Erik Darling thinks outside the column:
Sorts aren’t just for the column(s) in your order by — if you SELECT *, you need to all the columns in the * by all the columns in the order by.
I know I basically repeated myself. That’s for emphasis. It’s something professional writers do.
Dig it.
The principle Erik is talking about is having a monotonic relationship (that is, as one column increases, the other always increases; and as one column decreases, the other always decreases). If you can guarantee that, and if one of those happens to be indexed already, you can get a nice performance boost.
But wait, I was told there would be no math.