Evidence of skill?

The simulation on the previous page showed that there is considerable variability in the league table at the end of a season even if all teams are equally matched — the top team often has considerably more points than the bottom team even when we have given all teams equal ability in our simulation.

This variability in the league tables leads us to question whether an actual league table might be explained simply by natural variability of teams with equal ability. A simulation can throw light on whether all teams might have equal abilities.

English Premier Soccer League in 2013/14

The table below shows the points gained by all teams in the English Premier Soccer League at the end of the 2013/14 season. Each team played all other teams twice (once at home and once away) — a total of 38 games — earning 1 point for each draw and 3 points for each win. The Premier League Cup is won by the team with the greatest number of points at the end of the season (Manchester City in the 2013/14 season).

  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

Simulation

If teams have different skill levels, and therefore different probabilities of winning, then there will be more variability in the final points in the table than if all teams are evenly matched. (The difference between the points won by the best and worst teams will be greater.)

The simulation below assumes equally matched teams with P(draw) = 0.2, the proportion of draws in the actual league that year. We will use it to investigate measures of spread in the simulated league tables.

Click Accumulate then click Run League several times to simulate a few seasons. The diagram shows a dot plot of the range of points in the league table (maximum minus minimum). This jittered dot plot shows how large the range is likely to be if all teams are equally matched.

In the actual 2013/14 season, the top team got 86 point and the bottom team got 30 points, a range of 56 points, and the standard deviation of the points was 19.3. From the simulation with equally matched teams, such high spread of results seems extremely likely — so we can conclude that some teams really are better than others.

 RangeStandard devn
Actual 2013/14 soccer league     56 19.3
From simulation   between 15 and 50     between 5 and 12