It’s Eurovision time again! A chance for everyone to enjoy musical performances that are either good or so bad they’re good, ridiculous staging, and hilarious costumes, all sprinkled with a gently sarcastic Irish voiceover (if you’re lucky enough to be watching in the UK).

BUT WHAT’S THIS? They’ve changed the voting system? Don’t worry – some mathematicians are here to straighten it out for you.

What’s that then?

A hangover from an old attempt at a unified European TV channel, the Eurovision Song Contest takes place each year in the country that won it the previous year. That country, along with five other countries who put a lot of cash in (France, Germany, Spain, Italy and the United Kingdom) get automatic entry to the contest, and semi-finals are held in the week running up to decide which countries will make up the rest of the 26 entrants, whittled down from 40.

The previous system

Under the old Eurovision voting system, each country, including eliminated semi-finalists, held a telephone vote on the night of the show, with the option to vote for any of the 25 or 26 other countries (no, you can’t vote for yourself). The results of that phone poll, alongside the votes of a jury of musical experts, were condensed down to a set of points given by each country – 12, 10 and 8 down to 1, ranking their top 10 countries in order. The points awarded by each country are announced by one if its minor celebrities, one country at a time over a patience-stretching hour-and-a-half or so, slowly revealing the final ranking.

Previously, we’ve written about the way the phone and jury information is combined to give the final points total, which is somewhat mathematically arbitrary, and never clearly explained or even really acknowledged.

Clearly, the Eurovision producers are avid Aperiodical readers, as they’ve rejigged this part of the system for the 2016 contest.

The new system

Under the new scoring system, jury and televoting results are kept separate, and each create their own ranking and set of 1, 2, 3, 4, 5, 6, 7, 8, 10 and 12 points; so twice as many points are awarded overall. The soporific 90-minute results drip-feed will only cover the results from the juries. After that, the results of the popular vote will just all be added on at the end in one go (the word ‘thwumpf’ has been used). The idea is that this keeps the results announcement more interesting: in past years it’s become mathematically impossible for any but the currently-leading country to win well before the end of the show. Since fully half the points are kept back until the end now, in theory any country could take 1st place at the last minute – if the callers at home are sufficiently contrarian relative to the expert juries.

This new system raises a couple of important questions. Is it likely to produce different results to the old system? And that big exciting announcement of the last half of the points – how much of a shake-up is it likely to create in the table?

Luckily, the kind bods at Eurovision provide the full jury and televote results for the last couple of years on their website, so we can simulate what would have happened if the new system had been in place. It’s time for SOME MATHS.

SOME MATHS

Here’s a table showing the top part of last year’s results:

Under the new system, each score would be split into a jury score and a televoting score, and the countries would be ranked in order firstly using the jury scores, then again after adding in the televoting results. Here’s how that would look:

The most obvious fact here is that there’s not much difference between the rankings under the new system: we have the same winner, the same top 3 and top 5: in fact nobody moves by more than four positions. There would have been little change in 2014 either: the top 5 is place-for-place identical under the two systems.

So, we can rest easy that this switch probably won’t affect the overall results too much. But surely the big phone-vote reveal at the end is going to be total ranking chaos, rendering the entire jury reveal a pointless exercise?

In fact the data suggests not. There’s a lot of movement outside the top of the table – Serbia shoot up from 23rd to 11th and Cyprus crash from 9th to 17th – but the winner is unchanged. In 2014 the top 3 would all remain static, with Poland rising from 23rd to 6th the biggest change. In general we might suppose that ‘novelty’ acts are likely to shift up the table after failing to amuse the po-faced juries, but going down a treat with the more accepting/drunk public.

If you’d like to perform your own statistical analysis of the results of Eurovisions past, the data is all available on their website, and Excel spreadsheets can be downloaded for 2014 and 2015. Or, just watch it and cheer when the people are silly.