In my previous article I looked at the interplay between luck and skill in determining the league champions. There is another parameter though that also interacts with luck and that is the structure of the league itself. How many times have you heard the same tired, old cliché from football managers about how luck evens itself out over a season? But does it? Is a football season really long enough for the effects of chance to be cancelled out?
I used the same mathematical model as before to simulate 10,000 seasons of a league containing 20 teams. Skill levels were randomly assigned to each team from a normally distributed population with a mean of 0.5 and a standard deviation of 0.1. The length of the season was then altered to see how frequently the team with the highest skill level won the league depending on the number of matches played – teams either played each other once, twice, four times or eight times per season.
| Number of Teams | Frequency Teams Meet | Mean Win % | Best Team Win % |
| 20 | 1 | 60.2 | 32.11 |
| 20 | 2 | 75.3 | 45.9 |
| 20 | 4 | 82.2 | 48.5 |
| 20 | 8 | 85.2 | 50.8 |
Table One: Effect of Season Length on League Champions
The results in Table One show that as the length of the season increases the probability of the team with the highest skill rating winning the league increases too. The Champions also win a greater percentage of their matches too. Therefore, the more matches that are played the less of an influence chance seems to play in determining the overall league champion.
The second row of Table One matches the structure of four of the major leagues in Europe – Premier League, Serie A, La Liga and Ligue 1 – which all contain 20 teams that play each other twice per season. The Eriedivisie and Bundesliga only contain 18 teams though, so what affect does this have? Rerunning the mathematical model with 18 teams gives a lower frequency for the best team winning the league of 28.8%. This suggests that the smaller size of these two leagues makes them somewhat more competitive as there are fewer matches for luck to be evened out.
The Scottish Premier League (SPL) is smaller again, containing just 12 teams. The structure of the league is fairly unique in Europe, with teams playing each other three times, either twice away and once at home or vice versa. The league then splits in half and teams play a further match against the remaining five teams in their half of the league. If we apply the mathematical model to this structure then we come out with a frequency of 19.3% for the best team winning the league. This means the SPL should be one of the most competitive leagues in Europe, yet it has only ever been won by two teams – Celtic and Rangers. The reason for this is likely due to the large disparity in talent between Glasgow’s two largest teams and the rest of the league cancelling out the effect of chance.
Interestingly, with Rangers now relegated from the SPL for financial irregularities, the league is the closest it has ever been. It was thought that without Rangers present in the SPL, Celtic would go on to dominate a very one-sided division. Yet with Hibernian currently sitting top of the league, the reduction in disparity from the loss of Rangers may actually make it the most competitive and exciting year in the SPL’s history.
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