I think the only way to do this is to first query all events for the year. Then loop though all the events and load in the selected artists that played.
You can then use this data to increase a counter for each artist.
Then at the end of the loop, you will be left with counters for each artist which you can then find which one is the biggest and display that artists information.
If performance is a concern, I would swap the relationship field type, for a plugin called ‘posts 2 posts’