David writes in to ask, "It seems to me that Detroit would have been better off going for a two-point conversion after their kicker got injured, rather than having Ndamukong Suh attempt the PAT.
What kind of confidence should Detroit have had in Suh's leg to make kicking make more sense than going for two?"
With Lions' place kicker Jason Hanson out due to injury, rookie defensive tackle Ndamukong Suh was called upon to attempt an extra point. Suh was chosen because he had won a place kicking competition in training camp to be the back-up kicker. Suh hit the right upright and missed the extra point, which turned out make a crucial difference in the game.
The Lions had scored 6 points to take a 3-point lead, 13-10, with 9:04 left in the 3rd quarter. A successful extra point would make the lead 4 points, and there can be a world of difference between a 3- and 4-point lead.
A 3-point lead at that point of the game would give the Lions a 0.62 WP. A 4-point lead would give them a 0.66 WP. And a 5-point lead would give them a 0.69 WP.
Assuming the Lions' chances of success with the 2-point conversion isn't too far off from the league average (48%), the total expected value of going for 2 would be just over 0.65 WP.
We can solve for the break-even probability of success for the Suh extra point needed to equal the expected 0.65 WP for the 2-point attempt. The math looks like this:
0.6536 = 0.66x + (1 - x) * 0.62
So head coach Jim Schwartz needed to have confidence enough that Suh had an 86% chance of making the extra point.
...But, I suspect part of the marginal benefit of the 5-point lead over a 4-point lead is due to the fact that one more FG could put your team up by 8, which either puts the game out of reach of a single touchdown or forces the opponent to go for 2 points to tie. With the kicker injured, this is not likely. Any more scoring by the Lions would have to be by touchdown. That's really going to affect all the WP numbers, not just for the 5-point number. But as a quick-and-dirty estimate, let's assume that the value of the 5-point lead is the same as for the 4-point lead. In that case, Schwartz would only need to have a 48% confidence level in Suh's leg--the same as the 2-pt conversion probability.