Disclaimer: In this editorial, some opinions of the writer are expressed and do not reflect the views of our other editors, ESC United, or the EBU. Warning: Maths Ahead

Following the results of the 2023 Eurovision Grand Final in Liverpool, a few loud voices have expressed their will for jury reform due to the televote winner, Finland, losing to the jury winner, Sweden, which has got a marginal lead in the jury results. I decided to take that opportunity to look a bit deeper into one of the latest jury reforms the EBU has implemented in the past few years.

This is by no means a call for another jury reform or change of the voting system but a statistical overview of past changes, their benefits, and problems.

The Exponential Jury System

In 2018, the EBU announced that a new system would be used to calculate the points given by each national jury, the positively hyped “Exponential System.” Shortly, this system would try to minimize the effect of songs disliked a lot by one juror or 2, dragging down their average ranking massively and lowering their overall score. Whether that is desired or not is a personal opinion, but what is more interesting is that this supposedly significant change does not change much at all.

Let’s examine said change in detail. Until 2018, the ranking of each national jury in the semi-finals and grand final of Eurovision was calculated relatively simply. Each national jury consists of five members who rank all songs participating in the show (excluding their own country if applicable), and their combined ranking is made out of the average of these five individual rankings. The top 10 of said combined ranking receive the famous 1-8, 10, and 12 points from that national jury.

The implemented change was regarding the calculation of the combined ranking. Instead of taking the average of the rankings and sorting based on the minimum average, each placement given by an individual juror is transformed into a different number, a “weight,” and those weights are summed instead of the actual placement given by the juror. These sums are later sorted, and the higher the sum is, the better the placement the song receives from this national jury.

Okay but what does that actually mean?

The transformation of the placement is done exponentially, which, in simple terms, means that better placements have a higher weight than lower placements in a multiplicative way. In order to fully explain the model, here is the accurate formula that describes the exponential transformation done to the placement.

If a song receives a placement of X in an individual ranking, then the transformed number being summed instead of just X is (c^X). “c” could be any real number between 0 and 1. Different transformations occur for different values of c, which can result in a different result.

Below is a simple graphic that presents how different values of c affect the transformed numbers in a combined ranking:

Here’s an example to demonstrate how these transformations work and how different values of the exponent, “c”, can change the outcome in a ranking. Assume the following are the placements that 2 countries, Country A and Country B, received from a 5-member jury of another country, Country C:

Country A 1 4 9 10 3
Country B 2 12 3 9 2

We want to compare them using three systems with three different exponent values. System #1 will be the first extreme with an exponent that is very close to 1, which, without going into a bit more complex maths, is just equivalent to sorting by regular average as the differences between adjacent weights remain the same.

System #2 will have a middle value of c = 0.827, which is approximately the value used by the EBU since 2018 and acts as a somewhat middle ground between the other two systems. It means that every weight has a 0.827 of the value of the weight that comes before it.

Lastly, system #3 would be a more extreme exponent value of c=0.2. System #3 can also be simply described in the following way. To compare 2 Countries, one has to compare how many 1st places they got, and if there’s a tie in that amount, compare the 2nd places, and so on, until the tie resolves. That is because each weight equals a fifth of the weight of one placement higher, so even if a song received five 2nd places, it won’t match one 1st place. Here are the results across those systems:

As we can see, as we lower the value of the exponent, “c”, each weight has much less impact than weights bigger than it. Even to the point of the extreme case of system #3, where each weight has a fifth of the value of the previous weight, and the sorting is done as explained, by the amount of 1st places, with ties handled by counting the amount of 2nd places and so on until resolved.

Overall, even from this small exercise, we can learn that the value of the exponent can change the order in a ranking in numerous ways. That brings up the main problem with implementing this change suggested by the EBU: Transparency. The EBU does not reveal what is the value of the exponent that they are using each year. Upon researching the data posted by the EBU for several years since 2018, it seems that they are using the same exponent value each year, which is 0.827. However, there is nothing stopping them from modifying this value in the future, which may change the result, as we’ve just established.

Can the exponent change the results?

That also leads to a more important question, which is: How much can different exponents change the results? We’ve shown that different values of the exponent can change the order in a ranking of a national jury, but how much would that come into play when looking at a real data set from Eurovision? The answer is not completely one-sided. Here are the results of two different shows: 2021 grand final and 2019 semi-final 2, using the three different systems we have described earlier using different exponent values:

These imply somewhat mixed conclusions. On one hand, numerous songs move around a lot due to different exponent values. The more polarizing songs between individual juries benefit from a lower exponent, such as Belgium 2021, Ukraine 2021, and Norway 2019. The songs that receive more average places benefit from a higher exponent value, such as Cyprus 2021, San Marino 2021, and Albania 2019. On the other end, the impact is relatively small on the top placing songs, especially with the constant televote added.

However, one obvious conclusion can be deducted. This “Exponential System” can cause much trouble with little gain. The trouble comes from the need for more transparency of the EBU about the used exponent value, which can change the results, even to the point of changing the qualifiers. For instance, even with an exponent value slightly lower than the one used now, c = 0.7, Albania would not have qualified in 2019.

The lack of gain from using this system is that around half the countries in a show, mainly the top and bottom few, will not change their place at all, and the ones that will change place will almost always move one or two places up or down.

This problem has a straightforward solution. The EBU needs to regulate what exponent value they use yearly before Eurovision and make that information available to the public. It changes so little of the results to create such trouble, but even that little can change enough to justify the simple request for transparency.

What do #YOU think about the exponential system and the lack of transparency from the EBU? How would #YOU have the jury’s results calculated? Let us know on social media @ESCUnited, on our Discord, or on our forum page!

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