In this page, another example of randomisation is described to assess whether teams in a soccer league are evenly matched.
English Premier Soccer League, 2012/13 and 2013/14
We saw earlier that the distribution of points in the 2013/14 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 the teams' performances further.
If good performance in one year carries over into good performance in the following year, 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 these 23 teams.)
Points | ||
---|---|---|
Team |
2012/13 | 2013/14 |
Manchester United Manchester City Chelsea Arsenal Tottenham Hotspur Everton Liverpool West Bromwich Albion Swansea City West Ham United Norwich City Fulham Stoke City Southampton Aston Villa Newcastle United Sunderland Wigan Athletic Reading Queens Park Rangers Crystal Palace Hull City Cardiff City |
89 78 75 73 72 63 61 49 46 46 44 43 42 41 41 41 39 36 28 25 - - - |
64 86 82 79 69 72 84 36 42 40 33 32 50 56 38 49 38 - - - 45 37 30 |
We will now use the apparent consistency of the teams from one year to the next to ask:
Do the good teams in one season also tend to do well in the following season?
Randomisation
If there is no carry-over effect of performance from one season to the next, the 2013/14 points of 42 (which was actually obtained by Swansea City) would have been equally likely to have been obtained by any of the teams in that year. Indeed, any allocation of the points (64, 86, 82, ..., 38) to the 17 teams that played in both years would be equally likely.
The diagram below performs this randomisation of the results in 2013/14.
Click Randomise to shuffle the 2013/14 points between the teams (excluding the teams 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 hardly ever as far from zero as the actual correlation (r = 0.798). Since a correlation as high as 0.798 is unlikely when there is no consistency of performance from one season to the next, ...
There is strong evidence that the teams doing well in one season also do well in the following season.