Throwing this out there. Being there are no apparent in game awards to the specific gladiator competing or winning in the Battle Royal matches. Winners get trophies but to me that is not as enticing as gladiator points or awards.
That said...I think it would be helpful to eliminate the outstanding injuries that glads suffer during the event.
A glad suffering an injury can cause a poor performance in any matches afterwards that he is challenged in especially Blood Games fights that do carry a fairly beneficial upside.
Especially that there is only an hour in between the matches and doubtful many managers will be logging on in the wee hours of the morning to check for injuries.

Or perhaps just reverse the times of the Battle Royal and Blood Games matches.

Just my views on this Xmas eve morning.