English Premier Soccer League in 2013/14

  Team Pts
1 Manchester City 86
2 Liverpool 84
3 Chelsea 82
4 Arsenal 79
5 Everton 72
6 Tottenham Hotspur 69
7 Manchester United 64
8 Southampton 56
9 Stoke City 50
10 Newcastle United 49
11 Crystal Palace 45
12 Swansea City 42
13 West Ham United 40
14 Sunderland 38
15 Aston Villa 38
16 Hull City 37
17 West Bromwich Albion 36
18 Norwich City 33
19 Fulham 32
20 Cardiff City 30

Actual range = 56
Actual sd = 19.3

This is a simulation of a soccer league where the two teams playing each match are equally likely to win. The simulation examines whether the spread in points in the actual league table is consistent with all teams being equally skillful.

Select Simulation with teams of equal ability then click Run League to generate a simulated league. Click Accumulate and repeat several times.

Observe that the simulated range and sd are never as high as those in the actual league, so the data are not consistent with an equal-skills model.

There is strong evidence of a difference in the probability of winning of the best and worst teams.

(This is really an example of hypothesis testing and could be treated as a way of motivating it.)

The data are the points for all teams in the English Premier Soccer league in 2013/14. Each team played all other teams twice (once at home and once away), earning 1 point for each draw and 3 points for each win.

In the simulation, the probability of a draw is 0.25, the proportion of drawn matches in the actual league, and there are equal probabilities of winning and losing each match (0.375).