The English Premier League's (EPL) new season starts today. Last season Liverpool won its second championships in the Premier League era (ie beginning from 1993). Soon after it was discovered that the number of championships won by teams during the Premier League era matches the first 8 terms of the Fibonacci sequence. (In the Fibonacci sequence, the first 2 terms are 0 and 1 with the remaining terms being the sum of the 2 terms immediately preceeding it — the first 10 terms in the sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.) The distribution of Premier League championships won are as follows:
| Team | EPL Championships won | Any team without an EPL title | 0 | Blackburn Rovers | 1 | Leicester City | 1 | Liverpool | 2 | Arsenal | 3 | Chelsea | 5 | Manchester City | 8 | Manchester United | 13 |
After one season one team has the league's only title (at the time) while any other team has 0. This is very difficult to achieve after a few seasons. If the team successfully defends its title in the second season, the sequence fails to form. The next time it is possible to form the sequence is after the league's 4th season — one team has 2 titles while 2 others have 1 each. (The number of English Football League, EPL's predecessor, titles won after its 4th season matches the first 4 terms of the Fibonacci sequence. In this case, Preston North End had 2, Everton and Sunderland had 1 each.) After that it becomes difficult to form such a sequence — the right number of teams have to win the right number of championships within the right timeframe. (Sure, one can easily form a Fibonacci sequence of titles won over a non-consecutive period, but that would be cheating.)
Since the next term of the Fibonacci sequence is 21, we would have to wait until 2045 for the possibility of the number of championships won by teams during the Premier League era perfectly matching the Fibonacci sequence. For that to happen, one (and only one, otherwise, the number of championship winning teams would not match the number of terms in the sequence) team that has not won the championships since 1993 has to win at least once in the next 21 years. (As a Liverpool fan, it would be fantastic to have the team winning 19 championships between now and 2045, but that would be too much to ask.)
Since we can have only one extra team winning the Premier League championship in the next 21 years, the question is which team would it be? There are two types of answer — the team most likely to win and the team one wishes to win. For the former, it would be Newcastle United, which is owned by a state-owned investment fund (namely Saudi Arabia's Public Investment Fund). While it last won a top-flight league championship almost a century ago — 1927 —, seeing a team bankrolled by a sovereign nation winning a title reeks of the team buying the championship.
Two other teams high on the list of best teams without a Premier League championship are Aston Villa and Tottenham Hotspur. The former has been punching above its weight in recent seasons, but it would take finding a transcendent manager (the likes of Pep Guadiola or Jurgen Klopp) and developing (and, more importantly, holding on to) one (or two) player at the level of Lamine Yamal and Kylian Mbappé. The latter was closer to relegation than the title last season, so the team's ownership need to change the way it runs the club before it can think of winning the league title.
Perhaps a team can "pull a Leicester" and unexpectedly win the Premier League championship. While it is possible, the chance of all the big teams (all the teams that have previously won the Premier League championship and the teams listed above) faltering in the same season, so much so that the surprise team can finish on the top of the table, is indeed 1 in 5000 (the odds given by a number of bookmakers on Leicester City winning the title at the start of its title-winning season) or even smaller.
A 21-year-wait for the next chance of having the number of championships won by teams during the Premier League era matching part of the Fibonacci sequence sounds too long. However, it is possible to have form a Fibonacci sequence from number of titles won 3 years from now. Since Blackburn Rovers won its only Premier League championship in 1995, the number of championships won in the 33-year-period ending in 2028 would form the Fibonacci sequence if Blackburn Rovers (or any team that has yet to be crowned Premier League champions) wins one title over the next 3 seasons and Manchester United wins the other 2. (The chance of that happening is slim. Besides, I certainly don't want Manchester United to win another top-flight title before Liverpool is back alone on the perch — at the top the list of number of the top-flight titles won.)