Less Than A One in Hundred Chance – NFL, the Super Bowl, the Regular Season and Probability

There is less than a one in a hundred chance event that is taking place today. I thought I’d alert you to it as I try to restart my semi-frequent blogging exercise. The credit for the contents of this blog go to my son who told me about it, but thought it wasn’t worth writing up for others to see! So, what’s it all about?

The Seattle Seahawks are playing the Denver Broncos in a rematch of last year’s NFL Super Bowl (the ‘finals’ for American Football, for those who are wondering). The last time teams who met in the Super Bowl played each other in the next regular season games was in 1997! It has been sixteen years since that event has occurred.

Rare Super Bowl Rematch As Seahawks Host Broncos is the headline to an AP news story which appears in a number of different news outlets to capture the event. However, the headline notwithstanding, the article does not address the rarity of the event. Trey Wingo, of NFL Live tweeted –

How rare is a Super Bowl rematch the following season? Sunday’s @Broncos @Seahawks game will only be 6th such occurrence.— trey wingo (@wingoz) September 17, 2014

“…game will only be 6th such occurrence” doesn’t capture how rare it actually is. To understand how rare this even is we need a little NFL history, a little on the team structure of the NFL, how the NFL schedules games, a little NFL history and some very basic Statistics.

The National Football League (NFL) is divided into two conferences, The American Football Conference (AFC) and the National Football Conference (NFC). Each conference has 16 teams, slotted into four divisions (North, South, East, and West). Thus, the NFL has 32 teams. The Super Bowl is the championship game between the AFC and NFC champion. To become a champion you play 16 regular season games, and a few playoff games. Playoff games are only between teams in a conference (AFC teams play only AFC teams, and NFC teams play only NFC teams).

Regular season games can be inter-conference. In fact every team plays 4 inter-conference games every season. The way the games are scheduled, a team in one conference plays each of the teams from a division in the other conference on a 4 year rotating schedule. The way the games are scheduled every team in one conference will play every team in the other conference once in a regular season game every four years. This scheduling is structured and automatic. Thus there is a 25% chance that any team will play a team in the other conference in any given year.

The first Super Bowl was held in 1967, following the merger of the National Football League and the newer American Football League. Between 1967 and 1997, there was a rematch of the teams playing in the Super Bowl in the following season only 5 times. This hasn’t happened since 1997. In other words, it has taken 17 years for the teams that met in the Super Bowl to meet in the very next regular season.

So the question is, what is the probability that a game (or in probability terms an ‘event’) with a 25% chance of happening in a given year will not happen for 16 years and will occur in the 17th year? The answer is (0.75)16 * (0.25) = 0.0025, which is a quarter of a percent chance! So if you watch the Seattle-Denver game today please realize that you are watching something that is really rare.

A final note for inside the ballpark NFLers, and my colleagues who teach Statistics – in doing this calculation we have ignored the reorganization of the NFL conferences and divisions in 2002. We’ve assumed that 1997 to 2001 was organizationally the same as was post 2001. Taking that difference into account will change the result marginally, but the central story that this is really, really rare will stay on. My Stats colleagues who think it is worth making your students read this piece may want to ask them to go and research the organizational structure of the NFL pre-2002 and see how that will change this result!

P.S. The central ideas in this piece are Aditya Krishnan’s. So, I got a blog entry for the tuition payments we made!


Debate Time – I’d Like to Write Some Zingers

I’ve never been comfortable with the notion that politics is a game where the aim is to win power.

I do not buy the view that all politicians are scum bags who don’t care for the larger good. My sense is that most politicians have two hands which often work against each other – on the one hand they want to do well from a governance perspective, and on the other hand they care about re-election. The difference between the good politician and the not so good politician is in how they think about which hand is the objective, and which hand the constraint. The good politician thinks that she should maximize good governance subject to a re-election chances constraint, whereas the not so good politician tries to maximize re-election chances, subject to a minimum governance constraint.

But this evening I must stop trying to be overly analytical and must settle down to watch the game as Obama and Romney play to win. I must put my discomfort to rest and be entertained by the quadrennial sport called Presidential politics. It’s been going on for some time now and I’ve started many a blog piece based on the news of a particular day. None of them made it to the blog, because procrastination and the rest of life came in the way of seeing them to completion – even if highly delayed I will complete them and put them up as a ‘what I was thinking’ piece sometime in the not so distant future.

It is on a day like this that I hope that I was the part of a campaign where I could sit in a room with like-minded folk and come up with good one liners for my candidate, or that I could be on the staff of the debate moderator and make up the questions that would make or break a candidate’s political future. Unfortunately I am part of no campaign (nobody called and I don’t know how to get in touch with them), nor am I part of Jim Lehrer’s staff (nobody called and I don’t know how to get in touch with them), and so should be content putting up my one liners on this blog. Given that they are never going to be used, I simply provide one for each person.

For President Obama
Use any opening you get from Romney when he speaks about his competence and ability to get things done (as in I fixed the Olympics, etc, etc.) and say, “I agree with Governor Romney. He is a man of competence and that is the problem. He will be incredibly competent in executing his plan to end Medicare Care as we know it. It wouldn’t be a disaster if we elect somebody with Mr. Romney’s views if that person is incompetent, but given his ability to execute, we should be very careful.”

For Governor Romney
Look straight into the camera and tell the American people – “Give me a chance, and I will give you more than just hope. I will give you jobs, and peace, and prosperity.”

Question for Mr. Lehrer
What are the things that you must get done with no ifs, ands, or buts, failing which you will agree that your administration was a failure? Put differently, what can you promise the American public that you will get done if elected?

BTW, if anyone knows anyone who wants a one-line zinger maker for the next election cycle, please know, I am happy to interview for the job.

Memo to Penn State Board of Trustees – Please Pass it Along

Apparently Penn State’s Board of Trustees is scheduled to meet this weekend to ratify the university’s agreement with the NCAA. Yahoo reports that the Chairwoman of the Board of Trustees told her fellow trustees that they were leaders of the university, and that they needed to lead. That would be nice. And in case they plan to act on the need, I have a memo for them. It is a workable outline. The details can be filled in if they are willing to think on these lines.

To: The Board of Trustees, Pennsylvania State University
From: The guy who writes the No Consensus Here blog.
Subject: Center for the Study of Corruption in College Sports (CSCCS)
In the wake of all that has happened since the Sandusky tragedy, there are a number of levels at which the university must respond. One of these is to take a forward looking, thoughtful, intellectually rigorous approach to being able to understand the circumstances and culture which led to the tragic events on your campus. The still unfolding tragedy is one of a number of tragedies associated with college sports in America. The easy part of the analysis is to understand that these tragedies are cultivated on ground fertilized by incredible amounts of money involved in college sports, and watered by the jingoistic, emotional investment of alumni and other well wishers who want to see their institutions victorious in stadia and sporting arenas. The more difficult part is to tease out the causal financial, social, and power relations that lead to unwanted outcomes in college sports. This memo proposes a start in that direction. It proposes that Penn State University establish a Center for the Study of Corruption in College Sports.

What Will the Center Do and How Will It Do it?
This memo is not the place to outline all that is wrong and corrupt with college sports in America. Suffice to say, among the things that college sports can be charged with are that it is exploitative and ethically challenged. Different aspects of these two ‘Es’  can be studied from the perspective of many an academic discipline including economics, ethics, law, medicine, politics, and sociology. This is precisely what the center should do.

It isn’t very difficult to put the infrastructure into place. The center can start with a core group of 20 people – a Director, eight other faculty, eight post-doctorate positions, and three secretarial staff. Clearly this core group will collaborate with interested folk across the country in developing a research program. While it is difficult to predict the path that academic research will take, it clearly must be to understand different aspects of the seamy underbelly of college sports in America. The more structured mandate of the center will be to establish academic and outreach programs in a number of areas related to college sports.

What About the Finances?
I haven’t crunched the numbers, but it seems to me that If the university was to pledge $60 million (symbolism matters) then the program will be well funded. An endowment of $60 million should conservatively generate a working fund of about $3 million – a decent sum to start the ball rolling. Part of raising the money will be Penn State’s way of putting its resources where its apologies are, as it starts to dig itself out of the nightmarish circumstances in which it finds itself. Also, I think if Penn State takes this step, there will be a number of folks who will be willing to contribute to the project. I can already see the outlines of a proposal that can go to the Bill and Melinda Gates Foundation!

And Where Will You House This Center?
A fitting place to start will be somewhere in Beaver Stadium. As the center grows over time, it may outgrow Beaver Stadium, and may need a building of its own. In fact, ideally, over time, one can hope that the center does such a good job of understanding and changing the culture of college sports in America, that it no longer needs to exist. However, we all know that is not going to happen soon.

So instead of worrying about how to end the story, I request that you do the needful to establish the Center for the Study of Corruption in College Sports (CSCCS).

Penn State Football, the Death Penalty, and Drone Strikes

On November 10, 2011 I wrote a piece calling for the trustees at Penn State to “simply announce that Penn State will not field a football team for the next five years.”  I wanted this to happen because calling a halt to football sends a strong message – there are more important things than Football at State College. I further hoped (without being naive, or deluded that any of my hopes would come to pass) that Penn State would take the lead on starting a serious national dialogue on the role of sports in American colleges. And I hoped that the NCAA would join Penn State in starting a national dialogue on the role of sports in American colleges (to read that piece, click here.)

Now that the Freeh Report is out, there is a debate about what should happen to Penn State football. Fundamentally, the debate is about whether the NCAA should suspend Penn State from fielding a football team for a year or two – the so called ‘death penalty’. Really, death penalty? Give me a break. It is true that if Penn State cannot play NCAA Division I football for even a year they will have to spend quite some time rebuilding their program – but to rebuild is not death.

The argument against imposing this minor penalty on Penn State is that students and others associated with Penn State football will pay a price without having done anything wrong. The argument goes that punishing the program will penalize the students who signed up for Penn State football and who played no role in the disgusting details that the Freeh Report brings out into the open. And the economic consequences for those who make their money from Penn State football like motels and restaurants, who also did not play any role in the tragic events at State College, will be rather severe. This is a rather interesting and strange argument in a country where there is no serious public outcry against the use of drone strikes which kill innocent civilians in Pakistan and Afghanistan. The collateral damage if the Penn State program is suspended is as exaggerated as the claim that imposing the suspension is a death penalty.

So while I think that the “oh the innocent Penn State kids and others will suffer” argument is silly, I still do not think that the NCAA should suspend Penn State for a year. I think that the good people at Penn State should voluntarilyy suspend their program and detox themselves from the deleterious effects of football mania for a few years. And they should remove the statue of Joe Paterno from the stadium. Imagine how profoundly the mindset will change if Penn State football fans cannot go to a football game on Saturdays in Fall, in a stadium which no longer has a statue of  Joe Pa on its west side. The amazing thing is that the other things that the university does well will go on – the study of Mathematics, Ethics, Economics, Religion, Engineering, Business, …. all the things that should be primary in a university. Maybe people will start talking a little about the strength of Penn State’s academic programs.

Put bluntly, Penn State should act affirmatively and without coercion to put football (and other sports) in perspective – something that they enjoy and encourage, but something they can do without if the circumstances so demand. And the only way to show that you can do without something, is to do without it.

The Prediction Racket Again – Women’s Wimbledon Final

I am writing this while watching the beginning of the third set of the Radwanska-Williams Wimbledon final. Obviously I have no way of knowing what the outcome of the match will be, but there’s more to life than who is going to win.

In the U.S., one is listening to Chris Evert and some other guy whose name I don’t know tell us from the start that this match is one sided – Williams all the way. This is essentially what Pat McEnroe and Brad Gilbert said yesterday when previewing this match, Even though I am not a Radwanska supporter (never heard of her till the semi-finals) I was quite irritated that someone could be written off so easily in spite of making it to a Grand Slam final.

My irritation notwithstanding, the score in the first set and a large part of the second set made it look like they were right. However, it seemed to me that it was more a case of some points here and there that was the difference, and that the score board made the game look a lot more one sided than it really was. With Williams a point away, to take a 5-3 lead in the second set, Chrissie and her colleague were more or less ready with the appropriate questions for the post match interview with Serena. But the worm has turned – a point here and a point there which could have gone either way went Agnieszka’s way, and they are now even in the third set.

Once again, the lesson is clear! The pundits are full of it. If Radwanska wins we will hear about how brilliant she is and how she blah, blah, blah. If Serena wins, we will hear about how her nerves let Radwanska back into the game, but her winning was never in doubt. It happens every time, and we keep following their half baked predictions – why?

It’s now 2-1 Radwanska up in the third set. And for the record, nobody knows who is going to win!

P.S. At 11.35 a.m. (EST) – Serena won the third set 6-2!