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Ten thousand seasons again

Posted by Doug on June 5, 2006

You'd better read Thursday's post and Wednesday's if you haven't yet. Thanks to the many who posted thoughtful comments during the weekend, and apologies for not giving them the thought they deserve. I had a a busy weekend. But I will do my best to address some of them when and if I get a chance.

Today will just be a few more observations from the same experiment, but note that there will be a subtle shift in focus. Last week, I was asking questions about how often the actual best team won the Super Bowl. Today, I'll be investigating how often a team with a given record wins its division or a Super Bowl.

How often will a team with a sub-.500 record win its division?

In 10,000 seasons, a division winner had a sub-.500 record 870 times. If the league structure remains as it is now, we can expect this to happen about once every 11 or 12 years on average. I find this tolerable, I guess. We'll see shortly how often these teams go on to win the Super Bowl.

Amazingly, on two occasions teams won their division with a 5-11 record. This is pretty hard to arrange. Both times, the four teams in the division won a total of 17 games. Since there are 12 intradivision games, this means that those divisions must have been 5-35 in interdivision games.

Again, 10,000 years is a long time.

Because the teams' true strengths were rigged to be symmetric about zero --- which is a very reasonable assumption in general but might possibly break down at the extremes --- there is no point in computing how often a division produces four teams with winning records. It will be (theoretically) the same as the above.

How often will we see a four-way tie in a division?

I think a four-way tie would be cool. It happened 109 times in 10,000 simulated seasons, or once every 92 years on average. In one of the simulated seasons (#2702, if you must know), there was a four-way tie at 11-5 in the AFC West. The Broncos were left out of the playoffs despite having the best true strength in the division and having the best record in the AFC. The Bills won the AFC East at 8-8 and went on to beat the 9-7 Cardinals in the Super Bowl, which makes up for that time they went 15-1 but were bounced from the playoffs early. Strange year.

How often will a team with a sub-.500 record win the Super Bowl?

Fourteen times in 10,000 years. There is about an 13% chance of this happening at some point in the next 100 years. I find this to be tolerable also.

When this format was announced five years ago, I thought the small divisions created too much opportunity for a losing team to get into the playoffs, and hence win the title. But I'm finding that there is something aesthetically pleasing about the small divisions, and a 0.14% chance of a team with a losing record winning the Super Bowl is a price I'm willing to pay.

Here is the full list of the how often the Super Bowl champ had a given number of wins:


Wins Times
===========
7 14
8 135
9 665
10 1541
11 2344
12 2499
13 1728
14 779
15 255
16 40

How often will we see an undefeated team?

We saw 115 undefeated regular seasons, which means roughly one every 87 seasons. As you can see from the table above, 40 of those 114 undefeated teams won the Super Bowl. That might seem low, but it's about 35%. In the comments of the last post maurile computed that, when they make the playoffs, the best team in football wins the Super Bowl about 27% of the time. An average 16-0 team was probably a bit better than an average best-team-in-the-league. So 35% is in the ballpark of what we'd expect.

The moral of the story: going 19-0 is hard. It's probably even harder than the media folks who write and blab every November about how hard it is even realize. I am 34 years old right now. If I live to be 100, and if the NFL remains just as it is now, there is about a 23% chance that I will see a 19-0 team.

This entry was posted on Monday, June 5th, 2006 at 4:12 am and is filed under Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.