Monday, September 28, 2015

Will University of Kansas Football Win Any Games This Season?

My dual personalities have two responses to the the question in our title.

Levi the KU Football Fan: Absolutely not. They will lose every conference game, most by 3+ touchdowns, and be the embarassment of the Big 12 this year. 95% sure of this.

Levi the Statistician: 47% chance they will win a conference game.
Why the different responses?  Two real reasons: the cynicism of a KU Football fan and the way low-probability aggregation works.

KU FOOTBALL BACKGROUND

I became a KU Football fan after arriving on campus to start graduate work in Fall 2003.  KU Football wasn't very good compared to my undergraduate alma mater Kansas State University, but the games where more fun to watch, for a few reasons:

  • There's a hill on campus overlooking the stadium, so you don't have to pay to get into games (beer allowed).
  • The team wasn't expected to be very good, so everyone just had a good time and good food no matter what was happening in the game.
  • They celebrated "small victories."  In one of the first games I watched, they tore down the goal posts and threw them in a lake because they beat a 23rd ranked team in the country.  
Don't get me wrong, I still follow and enjoy K-State Football, but I also see why KU Football is fun: low expectations.  Recently though, expectations have hit rock bottom.

A quick overview of KU Football over the past few years.  In the mid 2000's (2006-2008) the team got really good.  As in Orange Bowl champions, finishing season ranked in top-10, sending pro-bowl caliber players to the NFL good.  Then the team had a couple of rough (read: normal KU Football) years, the coach was fired for supposedly being abusive to players.

This leads us to the current day in KU Football.  The last five years have seen three coaches, two seasons with no conference wins, and generally embarrassing play.  Rather than relive that nightmare with description here, I'll just post the conference results of the past five years.

Yeah. 3-41.  Ouch.

STATISTICAL BACKGROUND

To think about the probabilities of a winless season, we have to look at the mechanics of a college football season.  The above chart is just the conference schedule, but there's also a non-conference schedule.  In the years prior, KU would win one of their three non-conference games, which are generally easier, against non Division 1 FBS opponents.  The problem is, this year KU has already lost all of the non-conference games this year, so we can focus on the conference schedule now.  

To calculate the actual probability of a winless season, all we really need to do is calculate the probability of losing the last nine games consecutively.  But to know that, we need to know the probability of KU winning each game.  There's not a great way to do that because the team wins so few games, that a probability of winning any individual game is unknown.  The team is more likely to beat Iowa State than Oklahoma, but how much more likely?  At this point, KU winning a game is  more of a matter of random luck, or the other team having a tragically bad day.  

The futility of the KU Football program over the past five seasons make conference wins look like matters of random luck.  What would be a reasonable probability estimate of per-game futility?   Hard to say, but we have historical win percentage in recent conference games to use: .068 (see chart above).  

FINAL PROBABILITY

Now that we have a good estimate of per game probabilities, how do we extrapolate that out over the rest of the season.  Probability aggregation. And here's how that works.  Essentially, the probability of KU losing EVERY game for the rest of the season is the product of the probabilities of their opponent winning each game (1-.068): 93.2%.  So in this case, the aggregate probability of KU losing out can be computed by (.932) ^ 9 or approximately 53%.  The chart below shows how that probability will increase over the season if they continue losing each game.


But wait, KU has a 47% chance of winning a game this season, but they will be underdogs by roughly 93%-7% in each game?  How can that be?  This is a part of aggregate sports probabilities that gives some people trouble.  It's difficult to imagine that individual events with such low odds (KU Football Victories) will ever "occur" in real life, but over time, probability theory shows us it will.  An extreme non-sports case example would go something like this:

Setup an experiment where people walk across a field and you record whether they get struck by lightning.  The odds of each person being struck by lightning will be impossibly low, let's say 1 in 500,000.  So the odds of "winning" a single game would be impossibly low, but repeat that experiment 500,000 times, and the probability of a "successful" lightning strike increases to 63%.
Here's what that looks like.


 CONCLUSION

Looking back this is a lot of weird work to do on a college football team.  But a couple of takeaways:

  • The University of Kansas football team is so bad, that we are now only able to talk about them winning in low-probability aggregation terms.
  • The University of Kansas football team, has 53% chance of going winless this year.

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