It depends what age you start teaching them to use the potty.
i started teaching my daughter at 4 months and at 10 months we still use the diapers and we have a few accidents (most of them my fault because i don't pay attention to her cues all the time) but at night for some estrange reason we don't need diapers. I think is because she is so little and according to EC little mammals have an instinct not to go on their territory and i guess their bed is "THEIR" territory, so anyways... since 9 months my baby doesn't pee on bed but  i have to take her about 2-3 times to the potty at night (usually at 1 and at 6 but sometimes i have to take her at 11, 2 and 7)