Hey,From video 9, bayes_stats:How do you go about approximating the std deviation and mean for each statistic? This seems key to the lesson here and would have a significant impact on results, is there a way to do this step that is more concrete? Would a better way to do this be to filter for each situation where opponents have had>100 opportunities for some situation? (or some number) and calculate the std dev and mean from this data?This obv falls short if we don't have any opponents with >100 pops for some situation. In this event, what would you suggest would be a reasonable approach to determine these numbers? Thanks for your time.
Hi! sorry about the delay in getting back to you. For some reason I thought i had already answered it a while back, it seems i never actually hit the reply button :(
In any case, I think the issue is that it is very hard to do better than the methods i present in the pack. For instance your method would leave your data biased towards regs and away from complete randoms. The only other way I can think of is to try to do a weighted sum calculation, calculating something like:
Sum[ hi*((xi-u)^2) ] / [Sum[hi]
with xi being the observed frequency of the statistic we are interested of villain number i, u being the mean of the statistic, and hi being the number of hands for which it was possible for our villain to perform the action we are interested in, and the sum being taken over all villains. I don't see an easy way of computing this though as getting all of these numbers in a convenient form from PT4 won't be super easy and will still require a big sample...
In practice I think it's important not to lose the forest for the trees. In the end a difference of a few percent won't detract from your answer and will still give you a lot of insight into the situation. I tend to fall into the school of "subjective Bayesians" and believe that in practice our prior distribution will contain subjective judgements of opinion that cannot be rigorously justified. In my opinion this is a good thing as it gives us room to use our overall poker knowledge and expertice to good practice--if you feel you lack some of this you can ask a bunch of study buddies or your coach and try to pool together commone expertice. I think while it's good to be rigorous and try to get exact answers, in the end I think we shouldn't be looking to spend huge amounts of time increasing our precision unless we have a very good reason to--in this case I think it's unlikely that our strategy will be sensitive to villain's frequency to a few percentage points anyways so even if we are somewhat off in our standard deviation we will likely not be losing too much due to this mistake. We will certainly be losing more if we had not performed an estimation in the first place and were just guessing as to the estimated frequency.