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A true power law would say that there's a diminishing number of chess-players the further out you go along the long tail. But in practice, there are zero chess-
by denton-scratch 4y ago
A true power law would say that there's a diminishing number of chess-players the further out you go along the long tail. But in practice, there are zero chess-players better than the world champion. It may look like a power law within some window, but power laws don't have a cutoff point.
That is what I'm saying about smart people; I don't accept that there are people arbitrarily smarter than the average. My guess is that the cutoff is somewhere around double the average (modulo your method for measuring smartness).
- somenameforme 4y agoYou can see various visualizations of chess ratings here: https://nycdatascience.com/blog/student-works/visualizing-fide-chess-rating-list/ https://nycdatascience.com/blog/student-works/visualizing-fi... It is a textbook power law. There are only 2 humans better than 2800, and one is pushing near 2900. Then there are only 37 humans from 2700-2799, 168 from 2600-2699 and so on with an increasingly exponential gain in brackets near the median. And each bracket tends to be exceptionally dominant of brackets just one below, let alone more. A finite sample means any distribution will have a min and a max. If the odds of a Magnus are 1 in 10 billion, then we can expect to see one person of a roughly proportional skill every generation or two. But if the odds of the next tier of exponentially dominating outlier out are 1 in 500 billion then any given generation of humanity would be unlikely to see one, at least not until we start dramatically increasing our population sizes.