In a previous post, we built a Predictive Model based on FIFA Ranking and making the assumption that the points follow a normal distribution. If we look closer at FIFA’s Ranking Model we will see that it is based on the ELO System where the expected result of the game can be extracted from the following formula:
Simulate the Final-16 Phase Based on the Expected Result
Let’s run 10000 simulations to estimate the probability of the Euro 2020 Winner.
# get the UEFA Ranking
ranking<-list(bel=1783,
fra=1757,
eng=1687,
por=1666,
esp=1648,
ita=1642,
den=1632,
ger=1609,
sui=1606,
cro=1606,
net=1598,
wal=1570,
swe=1570,
aus=1523,
ukr=1515,
cze=1459)
win_prob<-function(a,b) {
w_prob<-1/(1+10^(-(a-b)/600))
outcome<-sample(c(TRUE,FALSE), 1, prob=c(w_prob, 1-w_prob))
return(outcome)
}
sim_champion<-c()
final<-c()
# number of simulations
n<-10000
for (i in 1:10000) {
#######################
#### Final 16
#######################
# game bel vs por
teams_game1<-c("bel","por")
game1<-win_prob(ranking[[teams_game1[1]]], ranking[[teams_game1[2]]])
if (game1) {
qualified_game1<-teams_game1[1]
} else {
qualified_game1<-teams_game1[2]}
qualified_game1
# game ita vs aus
teams_game2<-c("ita","aus")
game2<-win_prob(ranking[[teams_game2[1]]], ranking[[teams_game2[2]]])
if (game2) {
qualified_game2<-teams_game2[1]
} else {
qualified_game2<-teams_game2[2]}
qualified_game2
# game fra vs sui
teams_game3<-c("fra","sui")
game3<-win_prob(ranking[[teams_game3[1]]], ranking[[teams_game3[2]]])
if (game3) {
qualified_game3<-teams_game3[1]
} else {
qualified_game3<-teams_game3[2]}
qualified_game3
# game cro vs esp
teams_game4<-c("cro","esp")
game4<-win_prob(ranking[[teams_game4[1]]], ranking[[teams_game4[2]]])
if (game4) {
qualified_game4<-teams_game4[1]
} else {
qualified_game4<-teams_game4[2]}
qualified_game4
# game swe vs ukr
teams_game5<-c("swe","ukr")
game5<-win_prob(ranking[[teams_game5[1]]], ranking[[teams_game5[2]]])
if (game5) {
qualified_game5<-teams_game5[1]
} else {
qualified_game5<-teams_game5[2]}
qualified_game5
# game eng vs ger
teams_game6<-c("eng","ger")
game6<-win_prob(ranking[[teams_game6[1]]], ranking[[teams_game6[2]]])
if (game6) {
qualified_game6<-teams_game6[1]
} else {
qualified_game6<-teams_game6[2]}
qualified_game6
# game net vs cze
teams_game7<-c("net","cze")
game7<-win_prob(ranking[[teams_game7[1]]], ranking[[teams_game7[2]]])
if (game7) {
qualified_game7<-teams_game7[1]
} else {
qualified_game7<-teams_game7[2]}
qualified_game7
# game wal vs den
teams_game8<-c("wal","den")
game8<-win_prob(ranking[[teams_game8[1]]], ranking[[teams_game8[2]]])
if (game8) {
qualified_game8<-teams_game8[1]
} else {
qualified_game8<-teams_game8[2]}
qualified_game8
#######################
#### Final 8
#######################
teams_f8_1<-c(qualified_game1,qualified_game2)
game_f8_1<-win_prob(ranking[[teams_f8_1[1]]], ranking[[teams_f8_1[2]]])
if (game_f8_1) {
qualified_f8_1<-teams_f8_1[1]
} else {
qualified_f8_1<-teams_f8_1[2]}
qualified_f8_1
teams_f8_2<-c(qualified_game3,qualified_game4)
game_f8_2<-win_prob(ranking[[teams_f8_2[1]]], ranking[[teams_f8_2[2]]])
if (game_f8_2) {
qualified_f8_2<-teams_f8_2[1]
} else {
qualified_f8_2<-teams_f8_2[2]}
qualified_f8_2
teams_f8_3<-c(qualified_game5,qualified_game6)
game_f8_3<-win_prob(ranking[[teams_f8_3[1]]], ranking[[teams_f8_3[2]]])
if (game_f8_3) {
qualified_f8_3<-teams_f8_3[1]
} else {
qualified_f8_3<-teams_f8_3[2]}
qualified_f8_3
teams_f8_4<-c(qualified_game7,qualified_game8)
game_f8_4<-win_prob(ranking[[teams_f8_4[1]]], ranking[[teams_f8_4[2]]])
if (game_f8_4) {
qualified_f8_4<-teams_f8_4[1]
} else {
qualified_f8_4<-teams_f8_4[2]}
qualified_f8_4
#######################
#### Final 4
#######################
teams_f4_1<-c(qualified_f8_1,qualified_f8_2)
game_f4_1<-win_prob(ranking[[teams_f4_1[1]]], ranking[[teams_f4_1[2]]])
if (game_f4_1) {
qualified_f4_1<-teams_f4_1[1]
} else {
qualified_f4_1<-teams_f4_1[2]}
qualified_f4_1
teams_f4_2<-c(qualified_f8_3,qualified_f8_4)
game_f4_2<-win_prob(ranking[[teams_f4_2[1]]], ranking[[teams_f4_2[2]]])
if (game_f4_2) {
qualified_f4_2<-teams_f4_2[1]
} else {
qualified_f4_2<-teams_f4_2[2]}
qualified_f4_2
#######################
#### Final
#######################
teams_f<-c(qualified_f4_1,qualified_f4_2)
game_f<-win_prob(ranking[[teams_f[1]]], ranking[[teams_f[2]]])
if (game_f) {
champion<-teams_f[1]
} else {
champion<-teams_f[2]}
sim_champion<-c(sim_champion,champion)
final<-c(final, teams_f)
}
prop.table(table(sim_champion))*100
sort(table(final), decreasing = FALSE)/10000
Estimate the Winner
By running this simulation above, we can estimate the probability of each team to win the Euro 2020
Outcome:
sim_champion aus bel cro cze den eng esp fra ger ita net por sui swe ukr wal 1.68 16.22 3.74 1.33 7.64 10.17 6.53 14.70 4.75 6.83 5.99 6.21 3.38 4.37 2.28 4.18
| Team | Prob (%) |
| bel | 16.22 |
| fra | 14.7 |
| eng | 10.17 |
| den | 7.64 |
| ita | 6.83 |
| esp | 6.53 |
| por | 6.21 |
| net | 5.99 |
| ger | 4.75 |
| swe | 4.37 |
| wal | 4.18 |
| cro | 3.74 |
| sui | 3.38 |
| ukr | 2.28 |
| aus | 1.68 |
| cze | 1.33 |
As we can see, Belgium has 16.22% to win the Euro 2020 and it is the favorite according to this approach.
Estimate the Probability of Each Team to Reach the Finals
We can also estimate the probability of each team reaching the Finals.
> sort(table(final), decreasing = TRUE)*100/n final bel fra eng den net ger swe ita wal esp por cro ukr sui cze aus 24.91 22.66 21.63 16.54 14.81 12.62 11.34 11.23 11.12 11.06 10.89 7.96 7.01 6.87 4.93 4.42
| Team | Prob (%) |
| bel | 24.91 |
| fra | 22.66 |
| eng | 21.63 |
| den | 16.54 |
| net | 14.81 |
| ger | 12.62 |
| swe | 11.34 |
| ita | 11.23 |
| wal | 11.12 |
| esp | 11.06 |
| por | 10.89 |
| cro | 7.96 |
| ukr | 7.01 |
| sui | 6.87 |
| cze | 4.93 |
| aus | 4.42 |
As we can see, Belgium (21.91%) and France (22.66%) have the highest chances to reach the finals, but also England (21.63%). Compare Belgium and France in terms of chances to Win Euro (16.22% vs 10.17%) versus the chances to reach the finals (21.91% vs 21.63%). This has to do with the fact that England has an “easier” schedule compared to Belgium and France. When the schedule plays a role, then the need for a simulation is of paramount importance.
