The Washington Post had an interesting article on sports and the probability of winning depending upon strategic choices during a game or match. I have often noted the manner in which most coaches seem to make mathematically (in terms of expected value of the outcome based upon probability) incorrect strategic choices at the end of games. For instance, at the end of the 2006 NFL season, Cincinnati was playing on the road at Denver and needed a victory to get into the play-offs. They scored a touchdown in the last minute to get within one point and then, instead of going for a two point conversion to possibly win the game, they instead went for the tie, botched the kick and missed the play-offs.
In general, we should expect road teams to go for the two point conversion to win, rather than settling for a chance to win in overtime, and yet, even the most casual viewer of NFL football can tell you that this almost never happens. Coaches seem to overestimate the value of "momentum" which is derived from being the final team to score in regulation.
In basketball, you often see teams who are ahead by three points during the last ten seconds of the game, make the mistake of not "intentionally but unintentionally" fouling the other team, which gives the team with the ball only two shots and makes it difficult for them to have a chance to win, given the lack of time left.
Instead, they give the opponent a relatively uncontested three point shot which is often a better percentage than making three consecutive free throws would be.(For example, even an 80% free throw shooter has only a 51% chance of hitting three foul shots in a row. A 70% free throw shooter, which is about the norm in college basketball, has only a 34% of making three consecutive free throws, which is almost certainly a lower percentage than an uncontested three pointer.
There are many more examples, probably even some interesting ones from golf. I expect this whole line of inquiry to become a big deal in sports, in the same way that moneyball transformed the way fans think about baseball. My gut feeling is that certain coaches, like Dean Smith for example (a college math major), who are known for winning big games in the clutch, may have simply had an advantage in analyzing the probabilistic elements of endtime play.