The NYT has an interesting article about the Pete Carroll's decision to pass on the goal line as it pertains to game theory. They conclude that passing may not have been the wrong call after all. It's all about randomness and keeping the other team guessing. Which makes me think tat maybe they should have gone play action. This article may be stuck behind a paywall for you, but it's worth clicking.
It's the biggest moment in your N.F.L. coaching career: 26 seconds remain in the Super Bowl, your team is 4 points behind, you have the ball just one yard short of the end zone, it's second down, and your team has arguably the N.F.L.'s best running back. What's your call? Run or pass?