It's not a complete coincidence. Very many sets of random numbers are uniformly distributed on a logarithmic scale. See for example Benford's Law.
Fibonacci numbers are just a rounded version of phi^x. So the only coincidences are 1. that the number of teams is such that phi is a good base, and 2. that the rounding all happened to go the right way.
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.
In this case, it's a complete coincidence. I did this for UEFA Champions League winners over the last 33 years and found no Fibonacci sequence at all. I'm pretty sure it won't be found easily in other sports or competitions either.
A good observation, but it is also a coincidence of sorts that the sport lends itself to this distribution. Does it mean the league is especially fair? Or not fair? You wouldn’t expect to see this distribution in games of pure chance, or of pure monopolistic dominance.
It's absolutely not a game of pure chance, nor a level playing-field each year. Owners can decide how much to invest each year (unlike the US MLS) subject to some limits (UEFA Financial Fair Play Regulations) on how much. And many of these teams have been bought/sold/had stock market IPOs multiple times in that period. And also each team has widely differing revenue streams from TV rights (across all competitions, including Champions League and Europa League) and merchandise sales, with which to fund player salaries/transfers and stadium renovations.
If you redo this table to quote PL first/second/third/fourth position per £ pound invested, (or total points in a season (3 for a win, 1 for a draw, 0 for a loss)) you get a different picture, e.g. for 2023-4 season: https://www.dailymail.co.uk/sport/football/article-13446423/...
And even the Financial Fair Play regulations are nowhere close to the measures common in most American sports, like salary caps. They’re mostly intended as a speed bump for foreign oil magnates and Red Bull throwing all their money into their clubs and automatically winning everything.
Not even that, it's to prevent clubs going bankrupt all the time.
Without rules, every club is going to invest huge sums betting on achieving a top result that would give return on investment, and only a few can achieve that each year.
Investors throwing lots of money at the sport is a feature, not a bug, from the viewpoint of the people involved in the sport. So by itself that doesn't need to be prevented.
On the other hand you have the selection effect that someone only writes if there is a nice Fibonacci sequence somewhere in the top 30 or so leagues. So I agree, the distribution favors probably power laws with (1+ 2/3)^n but that it happened now is still kinda random.
Benford's law is as it is because it reflects the structure of our decimal system having a logarithmic pattern where each order of magnitude gets its own column. It's purely a function of the way we represent the data itself, not the underlying numbers. I don't think these football scores have anything to do with it. Likewise yes in nature this pattern appears a lot due to its great space-filling without overlapping property which has been evolved towards. The football scores thing is pure fluke.
The common definition of Benford's Law is written in terms of base 10 (or 100, 1000, etc. for subsequent digits), but the underlying principle applies to any base (I'm pretty sure this includes non-integer bases, though I'm not sure about negative bases).
When there are more teams but the min/max skill is unchanged, they must be closer together, so the base is lower. When there are fewer teams, farther apart, the base is higher.
The number of teams is constrained by "we need enough teams so there's actually variety" and "we can't have so many teams that we can't keep track of them all".
Fibonacci numbers are just a rounded version of phi^x. So the only coincidences are 1. that the number of teams is such that phi is a good base, and 2. that the rounding all happened to go the right way.