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ShareThisTen thousand seasons again
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.
Excellent work, Doug! The Bills beating the Cards was especially poignant, because my mother lives in AZ and follows the Cards! That'll show her who not to mess with
Out of curiosity, at some point do you plan on posting how many simulated Super Bowls each team won? This experiment has taken on a life of its own.
I also found out it's a bit controversial for some reason. The people I've spoken to about it (none of whom knew of this blog before I spoke of it) seemed uneasy about the concepts contained within. I was a bit surprized. Maybe some sacred cows were skewered or something.
Also, Doug, when's your bday? I'm also 34. Mine's on 11/16. What's the money line on which of us is older?
Another great post. I assume when you figured how many 16-0 teams there would be, you weren't considering the possibility of achieving home-field advantage and resting starters, right? Therefore, we should probably expect fewer than 40 16-0 teams over the next 10,000 years.
That's a fair point MDS, but to be perfectly clear there are 40 16-0 teams that won the Super Bowl; there were 115 total undefeated teams.
Oh, right, sorry. I should have said fewer than 40 19-0 teams, and fewer than 115 16-0 teams.
Good point MDS. I hadn't thought of that. If I had the time and energy, I would program that into the simulation. Once a team has clinched home field, they essentially revert to a true strength of zero (an average team) for the rest of the regular season. Since almost all undefeated teams would clinch early, I suspect this would have a rather large impact.
On the other hand, we still have yet to see a team (in real life) clinch while the dream of a perfect season was still alive. It's not clear that all such teams would rest starters.
I was thinking, how much would the simulation as you've done it (game outcome by game outcome) vary from a simulation done on a play by play basis (such as with a dice based football game or whatever)? The simulation you did was, as I understand, done using discrete probability functions based on circumstances outside the context of the game at hand (i.e., Houston's chances of beating Pittsburgh, for instance, were governed totally by team and league circumstances prior to, and therefore outside of, the game between the 2 teams), whereas a play by play simulation would be based on probability functions that also take into account the evolving circumstances of the game as it progresses. I guess my question is: is there reason to think such a distinction in simulation types would effect the big picture of such simulations in any way?
Combining a couple of Bill M questions:
Good question. I can't think of a reason why it would turn out too different. But then again there lots of things out there that I never think of. Worth pondering.
They all won basically 1/32 of them, which was pre-ordained. I just generated random strengths every year for each team so the Buffalo Bills of Simulated Season #7126 were unrelated (except for the vociferous support they received from Bill M) to the Bills of 7125 and 7127.
I think there are a great many people who would read these posts and the message they'd take from it is something like: some guy at some blog did a bunch of math and tried to prove that the Steelers didn't deserve the title last year. Probably a Colts fan.
I understand why that happens, but I'll reiterate that there are no value judgements in any of this. Whether the best team wins it 10% of the time or 70% of the time, the Super Bowl and the road thereto are incredibly exciting and the teams that won them have achieved something great.
"On the other hand, we still have yet to see a team (in real life) clinch while the dream of a perfect season was still alive. It’s not clear that all such teams would rest starters."
Didn't the Colts clinch home field before they lost to the Chargers? As I recall, they didn't rest their starters, so that might give an idea of what such teams would do. Then again, they lost their first playoff game, so maybe other teams in that position will rest their starters in the future.
What are my chances of living to 100? Hopefully not very high, I am not very good at saving money.
I am also 34. But you are older than me, Bill.
Oh, I get it.... I thought you did the strengths based on performance the previous simulated season. Making it random probably accounts for many of the schedule nuances, right?
#
As a statistical exercise this is very interesting. But any attempt to extrapolate its conclusions to football beyond the statistical implications is a very entertaining, waste of time. This is almost exactly what happens in economics all the time. People create models based on statistics, observe what happens in the very tightly defined model, and then conclude all sorts of nonsense about the world that is totally logically unjustified. What this model tells us, and it is very interesting in it’s tightly defined world, is that IF teams won or lost games based on this statistical model, than 24% of the time the best rated team would win the Super Bowl. That’s it. Nothing more. It tells us nothing about whether the best team in the NFL wins 24% of the time, 100% of the time or 0% of the time. Not a criticism of the work put into this analysis, just a reminder of the limitations of statistical models and the dangers of extrapolating conclusions beyond the boundaries of the model.