Battle Derby (1)
The publicly accessible battle derby was divided into two phases. The battle royale qualifying match and the actual race amongst the qualifying racers.
It was just unfeasible to have all the people who sign up to be in a race together. That was why they had the qualifying match. The qualifying match wasn't anything sophisticated.
You simply took out opponents and survived until there were only ten people left standing. Then those ten or less people would race. Sometimes people were a little battle happy and eliminated down to less than ten but that usually wasn't the case.
The battle royale arena was a massive plexiglass ball. Players entered the ball and then rolled around chasing each other and picking each other off. The middle bottom part of the ball opened up to drop the eliminated players out of the ball, so they didn't get in the way of other players.