Nationals Baseball: Awful Math by Peter King

Monday, March 01, 2010

Awful Math by Peter King

This has nothing to do with baseball but Peter King wrote this little gem today...

"On average, the NFL plays 12 overtime games a year. That means a team has a 75 percent chance of playing an overtime game in an average year."Really? Is that really what it means?

4 comments:

Anonymous said...

12 OT games = 24 teams in OT games

24/30 = 75%

What's the awful math?

Anonymous said...

make that 24/32 = 75%

Todd Lowman said...

You have to figure out how many total games are played and what the percentage of those games are OT.

32 teams * 16 games in a season =
512 games
divided by 12 OT games per season =
42.6667
divided by 16 (since it takes 2 teams to play =
2.67% chance of any team playing in an OT game any given sunday
and then multiply that 16 times by itself to get the probability of playing in an OT game in a given season

Harper said...

Anon - that only works if a team can only play 1 OT game per year.

Not quite Todd, but on the right track

There are (32*16)/2 games in a year or 256 (you can count it if you like)

So the chance of ANY SINGLE game being an OT game is 12/256 or 4.6875%

The chance of ANY SINGLE game for a single team over the course of a season going to overtime is a bit complicated so instead we figure out the opposite; the chance NO GAMES for a single team over the course of a season goes to overtime.

The chance ANY SINGLE game doesn't go to OT is the opposite of the chance is does go to OT or:
1-0.048675 = 0.953125.

then, the chance all 16 games don't go to OT for a single team in a season is 0.951325 x 0.951325 x 0.951325 x ... 16 times, one for each game. (0.953125 to the 16th, if you prefer) This gets us 0.46387...

As we said before, the chance ANY game goes to OT for a single team during the season is the opposite of the chance no games go to OT for a single team during the season or:
1-0.46387 or 0.536128.

So there iit is

53.6% is the answer.