I have a seemingly simple problem, that I just can't wrap my head around. So hopefully you can.

I run a music site, that often have competitions. It's heavily database driven, and have an advanced scoring system.

I've made a statistics page, that displays the top 10 in the various categories.

To get to the point, I'll explain with an example:

An artist has participated in 4 competitions, and have scored A points in competition 1, B in competition 2, C in 3 and D in 4.

In competition 1 there was a participating artists, b in competition 2, c in 3 and d in 4.

Now my problem is, I can't see what is the better average, for this artists score per participating artist. Is it:


or is it


I just want it to be a fair top 10.