After one of the more exciting and controversial fourth quarters in recent memory, it's probably safe to say that the first faint odor of victory was not smelled by Cowboys fans until Dan Bailey's extra point put the home team up 24-20 with only 2:32 left on the clock. With a four-point lead, and the field goal option off the table, most defenses–that aren't facing John Elway in 1987–can keep a team out of the end zone for at least a couple of minutes.

And in fact, the Cowboys did have a very good chance of winning the game after Bailey split the uprights. According to Advanced Football Analytics' Win Probability Calculator, in a game between two evenly matched teams, a team that is down by four points with 2:32 left in the game and 80 yards to go only has a 26% chance of winning the game. Sounds about right.

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But what if he hadn't made the extra point? In this alternate universe, Jerry Jones–after cutting the long snapper, holder and kicker on the spot–would have broken from Gov. Chris Christie's sad embrace to stare upon a field where the Lions now had an incredible, hope-inspiring... 18% chance of winning.

[record scratch]

Wait, what? So, according to this calculator, by making the extra point, the Cowboys' chance of winning actually went down by 8%. How could that be?

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LetsRun.com, your leading source of running- and kicking-related content, asked Brian Burke, the founder of Advanced Football Analytics, if he could do a writeup on this question. Here was Brian's response:

I probably wouldn't do an article on it, but here's what's going on. Teams down by 4 are more aggressive than teams down by 3. Down by 4, teams have no choice but to go for a TD to survive. But teams down by 3 see a tie as an intermediate victory and often settle for a FG attempt, which coaches often mistakenly think of as automatic. Playing for the TD is closer to the optimum risk-reward trade-off for an offense, so aggressive offenses tend to win more often.

(There is also some noise in the model, so it isn't always perfect. That's an important disclaimer.

(Presumably the "noise" in this model is the sound made by 100,000 Cowboys fans rushing the field and owner's box if Jason Garrett ever took a knee on an extra point with a three-point lead.)

But this noise–and the absolute dead-fucking certainty that no NFL coach will ever intentionally forego even a single point in our lifetimes–notwithstanding, there is a certain intuitive appeal to this argument. I mean, how many teams that are down by three ever really seem like they're trying for a touchdown? And if you assume that three points really only buys you a ticket in the 50/50 raffle that we call overtime, an 18% chance of winning seems correct.

Game theorists refer to this as the "don't kick the dog" problem. Actually, no they don't–I just made that up. But that's what they should call it, if it even exists.