On the Élö–Runyan–Poisson–Pearson Method to Forecast Football Matches
Abstract
:1. Introduction
1.1. State of the Art and Contribution
1.2. Computational Resources
1.3. Organization of the Research
2. The English Premier League: Preliminary Description
- Season: This identifies the official name of the tournament when the teams met.
- Matchday: This corresponds to one of the 38 matchdays that are played throughout the calendar of the season.
- Date: The day and month in which the match was played.
- Host: This bit of information corresponds to the team that plays in its own stadium.
- Guest: This stands for the name of the team that plays a game away from home.
- Goals for host/guest: This corresponds to the goals that are scored by the local/visiting team in each match.
- Points home/guest: This is the number of points obtained by the local/visiting team according to the outcome of the match.
- Goals for host/guest: This corresponds to the goals that are scored by the home/away team in each match.
- Goal difference (GD) host/guest: A difference will be established for the home/away team.
- Champion: This singleton is the first group.
- UCL: The second group corresponds to the squads that manage to play the European clubs tournament widely known as the Union of European Football Associations (UEFA) Champions League. This group includes the four best-positioned teams after playing the 38 rounds of the aforementioned championship. That is, the champion and the following three clubs on the leader board.
- UEL: The teams that finish the season in fifth and sixth places in the leader board get to play in a second European tournament known as the UEFA European League.
- Middle table: This is the largest group. It includes those teams from the seventh to the 17th positions in the final leader board.
- Relegation: This last group refers to the teams that lose the category at the end of each season.
3. The Rating of Football Squads
Algorithm 1:Élö–Runyan rating method. |
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The English Premier League: Élö–Runyan Analysis
- The score needed to be champion has a negative trend in the last two seasons.
- The Élö–Runyan score required to maintain the category has is much more fluctuating than the actual classification (which represented a much more constant score).
4. The Rise of Actual Champions
The English Premier League: Poisson Analysis
5. Test of the Élö–Runyan–Poisson–Pearson Model
5.1. The Élö–Runyan–Poisson–Pearson Model
- (i)
- In the case that we fail to reject this hypothesis, we take advantage of the fact that the Poisson mass function can be recursively written as
- (ii)
- If we reject the null hypothesis that the distribution of goals is Poisson, and the variance of the goals is lower than the mean, we use a binomial distribution with mean . In this case, we refer to Section II in [1] to interpret as the probability that a goal is scored at any of the 90 min in a match and take 90 as the total number of trials a team will have to do it. We profit from the fact that the binomial mass with parameters 90 and can be recursively written as
Algorithm 2: Generation of a Poisson realization. |
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Algorithm 3: Generation of a binomial realization. |
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- (iii)
- If we reject the null hypothesis that the distribution of goals is Poisson, and the variance is larger than the mean, we take advantage of the fact that the negative binomial random variable can be recursively written as
Algorithm 4: Generation of a negative binomial realization. |
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Algorithm 5: The Élö–Runyan–Poisson–Pearson model. |
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5.2. Russia 2018
- the Asian Football Confederation (AFC);
- the UEFA;
- the Confédération Africaine de Football (CAF);
- the Confederation of North, Central American and Caribbean Association Football (CONACAF);
- the Confederação Sul-Americana de Futebol (CONMEBOL); and
- the Oceania Football Confederation.
- UEFA: Belgium (1633.222), Croatia (1724.443), Denmark (1564.427), England (1604.612), France (1742.171), Germany (1426.583), Iceland (1550.110), Poland (1456.364), Portugal (1516.734), Russia (1577.244), Serbia (1485.873), Spain (1543.799), Sweden (1557.115), and Switzerland (1581.902).
- CONMEBOL: Argentina (1558.131), Brazil (1635.239), Colombia (1626.491), Peru (1521.952), and Uruguay (1646.054).
- CONCACAF: Costa Rica (1422.986), Mexico (1485.310), and Panama (1412.645).
- CAF: Egypt (1377.147), Morocco (1374.678), Nigeria (1384.316), Senegal (1377.673), and Tunisia (1371.521).
- AFC: Australia (1447.447), Iran (1458.788), Japan (1513.472), Saudi Arabia (1453.555), and South Korea (1443.991).
- the proportion of times that wins,
- the proportion of times that wins, and
- the proportion of times when the match ends up tied.
Algorithm 6: Results of the first phase for a Word Cup group. |
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Algorithm 7: Result of a second-phase match in a World Cup group. |
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5.3. Qatar 2022
- UEFA: Belgium (1662), Croatia (1571), Denmark (1659), England (1649), France (1659), Germany (1615), Netherlands (1711), Poland (1559), Serbia (1619), Spain (1645), Switzerland (1592), Portugal (1633), and Wales (1504).
- AFC: Australia (1574), Iran (1621), Japan (1693), Qatar (1552), Saudi Arabia (1558), and South Korea (1652).
- CAF: Cameroon (1552), Ghana (1512), Morocco (1675), Senegal (1636), and Tunisia (1584).
- CONCACAF: Canada (1613), Costa Rica (1545), Mexico (1573), and the United States of America (1638).
- CONMEBOL: Argentina (1732), Brazil (1760), Ecuador (1552), and Uruguay (1574).
5.3.1. First Phase
5.3.2. Second Phase
6. Aftermatch
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Source | DF | Adj. Sum Sq. | Adj. Mean Sq. | F Value | p-Value | |
---|---|---|---|---|---|---|
Regression | GD | 1 | 6118.31 | 6118.31 | 238.25 | 0.000 |
Error | 18 | 462.24 | 25.68 | |||
Lack of adj. | 16 | 385.74 | 24.11 | 0.63 | 0.765 | |
Pure error | 2 | 76.50 | 38.25 | |||
Total | 19 | 6580.55 |
Champion | UCL | UEL | Middle Table | Relegation | |
---|---|---|---|---|---|
Champion | 13 | 3 | 0 | 0 | 0 |
UCL | 3 | 39 | 5 | 1 | 0 |
UEL | 0 | 5 | 18 | 9 | 0 |
Middle table | 0 | 1 | 9 | 159 | 7 |
Relegation | 0 | 0 | 0 | 7 | 41 |
GROUP | 2005/2006 | 2006/2007 | 2007/2008 | 2008/2009 | 2009/2010 | 2010/2011 | 2011/2012 | 2012/2013 |
---|---|---|---|---|---|---|---|---|
Champion | 0% | 100% | 0% | 100% | 0% | 100% | 100% | 100% |
UCL | 100% | 100% | 100% | 100% | 75% | 75% | 75% | 75% |
UEL | 50% | 100% | 50% | 50% | 0% | 0% | 50% | 0% |
Midtable | 81.82% | 90.91% | 90.91% | 72.73% | 90.91% | 90.91% | 90.91% | 90.91% |
Relegation | 66.67% | 66.67% | 100% | 33.33% | 100% | 100% | 100% | 100% |
TOTAL | 75.00% | 90.00% | 85.00% | 70.00% | 76.25% | 81.25% | 86.25% | 81.25% |
GROUP | 2013/2014 | 2014/2015 | 2015/2016 | 2016/2017 | 2017/2018 | 2018/2019 | 2019/2020 | 2020/2021 |
---|---|---|---|---|---|---|---|---|
Champion | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
UCL | 100% | 100% | 75% | 100% | 100% | 75% | 100% | 100% |
UEL | 100% | 100% | 50% | 100% | 100% | 50% | 50% | 50% |
Midtable | 100% | 90.91% | 81.82% | 100% | 100% | 90.91% | 90.91% | 90.91% |
Relegation | 100% | 66.67% | 66.67% | 100% | 100% | 66.67% | 100% | 100% |
TOTAL | 100.00% | 90.00% | 76.25% | 100.00% | 100.00% | 81.25% | 90.00% | 90.00% |
Position | Real | Points | Poisson | Points | Accuracy | |
---|---|---|---|---|---|---|
Champion | 1 | Manchester City | 93 | Manchester City | 76.59 | 100% |
UCL | 2 | Liverpool | 92 | Liverpool | 75.46 | 100% |
3 | Chelsea | 74 | Chelsea | 67.47 | ||
4 | Tottenham | 71 | Tottenham | 62.50 | ||
UEL | 5 | Arsenal | 69 | Arsenal | 57.06 | 50% |
6 | Manchester United | 58 | West Ham | 55.46 | ||
middle table | 7 | West Ham | 56 | Leicester City | 53.87 | 81.81% |
8 | Leicester City | 52 | Crystal Palace | 53.85 | ||
9 | Brighton | 51 | Manchester United | 52.58 | ||
10 | Wolverhampton | 51 | Aston Villa | 51.64 | ||
11 | Newcastle | 49 | Brighton | 51.49 | ||
12 | Crystal Palace | 48 | Wolverhampton | 51.20 | ||
13 | Brentford | 46 | Brentford | 49.91 | ||
14 | Aston Villa | 45 | Newcastle | 46.28 | ||
15 | Southhampton | 40 | Burnley | 45.28 | ||
16 | Everton | 39 | Everton | 44.96 | ||
17 | Leeds | 38 | Southhampton | 44.80 | ||
Relegation | 18 | Burnley | 35 | Leeds | 40.31 | 66.67% |
19 | Watford | 23 | Watford | 38.01 | ||
20 | Norwich City | 22 | Norwich City | 32.11 |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Goals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Saudi Arabia | 1.88 | 2.10 | Poi | 0.85 | 0.98 | Poi | 1.70 | 4.81 | Poi | 1.70 | 1.91 | Poi |
Egypt | 1.30 | 0.99 | Poi | 0.43 | 0.33 | Poi | 0.76 | 0.53 | Poi | 1.24 | 0.77 | Poi |
Russia | 1.52 | 2.01 | Poi | 1.32 | 1.34 | Poi | 2.00 | 3.79 | Poi | 0.80 | 0.38 | Poi |
Uruguay | 2.33 | 1.89 | Poi | 0.78 | 1.28 | Poi | 1.09 | 0.71 | Poi | 1.00 | 0.96 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | var. Goals against as Host | Law | Mean Goals for as Guest | var. Goals for as Guest | Law | Mean Goals against as Guest | var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Spain | 3.00 | 3.47 | Poi | 0.27 | 0.20 | Poi | 1.67 | 3.82 | Poi | 0.87 | 0.78 | Poi |
Portugal | 1.91 | 2.81 | Poi | 0.68 | 0.70 | Poi | 1.79 | 2.06 | Poi | 0.63 | 0.86 | Poi |
Iran | 2.12 | 1.75 | Poi | 0.53 | 0.72 | Poi | 1.41 | 2.01 | Poi | 0.41 | 0.60 | NB |
Morocco | 2.19 | 2.44 | Poi | 0.48 | 0.25 | Poi | 0.62 | 0.85 | Poi | 0.46 | 0.25 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
France | 2.26 | 1.74 | Poi | 0.97 | 1.13 | Poi | 1.44 | 1.36 | Poi | 0.83 | 0.58 | Poi |
Denmark | 1.70 | 2.04 | Poi | 0.74 | 0.54 | Poi | 1.25 | 2.11 | Poi | 1.20 | 0.75 | Poi |
Australia | 2.65 | 3.03 | Poi | 0.90 | 1.19 | Poi | 1.23 | 1.18 | Poi | 1.15 | 0.98 | Poi |
Peru | 1.74 | 1.06 | Poi | 0.78 | 0.95 | Poi | 1.21 | 1.38 | Poi | 1.18 | 1.08 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Croatia | 2.72 | 5.31 | Poi | 0.39 | 0.24 | Poi | 1.17 | 1.81 | Poi | 1.17 | 1.72 | Poi |
Argentina | 2.07 | 3.44 | Poi | 0.66 | 0.85 | Poi | 1.89 | 4.09 | Poi | 1.11 | 2.30 | NB |
Nigeria | 1.58 | 1.66 | Poi | 0.83 | 0.72 | Poi | 1.11 | 1.36 | Poi | 0.84 | 0.98 | Poi |
Iceland | 1.78 | 0.95 | Poi | 1.00 | 1.11 | Poi | 1.61 | 1.56 | Poi | 1.39 | 1.62 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Brazil | 1.77 | 1.54 | Poi | 0.45 | 0.34 | Poi | 2.36 | 2.55 | Poi | 0.48 | 0.41 | Poi |
Costa Rica | 1.48 | 1.43 | Poi | 0.56 | 0.47 | Poi | 1.10 | 1.42 | Poi | 1.57 | 1.65 | Poi |
Serbia | 1.83 | 1.69 | Poi | 1.22 | 0.84 | Poi | 1.22 | 0.84 | Poi | 1.11 | 1.32 | Poi |
Switzerland | 1.15 | 3.71 | Poi | 1.05 | 0.71 | Poi | 0.95 | 1.20 | Poi | 2.21 | 0.79 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Germany | 2.28 | 2.51 | Poi | 0.94 | 1.06 | Poi | 2.06 | 5.27 | Poi | 0.94 | 0.72 | Poi |
South Korea | 1.24 | 1.25 | Poi | 0.91 | 0.97 | Poi | 1.04 | 1.12 | Poi | 1.40 | 2.23 | NB |
Sweden | 1.26 | 3.19 | Poi | 0.85 | 0.79 | Poi | 1.05 | 1.27 | Poi | 1.68 | 0.77 | Poi |
Mexico | 1.60 | 1.47 | Poi | 0.69 | 1.52 | Poi | 1.57 | 1.24 | Poi | 1.48 | 1.52 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Belgium | 3.33 | 5.67 | Poi | 0.67 | 0.67 | Poi | 2.47 | 2.65 | Poi | 1.07 | 1.53 | Poi |
Panama | 1.38 | 1.01 | Poi | 0.73 | 0.50 | Poi | 1.00 | 1.63 | Poi | 1.44 | 2.10 | Poi |
Tunisia | 1.75 | 0.75 | Poi | 1.00 | 0.70 | Poi | 1.56 | 2.36 | Poi | 0.83 | 0.58 | Poi |
England | 2.19 | 1.15 | Poi | 0.50 | 0.50 | Poi | 1.80 | 2.83 | Poi | 0.53 | 0.65 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Senegal | 1.95 | 1.68 | Poi | 0.50 | 0.52 | Poi | 1.36 | 0.69 | Bin | 0.95 | 1.23 | Poi |
Japan | 2.33 | 3.17 | Poi | 1.06 | 1.33 | Poi | 1.60 | 2.24 | Poi | 0.67 | 0.49 | Poi |
Poland | 2.40 | 3.28 | Poi | 0.96 | 0.68 | Poi | 2.31 | 4.37 | Poi | 1.15 | 1.51 | Poi |
Colombia | 1.35 | 1.23 | Poi | 0.85 | 0.73 | Poi | 1.42 | 2.24 | Poi | 0.85 | 0.98 | Poi |
Position | Real | Points | Algorithm 6 | Estimated Points | Accuracy | |
---|---|---|---|---|---|---|
Group A | 1 | Uruguay | 9 | Uruguay | 6.4842 | 100% |
2 | Russia | 6 | Russia | 5.1548 | ||
Group B | 1 | Spain | 5 | Spain | 5.6867 | 100% |
2 | Portugal | 5 | Portugal | 4.8296 | ||
Group C | 1 | France | 5 | France | 7.3876 | 100% |
2 | Denmark | 5 | Denmark | 4.0612 | ||
Group D | 1 | Croatia | 9 | Croatia | 6.3811 | 100% |
2 | Argentina | 4 | Argentina | 4.6111 | ||
Group E | 1 | Brazil | 7 | Brazil | 7.0674 | 100% |
2 | Switzerland | 5 | Switzerland | 4.1768 | ||
Group F | 1 | Sweden | 6 | Sweden | 4.7170 | 100% |
2 | Mexico | 6 | Mexico | 4.3551 | ||
Group G | 1 | Belgium | 9 | Belgium | 7.3368 | 100% |
2 | England | 6 | England | 6.1921 | ||
Group H | 1 | Colombia | 6 | Colombia | 6.0252 | 100% |
2 | Japan | 4 | Japan | 4.7146 |
Real | Algorithm 7 | Accuracy |
---|---|---|
Uruguay | Uruguay | 75% |
France | France | |
Brazil | Brazil | |
Belgium | Belgium | |
Russia | Spain | |
Croatia | Croatia | |
Sweden | Sweden | |
England | Colombia |
Real | Algorithm 7 | Accuracy |
---|---|---|
France | France | 50% |
Belgium | Brazil | |
Croatia | Croatia | |
England | Colombia |
Real | Algorithm 7 | Accuracy |
---|---|---|
France | France | 100% |
Croatia | Croatia |
Real | Algorithm 7 | Accuracy |
---|---|---|
France | France | 100% |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Ecuador | 1.81 | 1.87 | Poi | 1.81 | 1.85 | Poi | 0.90 | 1.75 | Poi | 1.24 | 1.49 | Poi |
Senegal | 1.68 | 0.94 | Poi | 0.48 | 0.41 | Poi | 1.38 | 0.48 | Poi | 0.75 | 0.91 | Poi |
Qatar | 1.82 | 2.35 | Poi | 1.13 | 1.29 | Poi | 1.47 | 2.52 | Poi | 1.10 | 1.89 | Poi |
Netherlands | 2.00 | 2.46 | Poi | 1.00 | 0.77 | Poi | 1.15 | 2.75 | Poi | 2.10 | 1.00 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
England | 1.65 | 3.00 | Poi | 1.41 | 4.12 | Poi | 1.02 | 4.14 | NB | 0.31 | 0.46 | Poi |
Iran | 1.73 | 7.24 | NB | 1.20 | 3.96 | Poi | 0.97 | 3.83 | Poi | 0.27 | 0.34 | Poi |
USA | 1.84 | 3.29 | Poi | 0.80 | 1.65 | Poi | 0.49 | 1.49 | Poi | 0.35 | 0.43 | Poi |
Wales | 1.22 | 1.34 | Poi | 1.02 | 1.28 | Poi | 0.57 | 1.20 | Poi | 0.52 | 0.90 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Poland | 1.71 | 2.14 | Poi | 1.10 | 0.86 | Poi | 1.57 | 2.33 | Poi | 1.43 | 2.07 | Poi |
Mexico | 1.61 | 1.79 | NB | 0.71 | 0.92 | Poi | 0.92 | 0.99 | Poi | 1.35 | 1.69 | Poi |
Saudi Arabia | 1.61 | 1.79 | Poi | 0.71 | 0.92 | Poi | 0.92 | 0.99 | Poi | 1.35 | 1.69 | Poi |
Argentina | 1.88 | 1.92 | Poi | 0.59 | 0.74 | Poi | 1.92 | 1.99 | Poi | 0.96 | 2.04 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Australia | 2.23 | 3.10 | Poi | 0.38 | 0.39 | Poi | 0.74 | 2.99 | Poi | 2.11 | 0.49 | Poi |
France | 2.50 | 3.61 | Poi | 0.82 | 0.72 | Poi | 1.48 | 1.30 | Poi | 0.81 | 0.63 | Poi |
Denmark | 2.35 | 3.92 | Poi | 0.38 | 0.39 | Poi | 2.08 | 2.16 | Poi | 1.08 | 1.49 | Poi |
Tunisia | 1.70 | 2.14 | Poi | 0.57 | 0.45 | Poi | 1.00 | 1.52 | Poi | 0.90 | 1.23 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Spain | 2.68 | 4.01 | Poi | 0.52 | 0.63 | Poi | 1.80 | 1.76 | Poi | 0.96 | 0.68 | Bin |
Costa Rica | 1.14 | 0.90 | Poi | 0.67 | 0.32 | Bin | 0.83 | 0.67 | Poi | 1.45 | 0.94 | Poi |
Germany | 2.90 | 5.47 | Poi | 1.14 | 1.08 | Poi | 1.84 | 1.71 | Poi | 1.26 | 2.19 | Poi |
Japan | 2.13 | 4.38 | Poi | 0.84 | 1.34 | NB | 2.40 | 10.24 | Poi | 0.33 | 0.36 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Morocco | 1.83 | 1.63 | Poi | 0.51 | 0.65 | Poi | 1.84 | 2.24 | Poi | 0.68 | 0.95 | NB |
Croatia | 1.81 | 0.85 | Poi | 1.23 | 1.25 | Poi | 1.45 | 2.75 | Poi | 1.40 | 2.44 | Poi |
Belgium | 3.13 | 4.69 | Poi | 0.88 | 1.03 | Poi | 2.04 | 1.78 | Poi | 1.00 | 1.48 | Poi |
Canada | 3.42 | 2.98 | Poi | 0.42 | 0.35 | Poi | 2.28 | 7.46 | NB | 0.92 | 0.43 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Cameroon | 1.30 | 1.69 | Poi | 0.43 | 0.33 | Poi | 0.96 | 1.12 | Poi | 1.00 | 1.48 | Poi |
Brazil | 2.17 | 2.64 | Poi | 0.39 | 0.35 | Poi | 2.17 | 2.23 | Poi | 0.35 | 0.31 | Poi |
Switzerland | 2.20 | 3.36 | Poi | 0.68 | 0.62 | Poi | 1.50 | 2.25 | Poi | 1.55 | 1.16 | Poi |
Serbia | 2.43 | 2.24 | Poi | 1.19 | 0.82 | Poi | 1.28 | 1.08 | Poi | 1.00 | 2.20 | Poi |
Team | Mean Goals for as Host | Var. Goals for as Host | Law | Mean Goals against as Host | Var. Gals against as Host | Law | Mean Goals for as Guest | Var. Goals for as Guest | Law | Mean Goals against as Guest | Var. Goals against as Guest | Law |
---|---|---|---|---|---|---|---|---|---|---|---|---|
South Korea | 1.88 | 2.41 | Poi | 0.64 | 1.08 | Poi | 1.87 | 2.92 | Poi | 0.67 | 1.02 | NB |
Uruguay | 1.68 | 2.64 | Poi | 0.53 | 0.57 | Poi | 1.41 | 1.01 | Poi | 1.19 | 1.82 | Poi |
Portugal | 2.32 | 3.56 | Poi | 0.44 | 0.32 | Poi | 2.05 | 2.13 | Poi | 1.00 | 1.09 | Poi |
Ghana | 1.29 | 1.06 | Poi | 0.64 | 0.80 | Poi | 0.63 | 0.24 | Poi | 0.84 | 1.21 | Poi |
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López-Barrientos, J.D.; Zayat-Niño, D.A.; Hernández-Prado, E.X.; Estudillo-Bravo, Y. On the Élö–Runyan–Poisson–Pearson Method to Forecast Football Matches. Mathematics 2022, 10, 4587. https://doi.org/10.3390/math10234587
López-Barrientos JD, Zayat-Niño DA, Hernández-Prado EX, Estudillo-Bravo Y. On the Élö–Runyan–Poisson–Pearson Method to Forecast Football Matches. Mathematics. 2022; 10(23):4587. https://doi.org/10.3390/math10234587
Chicago/Turabian StyleLópez-Barrientos, José Daniel, Damián Alejandro Zayat-Niño, Eric Xavier Hernández-Prado, and Yolanda Estudillo-Bravo. 2022. "On the Élö–Runyan–Poisson–Pearson Method to Forecast Football Matches" Mathematics 10, no. 23: 4587. https://doi.org/10.3390/math10234587