As some of you may know I am a big Patriots fan. Yesterday the Patriots lost to the Giants. It was pretty painful. But the midst of it all - and in between flashbacks to the Superbowl-That-Didn't-Happen - I started thinking. Mostly to distract myself from the pain as I did this over and over and over again: 

See, the weird thing about the Patriots this year (and the last few years) is that the team has been consistently inconsistent on both sides of the ball. Earlier this season, when the Patriots offense was setting records for scoring, the defense was setting records for being scored on; the Patriots barely squeaked out with shootouts in games they should have won handily.

Then, last night, the defense stepped up and held off the Giants for a scoreless first half...but the Pats offense itself was held scoreless as well. Through the second half, the Patriots would make a stop, and then have to punt; then, they would score, and immediately give up a score themselves.

That's when I realized that the 2011 New England Patriots could be roughly modeled using the following equation:

k = (o)(d) +/- (r)(s)

where:

• k = a constant value of the team's actualized potential to be good
• o = the offense
• d = the defense
• r = a coefficient of random chance
• s = special teams

Thus, how good the Patriots are is distributed proportionally across the offense and the defense, plus or minus the dice roll of Julian Edelman doing something awesome or horrific on any given play (it's a loaded die) (and it's loaded on "horrific").

There are obviously a few more complexities here. For example, the degree to which other teams match up against any given manifestation of k depends on the opponent and the game. And this model, like any model, is a simplification: it doesn't truly describe the ability of, say, Kyle Arrington to make a terrific pick on one set of downs before failing miserably on the next, though of course such variations are themselves merely another iteration of k.

Readers of this blog - MIT applicants and students - may be able to help me further refine this model to account for additional complexities, such as the chance of Vince Wilfork catching an interception because he sees the football and reflexively thinks it is a Christmas ham, or the chance that Tom Brady sees his own reflection in the shine of an oncoming linebacker's helmet and gets so distracted by how handsome he is that he forgets to dodge the sack. 

However, one thing is true:

The constant value of k, no matter how it is composed at any given period of time, is almost certainly insufficient to beat a good team in the National Football League.

Ugh.