ESPN Stats & Info did some great research on "icing" the kicker. It was brought on by the Cowboys essentially losing two straight when their kicker missed a potential game winning or tying FG after being "iced." Against the Cardinals, he was iced by his own coach and against the Giants he had his attempt blocked. Just in case you didn't know "icing the kicker" is when a coach takes a timeout moments before a kick.
The theory is that if you give the kicker more time to think about the kick and disrupt his rhythm, the more nervous he'll become. In reality, it doesn't appear to be true. In fact, kickers who were "iced" in the last :10 of a game were more accurate from every distance than kickers who were not iced. The biggest spread comes on 50+ yard kicks. Kickers who were iced made 77.8% of their kicks, while kickers who were not iced made only 37.5%.
So a coach is more likely to get a FG kicker to miss a kick at the end of a game by not icing the kicker, which begs the question... why do they still do it? My guess? It's game theory.
I once read this report that an economist did studying penalties in soccer. In that situation, the kicker stands just a few feet away from the goaltender, who is protecting a giant goal. The advantage is far in favor of the kicker. Usually, the goaltender just hazards a guess as to which way the kicker will go and dives that direction. Usually, kickers will fire the ball to either corner of the net, but the study found that those balls kicked straight down the center actually had the highest percentage of success.
So this economist talked to players about why they wouldn't kick the ball right down the middle more? The answer he got was that if you kick the ball down the middle and it gets saved, you look like a fool. If you fire the shot wide or the goalie makes the save when you're shooting for the corner, you may not get the goal, but you look kinda cool for attempting it. So the game theory here revealed that players are worried about more than just what the optimal way to score is. How they look doing it also affects their decision making.
My guess is that NFL coaches are the same way. If you call a timeout and try to ice the kicker and he makes it, no reporter will ask you "why did you that?" Fans will not call up sports radio to blame you for the kicker making the kick, because at least you tried, even though in reality you probably only made it easier for the kicker.
But if you do nothing and just let the guy kick the ball and he makes it... You will have to answer the question "why didn't you call a timeout?" Fans will call sports radio and claim that if you had just iced the kicker, he would have missed the kick and your team would have won the game. Damn those stats that say otherwise!
So that's the game theory here. Coaches' decision making processes aren't just about their own experience or what stats tell them is the right call in this situation. If it was, they wouldn't ever try to ice the kicker. These guys are in charge of everything that happens with the team. Every play is designed, planned and called painstakingly for every situation. Their predisposition is to always do something... which is problem when doing nothing is the call that needs to be made.