In this page, another example of randomisation is described to assess whether teams in a soccer league are evenly matched.
English Premier Soccer League, 2007/08 and 2008/09
We saw earlier that the distribution of points in the 2008/09 English Premier Soccer League Table was not consistent with all teams being evenly matched — the spread of points was too high. We will now investigate this further.
If some teams are better than others, the positions of teams in the league in successive years will tend to be similar. The table below shows the points for the teams in two seasons. (Note that the bottom three teams are relegated each year and three teams are promoted from the lower league, so we cannot compare the positions of six of the teams.)
Points | ||
---|---|---|
Team |
2007/08 | 2008/09 |
ManchesterU Chelsea Arsenal Liverpool Everton AstonVilla Blackburn Portsmouth ManchesterC WestHam Tottenham Newcastle Middlesbro Wigan Sunderland Bolton Fulham Reading Birmingham DerbyCounty StokeCity HullCity WestBromA |
87 85 83 76 65 60 58 57 55 49 46 43 42 40 39 37 36 36 35 11 - - - |
90 83 72 86 63 62 41 41 50 51 51 34 32 45 36 41 53 - - - 45 35 32 |
Manchester United, Chelsea, Arsenal and Liverpool were the top four teams in both years. However, ...
Excluding Manchester United, Chelsea, Arsenal and Liverpool, do there seem to be any differences in ability between the other teams? |
Randomisation
If all other teams have equal probabilities of winning against any opponent, the 2008/09 points of 45 (which was actually obtained by Wigan) would have been equally likely to have been obtained by any of the teams in that year. Indeed, any allocation of the points (63, 62, 41, ..., 53) to the teams (Everton, Aston Villa, Blackburn, ..., Fulham) would be equally likely.
The diagram below performs this randomisation of the results in 2008/09.
Click Randomise to shuffle the 2008/09 points between the teams (excluding the top four teams and those that were only in the league for one of the seasons). If the teams were of equal ability, these points would have been as likely as the actual ones.
The correlation coefficient between the points in the two seasons gives an indication of how closely they are related. Click Accumulate and repeat the randomisation several more times. Observe that the correlation for the randomised values is only as far from zero as the actual correlation (r = 0.537) in about 5% of randomisations. Since a correlation as high as 0.537 is fairly unusual for equally-matched teams, ...
There is moderately strong evidence of a difference in skill between teams, even when the top four have been excluded.