Predicting FIFA World Cup 2014: A simulation based study

Transcription

1 Predicting FIFA World Cup 2014: A simulation based study Recommended BSC-LEVEL for readers of XXx-level ECONOMETRICS specialty NL The national football competitions have come to an end and coaches have announced their squads for the World Cup. Football fans from all over the world are getting excited about the upcoming tournament. Based on statistics I modeled a simulation system to predict the outcomes of the World Cup. In this article I present my methodology and the most important results. Methodology This research is simulation based, I modeled the upcoming World Cup in Excel. Using international ratings and rankings all participating nations are given a value representing their strength. For every match the relative strength between the home and away team is used to determine the expected amount of goals per team per match. Then using a stochastic process the matches are simulated. After all group stage matches the remainder of the tournament is simulated. In case of penalties during one of the final rounds, both teams have a 50% chance of winning. The conclusions of this study are based on simulations of the FIFA World Cup. The next paragraphs are devoted to the rankings and modeling of the goal scoring process. ELO rating There are several rankings to consider when looking at international teams, of which the FIFA ranking is probably best known. However, the ELO rating has a few advantages over the FIFA ranking and therefore the ELO rating 1 is used. The system uses a weighting for the kind of match (World Cup finals are far more important than friendly matches), an adjustment for the home team advantage, and an adjustment for goal difference in the match result. Another advantage is the existence of an expected result formula, to determine the chances to win for both teams. An important feature of the expected result is the advantage for teams playing home. They get a bonus score if they play a home match, causing a higher probability to win the match. I decided to award Brazil 1. For more information see: 20 By: Bas Koolstra a bonus of 60 points, because the tournament takes place in Brazil. Furthermore statistics show that World Cups are very often won by a country from the same continent as where the tournament takes place. Therefore teams from South-America receive a bonus of 30 points. Goals In the end football is always about scoring goals and that is why modeling the amount of goals per team per match is so important. Literature learns us that goals in football matches have the tendency to follow a Poisson distribution, this was shown by Norman (1998) and used in several simulations, for example by Dyte & Clarke (2000). To verify this information I studied all goals during the FIFA World Cup in 2010 (figure 1). Over the entire tournament teams scored an average of 1,13 goals per team per match. The distribution of the goals looks very similar to a Poisson distribution with an average of 1,13. The only exception was an outlier of seven goals, which was caused by the match Portugal - North Korea. 0,4 0,3 0,2 0,1 Goals World Cup Figure 1: Goals World Cup 2010 Goals per team per match Poisson distribution with mean 1,13

2 specialty NL Predictions Unfortunately the expected result formula of the ELO rating only predicts the probability to win and doesn t take into account the amount of goals during the match. Combining the expected win formula of the ELO ratings and the knowledge of the distribution of goals enables me to make a new model to predict the tournament. Using several optimization techniques to mininize the difference between my own winning probabilities and the ones of the ELO rating system and constraining the average amount of goals between boundaries based on previous World Cups I came up with a formula for the expected amount of goals for both teams: This provides me with the expected amount of goals for the home team and away team for a specific match. Using this as input for a draw from a Poisson distribution with mean Goals home and a draw with mean Goals away the real amount of goals for both teams are determined. In this way teams with a lower amount of expected goals still have chances to win the match, however they are not favorite to win the match. The bigger the rating difference, the less likely it is that the stronger team will loose. Results It shouldn t be much of a surprise that simulations of the FIFA World Cup lead to a lot of different scenarios. Although I didn t compare every single simulation to every other simulation, it is very unlikely that two simulations are exactly the same. Even the chance that one of the simulations will be replicated exactly at the real World Cup is relatively small, because with eight groups consisting of four teams, the round of 16, quarterfinals, semifinals and final there are a lot of possible developments of the tournament. However, based on simulations there is more than enough to tell about general expectations of the tournament. What team is favorite to win the World Cup? Which nations might better stay home because they will never win and do certain countries have a disadvantage because of strong opponents in the group stage? The average results of the World Cup simulations are shown in figure 2 (page 22), the most interesting and most important outcomes are discussed per stage in this section. Group stage Traditionally the host of the World Cup is placed in group A, Brazil proves to be firm favorite in this group. With an average of 8.2 points (out of 9), a highly positive goal difference and an impressive percentage of 93.91% first places they are expected to win this group. The highly desired second place is mainly a competition between Croatia and Mexico, with Mexico as most likely candidate to win. Cameroon has to hope for a big surprise, because their chances of making it to the next round are very low. Group B is often considered to be the toughest in this year s World Cup. Spain and the Netherlands both made it to the final in the previous World Cup and Chile is performing very well at the moment. This is a disaster for Australia, because with an average of 1.1 points they are the worst performing team in the simulations of the group stage. Spain, as winner of both FIFA World Cup 2010 and UEFA Euro 2012 is most likely to take the first place in this group. The battle for the second place in this group is extremely tight, but Chile has a slightly higher chance to make it to the next There is no doubt about it that Brazil is the biggest favorite to win the World Cup this year round: 59.49% (Chile) versus 54.02% (Netherlands). This is definitely going to be an interesting group! The countries in group C are of less prestige than the nations in group B. Colombia seems to profit from this. They have high chances of progressing to the next round, although it should be noted that a lot of their good results in the past were inspired by key player Falcao and as he is currently injured this could be a big problem for Colombia. The others in the group have to fight for place two, with Greece as light favorite but Japan and Ivory Coast definitely have the possibilities to surprise. Group D also has a country that almost certainly will return home after the three group stage matches, BSC-LEVEL ECONOMETRICS specialty NL 21

3 Recommended BSC-LEVEL for readers of XXx-level ECONOMETRICS specialty NL Costa Rica only makes it to the next round once per eight tournaments. Italy and England are still important countries in football, but both have only performed very average over the last years and that s visible in the expectations for this tournament in Brazil. The two European countries have to battle for a second place, behind strongly performing Uruguay. In group E France is considered to be the strongest. Ecuador and Switzerland perform very similar and have about the same chances to make it to the round of sixteen. Honduras is going to have a hard time in this group, but a surprise should definitely be possible. Group F has a very clear favorite, Argentina is not expected to have much problems with Bosnia and Herzegovina, Iran and Nigeria. Those last three teams have about equal chances to win the battle for the second ticket to the next round. The best team in group G is Germany, with a first place percentage of about 70%. Portugal might be a problem for the Germans, and is favorite for place two in the group. The United States should be hoping for a small surprise and Ghana for a huge one. The last group, H, is not the strongest in the tournament. Belgium and Russia shouldn t have too much trouble, an average performance of them is enough to progress. However, it will be very interesting to see which of them is going to win this group. Round of 16 As the first and second team of every group in the first stage make it to the round of 16 it is not a surprise to see the same teams in this round as earlier mentioned to be favorites in their group. Countries like Brazil, Argentina and Germany are almost certain to make it to this round, while important teams like Italy, the Netherlands, England, Ecuador, Switzerland and Chile have serious chances of missing this round. Australia is least likely to make it to the second round, followed by Cameroon and Ghana. Quarterfinals Not surprisingly the teams that were present in the second round in most cases are also the teams that are mostly playing in the quarterfinals. However, there are some very interesting remarks to make about this. Let s have a look at a small comparison between Brazil and Germany. In the round of 16 Brazil played 99.23% of the matches, but they only played 67.55% of the quarter finals. This means that they lost about 32% of their matches in the second round. Germany played 91.38% of the matches in the second round, and 78.25% of the quarter finals. They only got eliminated in approximately 14% of their matches in the second round. A logical explanation for this would be the World Cup schedule, because the winner of group A always plays number two of group B. As earlier mentioned group B is a very Group Team Points GF GA GD Grp 1 Grp 2 Grp 3 Grp 4 Q16 Quarters Semis Final Brazil % 5.32% 0.74% 0.03% 99.23% 67.55% 51.43% 35.97% 23.95% 12.02% 11.23% 4.23% Cameroon % 9.37% 24.21% 66.17% 9.62% 0.57% 0.03% 0.01% 0.00% 0.01% 0.00% 0.02% A Croatia % 35.39% 42.02% 20.47% 37.51% 6.37% 1.78% 0.25% 0.03% 0.22% 0.37% 1.16% Mexico % 49.92% 33.03% 13.33% 53.64% 11.29% 3.81% 1.19% 0.20% 0.99% 0.70% 1.92% Australia % 3.35% 12.16% 83.88% 3.96% 0.43% 0.09% 0.02% 0.00% 0.02% 0.04% 0.03% Chile % 35.85% 34.15% 6.36% 59.49% 29.27% 17.03% 8.82% 3.60% 5.22% 4.32% 3.89% B Netherlands % 33.09% 38.17% 7.81% 54.02% 26.22% 15.34% 7.42% 2.97% 4.45% 4.26% 3.66% Spain % 27.71% 15.52% 1.95% 82.53% 58.30% 41.57% 26.41% 14.67% 11.74% 9.49% 5.67% Colombia % 22.84% 9.26% 3.90% 86.84% 48.84% 18.57% 9.33% 4.12% 5.21% 4.83% 4.41% Greece % 31.16% 29.66% 22.98% 47.36% 15.94% 3.64% 1.18% 0.27% 0.91% 0.79% 1.67% C Ivory Coast % 26.54% 31.12% 30.35% 38.53% 11.74% 2.58% 0.65% 0.15% 0.50% 0.46% 1.47% Japan % 19.46% 29.96% 42.77% 27.27% 7.50% 1.32% 0.33% 0.04% 0.29% 0.29% 0.70% Costa Rica % 9.20% 22.54% 64.97% 12.49% 4.21% 0.65% 0.17% 0.05% 0.12% 0.12% 0.36% England % 32.57% 28.32% 13.38% 58.30% 32.38% 10.19% 4.33% 1.44% 2.89% 2.32% 3.54% D Italy % 30.08% 33.33% 16.40% 50.27% 26.94% 8.24% 3.30% 1.01% 2.29% 2.13% 2.81% Uruguay % 28.15% 15.81% 5.25% 78.94% 52.45% 23.73% 12.90% 5.94% 6.96% 5.84% 4.99% Ecuador % 30.93% 28.08% 14.98% 56.94% 24.66% 8.79% 2.70% 0.75% 1.95% 2.24% 3.85% France % 28.68% 19.51% 8.79% 71.70% 38.83% 16.14% 5.09% 1.77% 3.32% 4.85% 6.20% E Honduras % 11.30% 23.79% 59.99% 16.22% 4.05% 0.84% 0.13% 0.00% 0.13% 0.10% 0.61% Switzerland % 29.09% 28.62% 16.24% 55.14% 24.65% 8.69% 2.54% 0.68% 1.86% 2.19% 3.96% Argentina % 13.06% 3.52% 0.97% 95.51% 70.01% 44.42% 24.37% 11.63% 12.74% 11.11% 8.94% Bosnia and Herzegovina % 27.65% 32.10% 34.68% 33.22% 11.96% 2.78% 0.61% 0.13% 0.48% 0.33% 1.84% F Iran % 31.07% 31.70% 30.59% 37.71% 14.18% 3.37% 0.48% 0.08% 0.40% 0.57% 2.32% Nigeria % 28.22% 32.68% 33.76% 33.56% 11.66% 2.46% 0.50% 0.08% 0.42% 0.46% 1.50% Germany % 21.97% 7.50% 1.12% 91.38% 78.25% 59.56% 33.33% 20.66% 12.67% 18.18% 8.05% Ghana % 6.19% 19.75% 73.11% 7.14% 2.70% 0.60% 0.17% 0.04% 0.13% 0.09% 0.34% G Portugal % 43.12% 28.84% 8.20% 62.96% 44.19% 23.44% 9.86% 3.71% 6.15% 6.24% 7.34% United States % 28.72% 43.91% 17.57% 38.52% 23.95% 10.43% 3.61% 1.02% 2.59% 2.61% 4.21% Algeria % 15.48% 29.80% 48.04% 22.16% 2.71% 0.70% 0.13% 0.00% 0.13% 0.05% 0.52% Belgium % 31.44% 16.11% 7.48% 76.41% 23.60% 9.23% 2.47% 0.59% 1.88% 2.06% 4.70% H Russia % 34.03% 19.17% 9.12% 71.71% 20.26% 7.41% 1.63% 0.41% 1.22% 1.57% 4.21% South Korea % 19.05% 34.92% 35.36% 29.72% 4.34% 1.14% 0.10% 0.01% 0.09% 0.16% 0.88% Figure 2: Average simluation results 22

4 Australia is least likely to make it to the next round! specialty NL strong one, so Brazil is almost certain to have a difficult match in the second round, whereas Germany is not likely to have much trouble with opponents like Russia, Belgium, Algeria or South Korea. Another important lesson from the teams in the quarterfinal is that if teams make it to the second round by surprise they have very little chance of causing another surprise. Cameroon doesn t make it to the second round often, but if they do they only have a 6% chance of making it to the quarterfinal. Australia performs a little better, they have an expectation of about 11%. Semifinals As the final gets closer surprises are getting rarer. Germany, Brazil, Argentina and Spain are the big four that we need to watch this summer, they make it to the semifinals most often. Under the condition that all four of them win their group during the first stage of the tournament, it is even possible that those four teams make it to the semifinals all together. In that case Germany would play Brazil and Argentina would play Spain. Winner There is absolutely no doubt about the favorite to win the World Cup this year, Brazil is the most likely contender. With years of strong performance, home advantage and a relatively easy start in the group stage they are top ranked to take the trophy home. Germany is a strong candidate as well, Brazil seems to be their biggest obstacle towards the final. Spain needs to have a good start, but if they succeed in that then there are great possibilities for them as well. Most likely tournament People that like to make a bet on not only the winner, but the entire tournament need to be careful. Although Germany wins the tournament most often after Brazil, they are not very likely to play the final against Brazil. This has to do with the structure of the tournament, both teams have large chances of taking the first place in the group stage. If they both do so, they will already play against each other in the semifinals, making it impossible to both make it to the finals. Another important factor is the absence of the Netherlands in the round of 16, they are victim of their strong group. Chile and Spain are more likely to make it through the group stage. The complete most likely tournament is shown in figure 3. Relative performance Figure 4 (page 24) shows the relative performance of teams, based on their rating and the amount of tournament wins in the simulation process. On first sight this comparison shows that most countries perform like expected. Chile, The Netherlands, Japan and Croatia seem to underperform, while Columbia and Portugal perform better than expected. Top teams like Brazil, Germany and Spain don t seem to overperform or underperform when we only look at the difference between rankings based on ratings and on tournament wins. However, a closer look shows something remarkable. Germany s rating is only 0,6% higher than the rating Spain has, however Germany wins the tournament 599 times more than Spain, which is an astonishing difference considering that Spain wins 1467 out of simulations. Round of 16 Brazil - Chile Quarterfinals Colombia - England Brazil - Colombia Semifinals Final 1 Brazil Spain - Mexico France - Germany Brazil - Germany Brazil - Spain 2 Spain Uruguay - Greece Spain - Uruguay Spain - Argentina 3 Germany France - Iran Argentina - Portugal 4 Argentina Germany - Russia Argentina - Ecuador Belgium - Portugal Recommended BSC-LEVEL for readers of XXx-level ECONOMETRICS specialty NL Figure 3: Most likely tournament 23

5 Recommended BSC-LEVEL for readers of XXx-level ECONOMETRICS specialty NL About the author Bas Koolstra Bas (23) completed his BSc Actuarial Science at the University of Amsterdam in the summer of Then he spent a semester abroad at McMaster University, Canada. After returning to the Netherlands he took a full-time position as chairman in the board of study association VSAE. He recently started his MSc Financial Econometrics and is expecting to finish mid Next to economics Bas is interested in sports, especially football and cycling. 24 Figure 4: Relative performance per country Conclusions The combination of the expected win formula of the ELO rating and the Poisson distribution of goals in football enable me to simulate the upcoming World Cup. These simulations prove that Brazil has high chances of winning the World Cup. Other strong opponents are Germany, Spain and Argentina. The simulations show that Colombia and Portugal have high chances of overperforming in this tournament, probably because of an advantegeous schedule. Chile, Japan and Croatia are expected to underperform based on these simulations. A deeper analysis also shows that Spain performs worse than their direct opponents for the top places. The simulations also confirm the low expectancy about the Netherlands for this World Cup. Their group is very strong and the possibilities of playing against Brazil in the round of 16 are high. However, according to the model they still have about 3% chance to win the World Cup. This is more than for example England, Italy and France. In the end it is important to note that we only have one tournament this summer and all countries have chances to win. This model predicts chances based on very large numbers, so the chances of the tournament developing like the most likely tournament are relatively small. References Dyte, D., & Clarke, S. R. (2000). A ratings based Poisson model for World Cup soccer simulation. Journal of the Operational Research society, 51(8), Norman, J.M. (1998). Soccer. In: Bennett, J. (ed). Statistics in Sport. Arnold: London, pp