Ring ramp up damage

People have complained time and time before about players staying in the ring and using it to get better placements.

The solution is usually to just make it deal more damage.

My idea is if maybe we should add a ramp up feature to it, where the ring does more damage after you stay inside of it for a certain amount of time, so if a player stays in the ring after lets say 10 seconds, then it would do increased damage. 

May not sound perfect and would obviously need some fine tuning, but do you think it could work potentially?