Chris asked the following:
The Saints had 4th and 3 on the Steelers 13 with no timeouts and 12 or 13 seconds left in the first half. The Saints lined up for a field goal and then changed it up to show that they were going to run a play. The Steelers called a timeout, and after the timeout, the Saints kicked the field goal.
In the post-game press conference, Sean Payton confirmed that the Saints were actually prepared to run a play and weren't just trying to get the Steelers to take a timeout.
I guess my question is this: would this fake field goal be a) a boneheaded call, or b) the most boneheaded call ever? I guess that Payton might have had some kind of spectacular play called, but it would have to be pretty spectacular to overcome the horrible odds that were against it. Only a touchdown (from the 13 yard line) would have given them a much better expectation than they had before the play, and most other results would have given them a far worse expectation.
At the end of the half, it's a slightly easier analysis because you don't have to kick off and a FG is worth a full 3 points and a TD is worth a full 7. Also, you don't need to worry about the EP value for missing the FG or failing to convert. It's just zero.
FGs are good from the 13 91% of the time, so a FG attempt is worth 2.7 EP.
Therefore, to go for the TD, you'd need the EP for going for it, regardless of whether it's a fake FG or normal scrimmage play, to be at least as high as the EP for the FG attempt. So:
x = 0.39
From the 13, a normal play from scrimmage might have a better chance, but I doubt it. The baseline success rate for 4th and 13 inside the 20 yd line is only 20%. As good as Brees and the NO offense is, I doubt they'd have better than double the baseline success rate.