8 - Finally "Nul Points" - Maybe I'm confused but I'm pretty certain you could still get "Nul Points"? If both juries and the public only award 1-8, 10 & 12, it's surely possible an entry may not get a single point from any jury or any public vote? So perhaps "Nul Points" is less likely, but it certainly still seems possible?
Yes, it's still possible, but it's far less likely. For a simplified example, let's say that Armenia has an unpopular song. In any given country, there's a 10% chance for a jury to put Armenia in their top 10, and a 10% chance for the televoters to put them in their top 10. Under the old system, if a country is in the top 10 of both the jury and televote of a country, they've got a 100% chance to get points from that country, becoming a 0% chance if they're in neither top 10. Let's say there's a 20% chance of averaging into the top 10, and therefore getting points, if they're in the top 10 of one category and not another.
Mathematically, this means each country can have four outcomes with their split votes:
- Top 10 in both categories (10% x 10% = 1% chance)
- Top 10 in neither category(90% x 90% = 81% chance)
- Top 10 in jury but not televote (90% x 10% = 9% chance)
- Top 10 in televote but not jury (90% x 10% = 9% chance)
Adding together outcomes 3 and 4, we end with 18% of likely outcomes, and if they result in a top 10 average (and therefore points) 20% of the time, we end with those situations giving points in 3.6% of the total situations. Added to outcome one, this means that each country has a 4.6% chance of giving points to Armenia - or a 95.4% chance of
not giving them points. In a 40-country contest, we can figure out the probability of Armenia ending with 0 points by calculating that 95.4% to the power of 39 (ie. 'what is the probability of Armenia receiving no points 39 times in a row'), which gives us the final result of a
15.94% chance of Armenia ending with no points.
However, what about the new system? This should be somewhat easier to calculate, as the two processes are now separate. Effectively, there are now 78 separate voting groups (39 x 2) that could give votes to Armenia, and each of them has a 10% chance to give them votes, or a 90% chance not to give them votes. In this situation, we can calculate the likelihood of Armenia receiving zero points by finding 90% to the power of 78, which gives us the end result of a
2.70% chance to receive no points.
The new system, then reduces the chance of Armenia scoring zero points from 15.94% to 2.70%; their probability of scoring nothing has reduced to almost a sixth of what it was before. Do note, also, that I've just used basic napkin maths here; the likelihood of a particularly bad song ending in either category's top 10 is likely lower than 10%, which would exacerbate the difference. If we were to look at less and less popular songs, you'd notice the ratio of difference between the two percentages growing: it's exponential rather than linear, so
particularly bad songs would be helped even more by the new system. Plus, the ratio of difference is likely understated in my calculations - I didn't consider songs that were popular with the televote but not jury (or vice versa), the inclusion of which would've further shown the difference between the two systems.
TL;DR: The new system doesn't
eliminate the possibility of ending on zero points, no. However, it's not true that doubling the point pool just takes the chances down to 1/2 of what they were: when you look at the specifics, it actually calculates to be more like 1/6th for the song in our example, growing to 1/10th or more depending on the song in question. It's not out of the question that we'll be seeing more 0-pointers, but if we were getting one, say, every 3 years at the moment, we can probably expect to only see one every 20-25 years under the new voting system.