Despite all the Tebow-madness, there were quite a few other games decided in the waning seconds. With 0:26 left in the game, Joe Webb and the Vikings were faced with a 4th-and-6 from the Detroit 12, down 6. If the Vikings were only down 3, this is a no brainer: Kicking the field goal results in a win probability of 43% versus only 33% if they go for it. Detroit, however, had tacked on a field goal early in the 4th quarter and their defense came up huge, stopping Webb at the goal line (ignoring any questionably missed face mask calls on the last play of the game). Let's take a look at Detroits' last scoring drive.
With 4:21 left in the 3rd, Matthew Stafford led a 7-minute procession that began on his own 10-yardline. The Lions converted on three separate 3rd-downs to keep the drive alive, the biggest of which was a 25-yard completion to Titus Young on 3rd-and-1 from their own 19. Using our Markov model, we can see how the drive developed:
The two biggest conversions were the aforementioned Young completion, which chopped the 63% punt probability in half, and a 7-yard 3rd-and-6 completion (play 9) to Brandon Pettigrew. Before the Pettigrew conversion, there was a 46% chance that the drive would end in a punt; after the catch, that probability dropped to 10% and the scoring probability jumped to 61%.
The Lions were ultimately stopped on a 3rd-and-2, took a delay of game penalty to make it 4th-and-6 and kicked the field goal on 4th down. Using Brian's nifty 4th Down Calculator, we can analyze Detroit's decision to kick the field goal. In terms of efficiency, going for it on the 4th-and-1, before the delay of game penalty, converts at 68% giving a total of 4.21 expected points. A field goal converts very close to 100%, yielding 2.39 expected points. Since it was late in the game, win probability is equally important in making the decision. Both going for it and kicking the field goal result in a 97% win probability; the break even point in terms of making the decision is a conversion rate of 66%.
Given a late surge by the Vikings, the field goal ended up making a substantial difference - although a 4th-down touchdown conversion would have made it a three-score game. Because of the length of the drive, the Lions' win probability increased by 14% which proved to be substantial.
So, the question becomes, in a situation where you are almost assured victory, do you take the guaranteed 3 points or follow expectation? Since the decision has a negligible affect on your team's chances of winning the game, a decision-maker cannot really be faulted one way or the other - even if the math leans ever-so-slightly toward going for it.
Keith Goldner is the creator of Drive-By Football, and Chief Analyst at numberFire.com - The leading fantasy sports analytics platform. Follow him on twitter @drivebyfootball or check out numberFire on Facebook.