Randomness in sports results
Although we like to think that the 'best' team wins in sports competitions, there is actually considerable variability in the results that can only be explained through randomness. For example when two teams play a series of matches, the same team rarely wins all matches.
English Premier Soccer League, 2008/09
In the English Premier Soccer league, each team plays every other team twice (home and away) during the season. Three points are awarded for a win and one point for a draw. The table below shows the wins, draws, losses and total points for all teams at the end of the 2008/09 season.
Team |
Wins | Draws | Losses | Points | |
---|---|---|---|---|---|
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. |
Manchester City Liverpool Chelsea Arsenal Everton Tottenham Hotspur Manchester United Southampton Stoke City Newcastle United Crystal Palace Swansea City West Ham United Sunderland Aston Villa Hull City West Bromwich Albion Norwich City Fulham Cardiff City |
27 26 25 24 21 21 19 15 13 15 13 11 11 10 10 10 7 8 9 7 |
5 6 7 7 9 6 7 11 11 4 6 9 7 8 8 7 15 9 5 9 |
6 6 6 7 8 11 12 12 14 19 19 18 20 20 20 21 16 21 24 22 |
86 84 82 79 72 69 64 56 50 49 45 42 40 38 38 37 36 33 32 30 |
Were all teams evenly matched?
A simulation can help us to investigate this question. We could be used to generate results from all 380 matches in the season for evenly matched teams, each result having probabilities 0.372, 0.372 and 0.255 of being a win, loss or draw for the home team. (A proportion 0.255 of games in the actual league resulted in draws.)
If there are differences between teams, we would expect the worst teams to have very few points at the end of the season and the best to have many. On the other hand, for evenly matched teams, we would expect all 20 finals points to be similar. The spread of final points in the league table should tell us something about whether the teams are evenly matched.
In the actual league table, the standard deviation of the final points for the 20 teams was 18.236. The diagram below shows the standard deviations in 200 simulated league tables with evenly matched teams.
The spread of points in the actual league table was much higher than the spread that would be likely for evenly matched teams, so:
There is strong evidence that the top teams are 'better' than the bottom teams.