The books actually hint that the distribution isn't random at all, after all every family member of harry's, beside his father, that we know off is a magic user. Molly's mother is a magic user, perhaps some of her siblings will show the talent, too.
That seems like wizardry is a hereditary thing which means you will not have an even distribution. I'm gonna bet that there are some crazy-old wizard families in europe or (not so crazy-old but still oldish) in new england.

One of the player characters in my game is a fire wizard who believes he comes from the purgatory and his task is to bring sinners on the right track to redemption. One of his aspects is "it was a terrible accident". Let's just say things tend to go boom around him. Literally and figuratively.