Did this a while back.
Some interesting statistics:
Last ten ESC:s the average start number for 1:st, 2:nd and 3:rd places are
1:st place: 17.5
2:nd place: 12.9
3:rd place: 11.2
If you look only at the last five years:
1:st place: 20.4
2:nd place: 13.8
3:rd place: 14.6
2:nd and 3:rd seem to be pretty smack down in the middle when the number of finalists has been between 24 and 26. However the average starting number for the winners is clearly higher.
I then did some further statistical analysis of the winner-data and found out that at a confidence interval of 95 % the winning starting number is between 13 and 22 (rounded numbers). This does not mean 95 % of all winners will have a starting number between 13 and 22, but as you collect more samples from different years the average is almost certainly in that range. In the past ten years three winners were outside that interval, one of which was nr 24.
Calculation numbers (the REALLY boring part):
n=10 years
x=17.5
s=6.169
df=9
t 0.975 (df) = 2.262
So the numbers are telling us the ideal starting number is in the second half of the final, but not quite at the end. Is this just a coincidence (sure winners getting high numbers), or does it play a big role (people at home more likely to vote for semi-late performances)?
The average since the introduction of televoting is 17.066.