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JGWeissman comments on Ability to react - Less Wrong
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For activities like competitive sports or extemporaneous acting, I could see what you're saying. But, I don't think that the quality of different performances of a given show, in which the actions are the same each performance, would be scattered in a Gaussian or other randomized way. A performer generally expects only to improve on a particular show, as long as one applies oneself, as will have been happening during the rehearsal period leading up to the performances. If there is a reduction in performance quality on a given show, either the performers are not applying themselves with the same intensity (as I suggested), or there is some other explanation.
Now, if you compared performance quality across different shows and different seasons, you might see something more like a random scattering around a mean.
Whatever factors, including intensitity of actors applying themselves, affect the quality of performance, themselves will have some distribution that can be mapped to a distribution of performance quality. If a particularly good performance occurs because all the actors had a good previous day, got good sleep the previous night, and applied themselves with full intensity, then the following performance is not likely to repeat that confluence of favorable factors and therefor is not likely to repeat the same quality of performance.