Friday, February 10, 2006

My follow-up Steelers Post

Before the Super Bowl, I posted this about the suprisingly consistant ability of the Steelers to get into the playoffs. I said some things in that post that I later wanted to check on, and I wanted to correct the fact that I left the Bills out of my initial graph. So, again. . .

The first image shows the playoff histories of all teams in the NFL since my birth. Notice that the Steelers, Cowbows, and 49ers are farthest to the left and have the most amount of playoff appearances. At the very far right is the Texans who have yet to be in the playoffs. Realistically, the Panthers, Jaguars, Ravens, and Texans should not be considered in this "study" since they have only been in the league for a few years, and one wouldn't expect them to have the same total playoff appearances as other, older teams. This means that the Cardinals are the epitome of ineptitude during the course of my lifetime. (FYI, I combined the old Browns with the new Browns rather than with the Ravens, simply because it made my counting easier, and to make the graph contain the whole league. By doing this, I put a 5 year gap into the Browns history, but I don't really think it's that big of a deal, and hell, I'm not getting paid for this.) In addition, the inclusion of the Seahawks and Buccaneers might be a bit biased, since they entered the league in my birthyear, and one wouldn't expect them to make the playoffs in their first couple years. However, it's been 30 years now, so I think it comes close to all washing out (again, see the comment of me not getting paid for this).

From looking at the first graph, one can see that the average number of playoff appearances is about 10 - 11 years. If you actually calculate it, you come up with a number of 10.3 (+- 5) where you include the Texans, Ravens, Jaguars, and Panthers are included, and a number of 10.9 (+- 4) where they are not. The median is 10.5 and 11 respectively. Those averages match very well with the probability of making the playoffs in the NFL. Here's a brief history of playoff selection during the past 30 years:

1976-1977 - 4 playoff teams / conf., 14 teams / conf.
1978-1989 - 5 playoff teams / conf., 14 teams / conf.
1990-1994 - 6 playoff teams / conf., 14 teams / conf.
1995-1998 - 6 playoff teams / conf., 15 teams / conf.
1999-2002 - 6 playoff teams / conf., 15.5* teams / conf.
2003-2005 - 6 playoff teams / conf., 16 teams / conf.

*The Browns were the 16th team in the AFC during this time.

If you do a weighted average of that, you find that the dumb luck probability of a team entering the playoffs if all games were decided by a coin toss would be 0.37. Multiply that number by 30 years, and you find that the most likely amount of years a team would be in the playoffs is 11.2.

One thing that I wanted to check was whether you could do a dumb luck random flip determination of whether teams could get into the playoffs. For example, currently in each conference there are 4 divisions. The teams with the best record in each of these divisions automatically make the playoffs. Then the next two teams (Wild Cards) with the highest records are selected, bringing the total to 6. But, what if there is a 7th team that has a better record than one of the division winners, but does not make the playoffs because it did not have the best record in its own division, and did not have a better record than the two Wild Cards. This team would be in the top 6, but not make the playoffs, seemingly throughing the probabilities a bit off. This could happen, but does it happen alot?

I looked back into the old standings, and found two times that it certainly did happen, the 1979 NFC and the 1985 AFC. (I believe it was the Vikings and the Browns that were the division winners to get in. Further, the '85 Browns were the only team to ever make the playoffs with a 8-8 record.). There were a further 6 occurances where the lowest division winning team was tied with the 7th best team in their conference. Without going back into old game records it's impossible to know who would win these tie breakers, and I didn't feel like doing that. So, without any good reason, I'll assume that in three of these situations had the 7th team actually finish with a better record than a division winner. That brings our total of 5 times where the best 6 teams didn't go to the playoffs out of a total of 60 (2 conferences x 30 years) playoff draws, or 8% of the time. Since it's under 10% and I'm an astronomer who likes to deal with order of magnitude calculations, I'm going to ignore this effect, and assume that the probability of entering the playoffs is the probability of being one of the best 6 teams in a team's conference.

Now, after all that, the question that I was really interesting in answering is whether the Steelers being in the playoffs so many times a function of dumb luck (i.e. if you flip a coin enough times eventually, you'll get 50 heads in a row) or some real effect. There was some research done on this about basketball player's (and some other sports) hot streaks. It turns out that the
streaks don't really exist, and it's more human perception putting added emphasis on low probability events. I read somewhere (I think Gould) that the only streak that holds up to this type of analysis and is truly statistically unlikely is Dimaggio's consecutive game hitting streak. So, are the Steelers doing something right, or is it dumb luck?

The second graph is a histogram of the number of teams who have made the playoffs a given number of times. You can easily see the peaks at 8 and 11 indicating that we do have some sort of Guassian, or really in this case a Poisson distribution since entry to the playoffs is a discrete thing. So, I ran a Poisson distribution centered at 11, and that is in the third picture (I normalized the model Poisson distribution to have it's highest value be 4, for easy comparison).

There is a long low end tail (where the teams haven't made the playoffs much) in the real data. Alot of this is due to the inclusion of the Ravens, Texans, Jaguars, and Panthers. If you remove these teams results (at 0, both at 3, and one at 4), the bottom of the histogram matches the Poisson model well.

It is on the upper end, however, that we see something odd. By simple dumb luck, there should not be so many teams in the playoffs 16, 17, and 18 times. The Poisson model says that we should have maybe one or 2 out that far, not 10. This region is out past the 1.5-2 sigma range of the Poisson distribution, so we really shouldn't see a signal so strong. I believe that if these were stars, we'd be claiming detection.

Of course the sample is small. There are only 28 teams with a 30 year history, and really the time scale is low. Thirty years isn't alot. But, it seems to me that several of these teams in the high end of the distribution are doing something that is enhancing their probability of making the playoffs. It's not dumb luck that's got them there this many time. (One could also say same thing about some of the teams in the bottom of the distribution.) I'm planning on running a simulation of some random seasons to see what kind of distribution I come up with, and how that affects the distribution. But for now, it seems that for all of the talk about parity in the NFL, it is isn't there yet, and that several teams have found a way to be good and stay good.

I'm looking forward to doing this again in a few years.


At 6:34 PM, Blogger Terry Smith said...

I think the Steelers will go undefeated in 2006


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