Given also the fact that many significant events seem to occur with on distributions with fat tails, assuming normal distributions may lead you to be systematically overconfident in your predictions. Though it’s still probably far, far better than using binary estimates.
You could make predictions from a t distribution to get fatter tails, but then the “easy math” for calibration becomes more scary… You can then take the “quartile” from the t distribution and ask what sigma in the normal that corresponds to. That is what I outlined/hinted at in the “Advanced Techniques 3”
Given also the fact that many significant events seem to occur with on distributions with fat tails, assuming normal distributions may lead you to be systematically overconfident in your predictions. Though it’s still probably far, far better than using binary estimates.
You could make predictions from a t distribution to get fatter tails, but then the “easy math” for calibration becomes more scary… You can then take the “quartile” from the t distribution and ask what sigma in the normal that corresponds to. That is what I outlined/hinted at in the “Advanced Techniques 3”