Shoe-in is a shoo-in in the Google horse race
So, my good friend and across-the-Duke-hallway interlocutor, Geoff Brennan, pokes his head in my door. He asks, "How do you spell (and then pronounces the phrase "shoo in").
I reply, confidently, because my confidence greatly exceeds my knowledge, "Oh, that is spelled 's-h-o-e dash i-n'." Geoff says he has a paper he is looking at, and it spells it wrong. In other words, Geoff agrees with me.
Bad idea. "Shoo-in" is clearly correct.
In terms of etymology, it's pretty obvious why: it's from horse racing. . For example, see here. An excerpt:
[Q] ...I was wondering if you could possibly find out the origin of the term shoe in, meaning someone will win for sure.”
[A] This one is spelled wrongly so often that it’s likely it will eventually end up that way. The correct form is shoo-in, usually with a hyphen. It has been known in that spelling and with the meaning of a certain winner from the 1930s. It came from horse racing, where a shoo-in was the winner of a rigged race.
In turn that seems to have come from the verb shoo, meaning to drive a person or an animal in a given direction by making noises or gestures, which in turn comes from the noise people often make when they do it.
The shift to the horse racing sense seems to have occurred sometime in the early 1900s. C E Smith made it clear how it came about in his Racing Maxims and Methods of Pittsburgh Phil in 1908: “There were many times presumably that ‘Tod’ would win through such manipulations, being ‘shooed in’, as it were”. (Emphasis added)
"Spelled wrongly so often that it's likely it will eventually end up that way..." Like when your mom said, "If you make that ugly look, your face will get stuck that way!"?
No, more like this:
Google search for "shoe-in" reveals 1.73 million usages
Google search for "shoo-in" reveals fewer than half a million usages.
So, shoe-in is a shoo-in, by more than a 3-1 ratio.