The Eurovision season starts in earnest for me when Wiwibloggs start releasing their jury videos. I love the discussions between all the panelists, and by the time the videos are coming out I’ve listened to the songs enough to have opinions on them. At the end of the video, they give an average of the scores from the jurors. The average* (strictly speaking, the arithmetic mean) is a great indicator of how popular a song is; generally, the higher the average, the more popular the song. However, Eurovision is won by people voting for you, not rating every song.
We can see how the average loses some of the detail by taking two fictional countries, Megalomania and Ruritania. Megalomania’s entry, ‘LovePanther’, is a pretty generic pop song, while Ruritania’s entry, ‘Loud Screaming for Peace’ is a divisive ethno-techno-metal number. If the entry from Megalomania received a six from every Wiwijuror, it would receive an average of six. If half the Wiwijurors gave the song from Ruritania zero points, while the other half gave it ten, it would receive an average of five. Based on the average, Megalomania would beat Ruritania. However, the people that really like ‘Loud Screaming for Peace’ would vote for it, while Megalomania might not receive any votes because, while no-one objects to it, they’d be voting for their favourites instead.
One way of capturing this spread of votes is the standard deviation. This gives us an indication of how ‘controversial’ a song is (in the sense of people disagreeing about its merits). A low number means more agreement, and a high number means less agreement.
| Country | Standard deviation | Country | Standard deviation |
|---|---|---|---|
| Switzerland | 0.76 | Australia | 1.61 |
| Malta | 1.04 | Azerbaijan | 1.61 |
| Sweden | 1.17 | Latvia | 1.63 |
| Croatia | 1.27 | Finland | 1.69 |
| San Marino | 1.27 | Spain | 1.71 |
| Belgium | 1.28 | Poland | 1.75 |
| Israel | 1.31 | Austria | 1.78 |
| Iceland | 1.37 | Slovenia | 1.84 |
| United Kingdom | 1.38 | Estonia | 1.84 |
| Ireland | 1.40 | Ukraine | 1.84 |
| Greece | 1.42 | Serbia | 1.97 |
| Moldova | 1.44 | Portugal | 2.01 |
| Romania | 1.48 | Italy | 2.03 |
| Russia | 1.48 | Bulgaria | 2.07 |
| Cyprus | 1.50 | Norway | 2.09 |
| Lithuania | 1.51 | Germany | 2.12 |
| North Macedonia | 1.55 | Netherlands | 2.16 |
| France | 1.58 | Denmark | 2.21 |
| Albania | 1.58 | Czechia | 2.23 |
| Georgia | 1.59 |
However, controversial doesn’t mean good. Franc and Albania are equally (according to the Wiwijury) controversial in that they have the same standard deviation. However, Barbara Pravi’s ‘Voilà’ is a masterpiece of composition, writing, and performance that is pushing for the very top, while Albania’s Balkan ballad is, I fear, going to struggle to get out of the semis (sorry, Anxhela!). I’m slightly surprised that the Netherlands has such a high standard deviation, but I can easily see that the naff lyrics and Melfest-machine-feeling of Benny Cristo’s ‘Omaga’ from Czechia would be divisive, as would the eighties styling of Fyr & Flamme’s ‘Øve os på hinanden’; for some reason, there are people who look back at the eighties fondly. ‘I Don’t Feel Hate’ by Jendrik from Germany is also divisive, which makes sense; some people like the wackiness, while some people just see it as lyrically annoying and preachy and musically too many things mashed together.
I’ve been trying to think of a single number to capture both central tendency and dispersion (average and standard deviation), but I just don’t think it’s possible. The best I could come up with was average plus one standard deviation, but that is basically pulled out of the air – about two-thirds of votes come within one standard deviation above or below the mean in a normally distribution (though, as we will see, not all the songs’ verdicts from the Wiwijury are normally distributed).
A better alternative than trying to boil everything down to one number is, I think, to represent it graphically.
The fat bit just before 7.5 indicates where lots of votes went for Croatia, with a few higher and a few more lower. Croatia has an average of 6.73 and a standard deviation of 1.27. Basically, there’s a lot of agreement that is a really good, but not spectacular, song, with a few people rating it higher and a few lower. The highest score was a 9, while the lowest was a 4.5. The curve suggests what the distribution might be if there were more people in the Wiwijury.
On its own, though, that doesn’t tell us much. Let’s put them all together and see what we get.
This list is sorted by average, which actually suggests that the average is a pretty good indicator of how good a song is – remember, the fatter a section is, the more Wiwijurors went for that score for that song. However, it does provide some possible insights for how songs close to each other might do.
Let’s start at the top. France and Malta are an interesting pair to consider and raises a really interesting question about how we interpret these graphs: how far from in from the right should we go? If we were just looking at scores of ten, we would clearly rather be France than Malta. Because France has a longer tail, though, there comes a point at which Malta has more high scores than France. If we say that votes from the Wiwijury of 9+ translate to points from the public televote and the professional juries, France is in the better position. If it’s 8+, they’re probably very close. If it’s 7+, it’s probably Malta that will edge it.
This brings us onto Switzerland. With the caveat from the paragraph above, I think we might actually expect, based on Wiwijury ratings, France and Malta to do better than Switzerland, even though their averages are lower, as they have more of the highest scores. That’s best seen with France – it has a long tail to the left of people who aren’t as keen on the song, which drags the average down. However, you can’t vote against songs.
On a similar basis, I think we might expect Italy to do better than the average would suggest. I’m a little worried about the UK; James Newman is piling up the sevens, but few scores higher than that. Of course, a fantastic stage show would help, and the gaps between verses and lyrics, and the refrain of ‘light up the room!’ suggest that there’s going to be fireworks from Blighty, figuratively and possibly literally.
Portugal have entered another song that I love that no-one else seems to (I still listen to ‘O Jardim’), but the bulge to the right of its ridgeline suggests they might do better than the average suggests (unless those are all the Wiwijurors who know the story behind the song). You can see how controversial Germany is with how wide its distribution is. I think Ukraine might do worse than its average suggests (which makes me sad, as I will almost certainly be voting for GO_A on the night) as it has a peak at around seven and a long tail to the right. Austria might be above where the average would indicate, and so on.
I might look back at previous years and see how well something like mean plus standard deviation, or mean plus interquartile range, of Wiwijury results ranks performances against their actual results. Of course, the Wiwijury results don’t take into account stage performances, national voting patterns and so on, but it’s interesting nonetheless. I suspect that there’ll be a score that effective translates into votes/not votes, and that will answer some of the questions above. Another alternative would be to use a Borda count to rank the songs, as we know how each juror voted.
* Wiwibloggs drops the highest and lowest score when calculating their average to deal with bias; I don’t think there’s a good statistical reason to do that, so I don’t do it.