This is where the "math" guys err- this isn't just an "average" play call, this is a play call under these UNIQUE circumstances which have never previously occurred, nor will they ever occur again. You can run all the numbers you want, but there's no way you can say difinitively that the "correct" call on 3rd and 5 in THIS situation is to pass. Impossible.
Sure, they might throw an incomplete pass. Or, they might run for a 70 yard TD. Or the center might snap the ball over the QB's head and out of the back of the endzone for a safety. There are an infinite number of things that could happen on this one particular play, which I agree has never happened before and will never happen again exactly as it will in this particular moment. The same could be said for every play in every game, ever. And
on average, passing plays are better at picking up more than 5 yards than rushing plays. If my opponent needs 5 yards, I'd strongly prefer that he try to gain those 5 yards by rushing. It doesn't mean I'm guaranteed to stop him if he does. I'm just more comfortable with my chances.
Again, this is all subjective- opinion. Just about every play in the NFL has an impact on the rest of the game- there is no way no know in advance the outcome of most play calls. You haven't made any conclusive arguments why the information gained is an enormous net positive for the trailing team either. Both teams will have access to the same exact information. How is that information more valuable to one side over the other?
The fact that the information is more useful to the trailing team is almost indisputable. I'm honestly surprised that anyone has even tried to attack that part of the problem. The trailing team gets so much more benefit by knowing than the winning team. The team in the lead has one primary goal - hang on to the lead and run out the clock. Whether up by one or two, that goal doesn't change. How they attempt to achieve that goal might change a bit, but as has been pointed out, I think even that change inadvertently benefits the trailing team. Just like playing prevent defense protects against a quick-strike score but sacrifices boatloads of yards in the process. A team up by two scores, if anything, will play more conservatively - they need to just take time off the clock - while a team up by what is potentially just one score still has the primary objective of taking time off the clock but will also try a little more aggressively to put additional points on the board. But I agree that this bit is somewhat subjective, and some might disagree. That's fine, it's a perfectly valid disagreement. The point is that their goal is essentially the same either way. Whether up by one score or two, they're just trying to take as much time off the clock as possible.Meanwhile, the offense has two competing goals. If they need two scores, they want to get the first one as quickly as possible. On the other hand, if they just need one score then obviously they still want to score, but in the process they ideally want to take as much time as possible and leave little or no time left for the opponent to kick a game-winning FG. Unfortunately for the trailing team, they have no idea whether or not they need one score or two if they kick the PAT first. So that information is a zillion times more useful to them than it is to the team in the lead.