in WSG and AB atleast the leader is the last person of the largest 'join as group' in the queue to enter the game. Ive gotten yelled at a few times on my hunter for not realizing im the leader when doing guild bgs (since we are usually atleast 5) in AV i think its the first to join, I assume eots is the same as wsg/ab but cant say for sure.

It used to be the person with the highest rank but that was changed when they removed the ranking system.