The best predictions for the World Cup 2022 (pt. 4)

4 min readNov 22, 2022

The final tweak: Expected Value

In blog #1, we used the most common outcome overall and predicted it everywhere.

In blog #3, we calculated the chance for each outcome for a specific difference in FIFA rating between the two teams and predicted the one with the highest chance.

In this blog #4, we will use these same changes but instead also consider the rewards for each prediction. We do this by calculating the expected value, or EV.

*“A large die being rolled over a bright green football field. Digital art.” [image by Dall E]*

Expected what?

Expected value, or EV for the remainder of this blog.

I have written about EV before during the Euro Cup 2020, but I will give a small recap below.

EV is the value we get on average.

For a dice roll, it is 3.5. We cannot roll a 3.5, so you will never get it in one roll, but if you look at all the options:

Multiply the value of the outcome by the chance of it happening, add it all up, and we get:

1 * 0.167 + 2 * 0.167 + 3 * 0.167 + 4 * 0.167 + 5 * 0.167 + 6 * 0.167 = 3.5

And there the expected value appears.

A more detailed explanation and two more examples can be found here.

Football is not a dice roll

Indeed, it is not. But we can construct an imaginary die of sorts to mimic this.

For this, we look back at the graph from blog #3:

Occurrences of six different match results for each rating difference as a density function after data cleaning. [image by author]

Our example game will be:
Monday, November 25, Netherlands vs Ecuador

rating Netherlands = 1694.51
rating Ecuador = 1464.39
rating difference = 1694.51 - 1464.39 = 230.12

Which is this position on the graph:

Occurrences of six different match results for each rating difference as a density function after data cleaning. The red dotted line shows the rating difference between Netherlands and Ecuador. [image by author]

If we only consider these six possible outcomes, our “die” would look like this:

Of course, many other outcomes are possible but we will get to that later.

The point system

To calculate the EV for a die like the above, we need to know the number of points each result will yield.

My poule uses the following rules:

For example:
We predict 1–0, and the outcome is 2–0, we get 5 points for the correct winner and 2 points for the correct goal count for the away team yielding a total of 7 points.

Expanding the die table

We can now use the scoring to expand the table we constructed earlier.

We will create a column for each of the predictions we are considering at the moment showing the number of points we get when each of the outcomes would occur.

A table showing the number of points received for each combination of predictions (headers) and outcomes (first column).

We are ready to calculate the EV. Let’s do the calculation for the prediction of 1–0 first, note that for each outcome we add chance * points.

0.137 * 10 + 0.056 * 0 + 0.086 * 2 + 0.098 * 2 + 0.106 * 7 + 0.026 * 0 = 2.48

We can repeat the process for all six predictions and get the following:

A table showing the number of points received for each combination of predictions (headers) and outcomes (first column). The bottom row in bold shows the total expected value for each of the predictions.

We should choose the highest EV as our prediction, which in this case stays the same: 1–0.

However, not all positions stay the same: 1–1 has a higher chance of occurring than 0–0 but 0–0 has a higher expected value!

This happens because the prediction of 0–0 yields more points on other outcomes. When the actual outcome is 2–0 or 0–2, the prediction of 0–0 still results in 2 points, whereas a prediction of 1–1 would return nothing.

Final steps

For the final result, we need to consider more outcomes than only the six we have used so far. The process is the same, just add more rows and columns. Then construct it for each upcoming match and pick the prediction with the highest EV each time.

Updated predictions

Below is the full table with my updated prediction for the group stage. A prediction in bold italics means it is different from using only odds.

Also, I added a bonus prediction below.

When I add up all my EVs, I get the number of points I expect to end up with after the group stage, not considering any other point bonuses.