Football: Was points per game fair?

By 
Salim Neil Khan

Football: Was points per game fair?

Due to the COVID-19 pandemic, many football leagues around the world had to finish their seasons early with fixtures unfulfilled. Some of those leagues abandoned their seasons altogether, ruling them null and void, resulting in no promotions nor relegations. Alternatively a number of curtailed leagues decided to award final placings based on results that had been achieved so far. In those cases, the average points per game (PPG) was used as the deciding measure.

Football as virus

Due to COVID-19 football leagues had to be suspended.

However, in an earlier article, I suggested that PPG may not be a fair performance measure as it didn't take into account the following two important factors. Firstly the number of home and away games played should be considered. When included, this gives us a new measure which has since been called weighted points per game (WPPG) in many quarters. Secondly, crucially we should consider the difficulty of opponents that teams had played so far. I proposed an alternative measure, adjusted points per game (Adj PPG) which accounted for both these factors.

Some leagues, such as the Premier League, managed to complete their remaining fixtures. Hence in this article I use the Premier League results to compare what actually happened with what was predicted using PPG, WPPG and Adj PPG, and determine which of those three was the most accurate, or fairest.

Qualification for Europe and relegation

Below is the final Premier League table and the tables which show what the result would have been if Adj PPG, PPG, or WPPG had been used.

Final Premier League table, Adj PPG table, PPG table, and WPPG table.
Position
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TeamPoints
Liverpool99
Man City81
Man Utd66
Chelsea66
Leicester62
Tottenham59
Wolves 59
Arsenal56
Sheffield Utd54
Burnley54
Southampton52
Everton49
Newcastle 44
Crystal Palace43
Brighton41
West Ham39
Aston Villa35
Bournemouth34
Watford34
Norwich21
TeamAdj PPG
Liverpool2.740
Man City2.091
Leicester1.824
Chelsea1.644
Man Utd1.554
Wolves 1.548
Sheffield Utd 1.524
Tottenham1.464
Arsenal 1.383
Burnley1.330
Crystal Palace1.299
Everton1.246
Newcastle 1.201
Southampton1.195
West Ham0.979
Brighton0.957
Watford0.937
Bournemouth0.918
Aston Villa0.873
Norwich0.769
TeamPPG
Liverpool2.828
Man City2.036
Leicester1.828
Chelsea1.655
Man Utd1.552
Sheffield Utd 1.536
Wolves1.483
Arsenal1.429
Tottenham1.414
Burnley1.345
Crystal Palace1.345
Everton1.276
Newcastle 1.207
Southampton1.172
Brighton1.000
West Ham0.931
Watford0.931
Bournemouth0.931
Aston Villa0.893
Norwich0.724
TeamWPPG
Liverpool2.821
Man City2.049
Leicester1.821
Chelsea1.657
Man Utd1.538
Sheffield Utd 1.531
Wolves1.483
Tottenham1.429
Arsenal1.405
Crystal Palace1.340
Burnley1.338
Everton1.293
Newcastle 1.217
Southampton1.181
Brighton1.010
Watford0.940
Bournemouth0.940
West Ham0.936
Aston Villa0.921
Norwich0.736

Undoubtedly the most important outcomes to examine are the top four positions (i.e. those who qualified for the Champions League), the 5th and 6th positions (i.e. those who qualified for the Europa League), and the bottom 3 (i.e. those who were relegated).

We can see from the table above that all three measures forecasted exactly the same top five positions. They were successful in predicting which teams would make up the top five, but placed Leicester (who finished 5th) and Man Utd (who finished 3rd) the wrong way around. The final Europa League place was taken by Tottenham, but this was not predicted by any of the measures.

Regarding the bottom three, Adj PPG and PPG both correctly predicted two out of the three teams that were relegated, namely Norwich and Bournemouth, whereas WPPG only predicted 1 correctly, erroneously projecting West Ham for the drop.

Based on these simple indicators, this suggests that Adj PPG and PPG would have been equally appropriate measures, with WPPG less so.

Points Comparison

More importantly, it would be informative to assess the overall predictive accuracy for the whole table for each of the three measures. One way to do this is to compare the actual final points for all the teams with the points predicted by each measure.

By multiplying the values from the table above by the number of games played, 38, we can obtain the predicted number of points for each team. These are shown in the table below along with their differences from the actual points.

Premier League teams’ final points and their predicted points according to Adj PPG, PPG, and WPPG.
TeamsActual points Predicted points
Adj PPGPPGWPPG
Arsenal5652.654.353.4
Aston Villa3533.233.935.0
Bournemouth3434.935.435.7
Brighton4136.438.038.4
Burnley5450.551.150.8
Chelsea6662.562.963.0
Crystal Palace4349.451.150.9
Everton4947.348.549.1
Leicester6269.369.569.2
Liverpool99104.1107.5107.2
Man City8179.577.477.9
Man Utd6659.159.058.4
Newcastle4445.645.946.2
Norwich2129.227.528.0
Sheffield Utd5457.958.458.2
Southampton5245.444.544.9
Tottenham5955.653.754.3
Watford3435.635.435.7
West Ham3937.235.435.6
Wolves5958.856.356.4
Difference from actual points
Adj PPGPPGWPPG
3.41.72.6
1.81.10.0
-0.9-1.4-1.7
4.63.02.6
3.52.93.2
3.53.13.0
-6.4 -8.1 -7.9
1.7 0.5 -0.1
-7.3 -7.5 -7.2
-5.1 -8.5 -8.2
1.5 3.6 3.1
6.9 7.0 7.4
-1.6 -1.9 -2.2
-8.2 -6.5 -7.0
-3.9 -4.4 -4.2
6.6 7.5 7.1
3.4 5.3 4.7
-1.6 -1.4 -1.7
1.8 3.6 3.4
0.2 2.6 2.6

The averages of the absolute differences (i.e. ignoring the minus signs) are:

Average of absolute difference
Adj PPGPPGWPPG
3.74.14.0
PPG scored the worst (4.1), WPPG performed slightly better (4.0), and the best achieving was Adj PPG (3.7). This suggests that Adj PPG is the most accurate of the three at predicting final league points.

Conclusions

None of the three measures, Adj PPG, PPG, and WPPG, were by any means perfect at predicting what actually happened in the Premier League. However, based on the calculations above, it can be asserted that PPG, the method actually employed globally by many football leagues for deciding curtailed seasons, is not as fair as Adj PPG. If faced with the same decision again, and with the COVID threat still lingering over us this is a not altogether unlikely possibility, the football leagues should think carefully about whether PPG is most appropriate, or whether Adj PPG would be more suitable.


Slim Khan

About the author

Slim Khan is a Teaching Fellow at Warwick University, and is particularly interested in mathematics and statistics related to games and sports.

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