But you asked me where my ideas come from, not where expected distributions come from.I answered where my ideas come from, and you respond with where expected distributions do and don't come from.Your responses indicate you are confused about both what you asked and what I answered. Despite you saying you understood perfectly, it seems you still don't.So tell me, why does everyone else get to make some sort of point about EPO, causing the one data point at the very tail of the distribution, without doing any math and showing their work? If someone says, EPO causes 9 minutes of benefit, or saying the real question is what kinds of drugs did Paula take to run 2:15, why isn't "Mr. Obvious" saying, hey wait a minute -- show us your math, show your work, show us your assumptions?Like everyone else, I can form an opinion about the potential causes, and unlikely causes, of the tail. I can expect that both clean peak performance levels, and EPO benefits, can be characterized by random distributions, without having to provide the equations. A 3 minute gap from these two identified sources would be an extremely low probability event, but of course, not impossible. I suppose, I could make assumptions, about averages, standard deviations, distributions, etc., and do some numerical calculations to illustrate the point. But this would be highly dependent on my assumptions. And it is not necessary, because thanks to my mathematical and statistical ability and intuition, I already know the outcome -- a low EPO benefit scenario is more likely to produce a big outlier, due to other, unique causes, independent of talent and drugs, than a high EPO benefit, that would mask or overshadow these other causes.If this is a nonsense statement that doesn't mean anything, then all opinions about EPO causing improvements in the marathon are nonsense statements that don't mean anything, because they all have the same basis, based on someone's notions of something where they do not have any data, and have not yet done the math and shown their work.
Mr. Obvious wrote:
That's where expected distributions come from.
If you want to make some sort of point about EPO based on expected distributions, you should actually do the math and show your work.
Just saying it is based on your ideas about fundamental notions is a nonsense statement that doesn't mean anything.
You seem to have a very poor understanding of math and statistics. In particular you seem to have a poor understanding about what conclusions you might be able to show from one data point at the very tail of a distribution. This is not where the power of statistics lies.