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.
ganiszulfa · 1h ago
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.
brookst · 2h ago
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.
smcin · 1h ago
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/...
philwelch · 13m ago
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.
emmelaich · 1h ago
Winners get money and money buys good players. So I think that's the source of the distribution.
notphil · 1h ago
> that the number of teams is such that phi is a good base
Any theories why this might be the case?
> 2. that the rounding all happened to go the right way.
+1. See how close some title races are: 2013-2014 comes to mind.
o11c · 11m ago
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".
class700 · 32m ago
2018-2019 and 2021-2022 were decided by a point, 2011-2012 on goal difference.
xbmcuser · 27m ago
Its quite a good coincidence as the other 2 teams with 1 victory had no chance as 1 was already relegated previously and the the 2nd will be relegated . So any other team apart from Liverpool winning would have stopped the sequence from being created.
Reading the comment I can see a lot of people don't understand the meaning of the words coincidence or sequence.
arduanika · 1h ago
Really cool!
But in your next interview, just know that this is not the most computationally efficient way to generate the sequence.
sollewitt · 1h ago
It’s not a sequence if you produce it by ordering aggregates. Next year no matter what happens the sequence will be broken until at best everyone advances one place (so best case scenario in 21 years), or a new team wins 21 straight titles.
Now if in twenty one years the distribution has been maintained, there’s one new team and all the other teams have won Fib(n+1) - Fib(n) titles, or one team has won 21 straight titles, reproducing the sequence, I’ll come back in 2046 and eat my hat.
smcin · 1h ago
Neat. We have some wiggle room to rig it by deciding what year to start the Premier League Table Wins (1992 or a more recent year).
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.
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/...
Any theories why this might be the case?
> 2. that the rounding all happened to go the right way.
+1. See how close some title races are: 2013-2014 comes to mind.
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".
But in your next interview, just know that this is not the most computationally efficient way to generate the sequence.
Now if in twenty one years the distribution has been maintained, there’s one new team and all the other teams have won Fib(n+1) - Fib(n) titles, or one team has won 21 straight titles, reproducing the sequence, I’ll come back in 2046 and eat my hat.