Right, let's see if I can present some statistics here.

I was interested by a question in the chat a while ago, who was the best winner in ESC history. I interpreted the question thusly: What winner has obtained the greatest proportion of points, when their points are given in percentage of maximum possible amount of points?

The problem is that throughout history, there have been several different point systems. I could just take into account the competitions that have taken place since 1975 (when the current system was introduced), but because it is interesting, I'm going to include all of them.

The votes of the first competition was secret, so there is no use trying to compare that to other competitions. The second competition saw a system that was used 10 times, and not entirely consecutively. After several other voting systems were experimented with, they always went back to the system of having 10 jury members give their favourite songs 1 point. It was unlikely that a country would take maximum points from any other country, and therefore the winner's percentage of maximum amount of points was rather low. 1962-1966 saw some experimentation, but it is not until the system of 1971-1973 that the winners start taking more than 75% of the possible amount of points. In that system, jury members did not have to rank songs, or decide where to give their points, but they gave all songs 1-5 points, resulting in a higher amount than previously seen. Because of some unfairness in the system (the one I remember is that this meant that not all juries necessarily gave the same amount of points), the system of 10 jury members was revisited in 1974, when ABBA won.

Since 1975, the system has consistently been that of 1-8 points, then 10 and 12 points, to the top 10 of each country. There have been changes in the method of deciding these points since 1997, when televoting was first introduced, but the points principle has been the same. Each country must identify a top 10 list, and each country gives the same amount of total points. There are loads of things that can be done in order to analyse historical statistics of Eurovision points, and it would no doubt be fun, but as I am only trying to see the "best" winner in history, I'll try to keep to that subject.

In the second year of the 12 point system, UK won with "Save Your Kisses for Me", which got 80.39% of the maximum possible points. This remains the greatest proportion of points obtained by a winner in the competition with the 12 point system. Interestingly, the second place was only 17 points behind, with about 72% of the maximum possible points. This makes me think it would be interesting to take all points given in all competitions and look at which was the most equal and which was the least so. Actually, Luxembourg's win in 1973 "Tu te reconnaîtras", got 80.63% of max points, but the scoring system is not easily comparable to the current one.

The recent day record breakers and runaway winners don't come close to challenge UK's record. The exception is Norway's Fairytale, which got 78.66% of the maximum points and is the third best winner in history, according to this criterium (I won't claim that the song qualities are actually in the order presented here. That's way too subjective). The second best winner in history is Germany's 1982 win, Ein bißchen Frieden. 4th and 5th place go to Ireland 1994 and UK 1997 respectively. All of these songs got between 78% and 79% of maximum points in their year. This year's win by Sweden is the 7th best, raking in 75.61% of max points.

The winner does not necessarily need to take more than half of the maximum possible amount of points. The 5 worst winners since the 12 point system was introduced were Azerbaijan 2011 (43.85%), Greece 2005 (50.44%), Germany 2010 (53.95%), Russia 2008 (53.97%) and Yugoslavia 1989 (54.37%). It is not surprising that so many of the "worst" winners come from recent years, since in those competitions, a much larger batch of countries has been allowed to vote than before, even though these countries did not make it to the actual final. The chance of obtaining maximum amount of points seems to increase as fewer countries vote. In 1976 there were 18, while in 2011 there were 43 (the formula for maximum amount of points of course being
(number of countries-1)*12)

The whole table I made in Excel can be seen below. Please answer if you spot any errors in facts or data, and some day I might not be too lazy to fix it.