How often does the best team win the league? Probably not as often as you think as it is not just talent that is required for success; a decent amount of luck is needed too.
To investigate how big a role luck plays compared with ability I created a mathematical simulation based on the English Premier League (EPL) containing 20 teams that play each other twice per season. Each team was randomly assigned a skill level drawn from a normally distributed population with a mean of 0.5 and a standard distribution linked to the spread of talent across the league so that the disparity between the top and bottom clubs could be controlled. The simulation was then run for 10,000 seasons at various disparity levels and the number of times the team with the highest skill level won the league was measured.
| Mean Skill Level | Disparity | Mean Win % | Best Team Win % |
| 0.5 | 0 | 65.5 | 0 |
| 0.5 | 0.02 | 65.9 | 10.3 |
| 0.5 | 0.04 | 67.4 | 22.7 |
| 0.5 | 0.06 | 69 | 32.4 |
| 0.5 | 0.08 | 72.1 | 41.2 |
| 0.5 | 0.1 | 76.4 | 46.4 |
Table 1: Effect of Disparity on League Champions
The first row in Table One shows what would happen if all teams in the league were identical. Each team has a skill level of 0.5, meaning that they would each be expected to win 50% of their matches and lose 50% (ignoring draws to keep the model simple). Due to random chance though some teams will win more than 50% and some will lose more than 50%. You can see that the average number of matches won by the league champions over 10,000 seasons was 65.5% so in an evenly matched EPL you would just need to be lucky enough to win an extra 15% of matches to be champions.
As the disparity increases though, the influence of chance decreases and the best team goes on to win the league more often and more of their matches in the process. Take a look at this season’s EPL and while it is possible that QPR could go on to fluke wins in all their remaining matches and go on to win the league it would take a colossal amount of luck compared to say the amount of luck Manchester City would need to finish ahead of Manchester United since their skill levels are closer.
This leads to the question though of what is preferable, an evenly matched, competitive league in which luck is a major determining factor in winning or a league that is perhaps fairer as it has enough disparity that the best team is predominantly likely to win?
Submit your comments below, and feel free to format them using MarkDown if you want. Comments typically take upto 24 hours to appear on the site and be answered so please be patient.
Thanks!