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    • Football: Was points per game fair?

      5 August, 2020

      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.

      Read more about...
      mathematics in sport
      football
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      Comments

      Phil

      6 August 2020

      Permalink

      It would be interesting to see how this would have looked using an ELO calculation

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      Read more about...

      mathematics in sport
      football
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