Re:Liverpool's title win has completed a mysterious Fibonacc...
by dmurray on Friday May 02, 2025 @03:11AM
(#43867024)
There is no "the number of teams", because this league has a promotion/relegation system. There are 20 teams in the league at any point in time, but 150 or so professional clubs and tens of thousands of others who participate in the league pyramid and have at least a theoretical chance of promotion and ultimately winning the premier league.
There's a fair bit of churn in these numbers: 51 clubs in total have been in the premier league in the period of interest (the last 33 years).
After some small threshold, I think the number of clubs doesn't matter. You could get the same result if the top 100 or all 40,000 clubs played in the same league every year, ignoring the minor scheduling problem this would cause. Resources are distributed approximately in a power law, as you suggest. What matters is the level of inequality near the top, which is apparently such that each team has approximately phi times the resources (measured over a long period) of the team below.
There's a fair bit of churn in these numbers: 51 clubs in total have been in the premier league in the period of interest (the last 33 years).
After some small threshold, I think the number of clubs doesn't matter. You could get the same result if the top 100 or all 40,000 clubs played in the same league every year, ignoring the minor scheduling problem this would cause. Resources are distributed approximately in a power law, as you suggest. What matters is the level of inequality near the top, which is apparently such that each team has approximately phi times the resources (measured over a long period) of the team below.