Attention geeks: As detailed yesterday, I am pondering how to address the issue of black-swan events. It seems to me that the correct approach is not to assume a larger value for the Meta-analysis standard deviation (MMSD), but to use a distribution that has fatter tails.
I am currently considering using the t-distribution. For instance, the t-distribution for a 2.0-sigma lead and 3 degrees of freedom gives tcdf(2.0,3) = 0.93, a 93% win probability. The normal distribution gives normcdf(2.0,0,1) = 97.7%. (Recall that I very roughly estimated the black-swan frequency as about 8%.)
Under current conditions, the re-elect probability would then be tcdf(3.0/2.2,3) = tcdf(1.36,3) = 87%.