I was disappointed to see that there is no way to switch draft order or to swap Battleborn choices, but I thought that random pick order wasn’t a horrible option. However, it appears that the order of picks within a team is not random. I have played ~30 games of versus draft, and I have been the first person to pick >50% of the time. This is either a very unlikely statistical aberration or the order of picks is not random. My hypothesis is that the order of picks is determined by the order in which people connect into the lobby. My internet connection is unusually fast and when I connect into the game I often see others still connecting (signified by the computer monitor emblem instead of their emblem).
As I have said in a previous post, the best option would be to allow some sort of switch/swap/trade system for battleborn picks. In lieu of that, please make the pick order random (or verify to me that my experience has resulted from an exceedingly unlikely statistical aberration).