The Statistical Likelihood of Winning the AFC East

Every year, every team has two goals. The first is to win the division, as this ensures a playoff spot, and the second is to win the Super Bowl.

Since 2001, the New England Patriots have won the AFC East ten times out of a possible twelve. The other two were the New York Jets in 2002 and the Miami Dolphins in 2008. With Tom Brady at the helm, the Patriots are incredibly likely to win the division every year. In fact, since 2001, they have not had a losing season.

So that got me to thinking about the likelihood of winning the AFC East. Is it possible for one of the three other teams to beat out the Patriots? Of course. But what is the likelihood, the actual percentage? The easiest way to do this is by calculating the likelihood the Patriots will win the division, as they are the most likely (it's also difficult to look at the Jets individually because there is so little data to go by, as they haven't won the division since 2002. The Patriots offer a much clearer track record and larger data set). Whatever is left is the probability of the three other teams.

There are nearly infinite number of things-Brady's age, the receiving weapons he will have, injuries- that would need to be considered to have a "true" percentage, many of which cannot be enumerated, but one rough guide is to use what's called Bayes' Theorem. As a side note, I'm note sure that those other factors that I previously listed will affect the ultimate percentage that significantly. If the Patriots will win 90% of the time, the 10% of the time they lose will invariably account for those possibilities.

Bayes' Theorem was invented by Thomas Bayes and is heavily used by statisticians such as Nate Silver to predict conditional probability. It is one of the most fundamental formulas used in statistics to predict the likelihood of an event occurring. Football is more difficult to predict than possibly any other sport, but it is not immune to certain fundamental truths, such as that a consistently good team is more likely to win the division than a consistently bad team. Today, we will try to measure that likelihood.

The theorem involves three known quantities and one unknown quantity (that is, the end result we're looking for). It tells you the probability that a theory is true if some event has happened. For example, an example Silver has used is to calculate the probability of your significant other cheating on you if you've discovered a mysterious set of underwear in your apartment. For the purposes of this hypothetical, let's use the conditional event as "Bill Belichick will be the head coach all sixteen games this season." The reason I've chosen this event is because the one constant throughout the past twelve years has been Belichick. Even when Brady was injured, Belichick still coached a successful team.

The formula itself is (xy)/((xy)+(z(1-x))). So that means we need an X, Y, and Z.

The X variable is the initial estimate of how likely it is the Patriots will win the division before the season begins. This is a guesstimated number, what you think the likelihood is before anything actually happens. I am going to go with 83%, as that is the 10/12, or the number of times the Patriots have won the AFC East, ten, in the past twelve years. I think that's a fair number, as past success is generally a good indicator of future short-term success. We obviously can't use that number to predict the Patriots in the long-run, but if you've been great for the past twelve years, you're obviously likely to be good in the near future.

The Y variable is the probability of the Patriots winning the division as a condition of the hypothesis being true. Our hypothesis being, of course, that Belichick coaches all sixteen games. It's incredibly doubtful that Belichick doesn't coach all sixteen games, but something, theoretically, could happen (sex scandal, health issues, etc.). So let's put that percentage at 98%. It's almost certain that he's going to coach all the games, but it's possible he doesn't.

The Z variable is the probability of the Patriots winning the division as a condition of the hypothesis being false. Whereas the earlier numbers are easier to predict, what about if Belichick doesn't coach all sixteen games? This is obviously really difficult to calculate. One method would be to look at the Patriots' record before he became a head coach, but I don't know that you can truly do that on a Brady-less team that was so vastly different than what he's built the past few years. This is where some of you might disagree, but if Belichick weren't the coach, I'd put their chances at 20%. This is a very subjective number, so you can fill in your own number if you disagree.

Using the formula, and the three variables we just calculated, we can come up with a rough number of a 95.98% likelihood that the Patriots will win the division, assuming Belichick remains their head coach. That means that, effectively, you can simulate this season ninety-six times, and the Patriots will win all of those times. But four of those times, either the Dolphins, Jets, or Buffalo Bills will win. So, I'm saying there's a chance.