Median is a game of reflexes more than anything.
If someone is used to low ping, then anything higher than 150 will seem like huge input delay and make gameplay much less enjoyable.
However if you're used to playing with 250+ then you automatically account for that 1/4 s delay.
I played a few games with constant 200ms, and I can't imagine 400 being acceptable. That's almost a full second of delay if you add human reflexes delay.