league?[1]  What would their chances be of winning the cup?

Would you believe that they're more likely not to win the cup?

There.  That made me feel better.  (Okay, not really.  Sigh.)


[1] It's tricky to define what "twice as good" might mean.  For simplicity, I'll define "twice as good" as being twice as likely to win a single game.

Looking at this year's regular season, the top-ranked team earned 117 points, while the bottom-ranked team earned 62.  If all those games were played against each other, then the top team earned 65% of the points, which is 1.88 times the points earned by the bottom team.  If you only compare teams that made the playoffs, then you're looking at 117 to 93 points, which is only 1.25 times as many.

1 comment:

  1. Okay, I was going to leave the math as an exercise for the reader, but I'm not that nasty.

    If team A is 66% likely to win each game against team B, then it will win a best of seven match 82% of the time. This means that team A has an 82% chance of advancing to the second round, 68% chance of making the third round, 56% chance of making the finals, and a 46% chance of winning the cup.