Bathtub overflow drain

Water comes in faster than my overflow drain can get rid of the water. Is this common or is it indicative of a problem with the drain?

Common on all tubs

Humm, a drain line is probably 1.5", and the supply is probably 1/2" (although under pressure). I'd expect a drain line to be able to handle most supply situations without backing up. While not using the overflow to drain, my tub drains about in half the time it takes to fill up. The overflow goes to the same place as the main drain. Anybody else?