2 ms·

> long-tailed power scale Yeah, but a power scale implies that there are outliers at any distance from the median. That can't be true, so the model is defectiv

> long-tailed power scale Yeah, but a power scale implies that there are outliers at any distance from the median. That can't be true, so the model is defective.

somenameforme 4y ago
Except it is true! That is precisely what I was getting at with chess. Right now the #1 player in the world is rated 48 points higher than the #2 player, and this difference is typical and often even more extreme. And the #2 is rated almost 20 points higher than the #3 player! I could try to explain what those numbers mean mathematically, but I think there's an even easier way to get the gist of it. There are hundreds of of thousands of FIDE rated players. That #1 player's rating is 2859. For him to be 50 points higher than the #2 player is insane in terms of any notion of broad-level approximate human equality, but perfectly normal in the not-even-remotely-equal reality of what we see in chess. And this is mirrored everywhere, even in sports where the physical limitations on the body are presumably more limiting than the cognitive ones. Running is nice because it's a field where we are going to miss close to 0 outliers, and you can fairly compare generations regardless of time. Imagine we take Usain Bolt at his peak, and have him run a 200m race against the 200th fastest human to have ever lived at his peak. People might expect this to be a pretty close race. In reality? He'd finish about 9.8 meters, more than 32 feet ahead of the other guy. It would look like 'fast' guy vs 'meh, more or less average' guy. When in reality that 'more or less average' guy is one of the fastest humans to have ever lived!
- 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 ago
    You 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.

> long-tailed power scale Yeah, but a power scale implies that there are outliers at any distance from the median. That can't be true, so the model is defective.

somenameforme 4y ago

Except it is true! That is precisely what I was getting at with chess. Right now the #1 player in the world is rated 48 points higher than the #2 player, and this difference is typical and often even more extreme. And the #2 is rated almost 20 points higher than the #3 player! I could try to explain what those numbers mean mathematically, but I think there's an even easier way to get the gist of it. There are hundreds of of thousands of FIDE rated players. That #1 player's rating is 2859. For him to be 50 points higher than the #2 player is insane in terms of any notion of broad-level approximate human equality, but perfectly normal in the not-even-remotely-equal reality of what we see in chess. And this is mirrored everywhere, even in sports where the physical limitations on the body are presumably more limiting than the cognitive ones. Running is nice because it's a field where we are going to miss close to 0 outliers, and you can fairly compare generations regardless of time. Imagine we take Usain Bolt at his peak, and have him run a 200m race against the 200th fastest human to have ever lived at his peak. People might expect this to be a pretty close race. In reality? He'd finish about 9.8 meters, more than 32 feet ahead of the other guy. It would look like 'fast' guy vs 'meh, more or less average' guy. When in reality that 'more or less average' guy is one of the fastest humans to have ever lived!

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 ago
  You 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.