Saturday, January 28, 2012

What are the odds of that!

So, last year at the AP Reading, we played putput golf at one of those kitschy golf centers in Daytona Beach. Somehow, I managed to trap the ball on a cylindrical totem pole on a steep incline on the 8th hole. No! It is not a testament to my skill since I very smartly brought up the rear in our six-some. However, how does one manage to trap the ball on so impossible a spot? I had been thinking about the occurrence (probably far more than it merited), because when I came back to the hotel I wrote about it… Months later as I am clearing up the random thoughts that I am given to confiding to my computer and I have come across this one. I am not sure how much clarity in this train of thought was induced by the half dozen G&Ts I consumed before I put fingers to keyboard…

According to Bayes' theorem, the probability of event A (trapping the ball on the totem) given event B (finding a totem on a green) depends not only on the relationship between A and B (i.e., finding a totem on a green) but on the absolute probability (trapping the ball on the totem) of A not concerning B (i.e., trapping the ball on the totem in general), and the absolute probability of B not concerning A (i.e. the probability of finding a totem on a green). Thus, if 95% of the putts sucked so much as to trap the balls on the totem, this could be due to 5% false positives, 5% false negatives (good putts), or a random mix of false positives and false negatives. Using Bayes' theorem allows one to calculate the exact probability of trapping the ball on the totem, given a consistently bad putt for each case, because the probability of B (finding a totem on a green) will be different for each of these cases. It is worth noting that if 5% of bad putts result in a trapped ball, then the probability that an individual traps the ball on the totem is rather small, since the probability of totem actually showing up on a putting green is closer to 1%. The probability of a totem on a green is then five times more likely than the probability of trapping the ball on the totem itself. Answering your question, it is entirely possible!

Clearly, I have far too much time on my hands….!