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Using the  FIFA World Ranking and the Elo rating system we will try to estimate the probability of England winning its first Euro in history! The expected result of a game is given by the formula:

where dr is the difference between two teams’ ratings before the game. Let’s see the function of the Winning Probability versus the Ranking Difference:

```diffs<-seq(-1000,1000)
probs<-1/(1+10^(-(diffs)/600))

plot(diffs, probs, main="Winning Probability vs Ranking Difference", xlab = "Ranking Differences", ylab = "Winning Probability")
```

## The Wembley Factor

Provided that England will qualify for the Finals, it will play both games in Wembley, i.e at Home. This is a key factor in the predictions. Looking at the descriptive statistics in Premier League, teams consistently win around 46.2% of home games, while the draw occurs around 27.52% of the time and the away team is victorious in 26.32% of games. If we normalize the probability to win by excluding “draws” (46.2/(46.2+26.32)) we get that the probability to win is 63.7%. This is the “Wembley factor” to qualify for the next two games.

## How the Home Effect is Translated in ELO System

In order to adapt the Home Effect in the Winning probability, we will need to find out what is the required difference for a team to have 63.7% chances to win. We can solve it numerically.

```diffs[(probs>0.637)][1]
[1] 147
```

Thus, the Wembley effect is like a boost of 147 points in the ELO System.

## Probability to Qualify to Finals

Taking into consideration the Wembley Effect and the ELO Winning Formula, the probability to qualify against Denmark is 68.46%.

```england = 1687 + 147
denmark = 1632

1/(1+10^(-(england-denmark)/600))
[1] 0.6846455
```

## Probability to Win Euro 2020

In the finals will be either Italy or Spain where both teams have the same FIFA Ranking. Let’s see what will be the probability to win Spain.

```england = 1687 + 147
spain = 1648

1/(1+10^(-(england-spain)/600))
[1] 0.6712406
```

According to the formula, the probability is 67.12%. Thus to probability to win the Euro 2020 is 67.12% x 68.46% = 45.95%.

So according to this approach, England has around 46% chances to win the Euro for the first time in history!

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