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. Much of this variability can be considered to be random — if the same teams play again, the results are often different. The most obvious examples of this randomness occur when a series of matches is played between the same two teams.

Since the teams are virtually unchanged in any series, the variability in results can only be explained through randomness.

Randomness or skill?

When we look at sports results, can we tell whether all teams are equally matched with the same probability of winning? Or do some teams have a higher probability of winning than others?

There are different ways to examine this question, depending on the type of data that is available. The following example assesses an end-of-year league table.

English Premier Soccer League, 2013/14

In the English Premier Soccer league, each of the 20 teams 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 2013/14 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

We observed in an earlier simulation that there is considerable variability in the points, even when all teams are evenly matched. However, ...

If some teams are more likely to win their matches than others, the spread of final points is likely to be greater — the top and bottom teams are likely to be more extreme.

A simulation

To assess whether there is any difference in skill levels, we can therefore run a simulation of the league, assuming evenly matched teams and generating random results with probabilities 0.4, 0.4 and 0.2 for wins, losses and draws. (A proportion 0.2 of games in the actual league resulted in draws.)

Click Simulate to simulate the 380 games in a season. The standard deviation of the final points is shown below the table. Click Accumulate then run the simulation about 100 times. (Hold down the Simulate button to speed up the process.)

The standard deviation of the points in the actual league table was 19.3. Since most simulated standard deviations are between 5 and 15, we conclude that such a high spread would be extremely unlikely if the teams were evenly matched.

There is strong evidence that the top teams are 'better' than the bottom teams.