To be honest I've found that ping times really depend on the game. Some games will play better with lower bandwith and higher ping times and others will be unplayable.
Actually if you playing on a higher ping in a shooter there is a strategy to it.
IE if you know your pinging at 200ms you'll want to lead whoever your shooting but 2/10th's of a second. Just like shooting a moving deer you don't aim were it is but where its going.
Its tricky and I just prefer getting angles on people and shooting them while there running in a straight direction or when there trying to pick up a item or activate something.