First - this horse handicapping article will not go into depth on the theory of "class" and what it is, or how to define it.
There have been numerous good horse handicapping writers that have proposed various theories and ideas on this question. Needless to say, there is not a consensus on the subject. The term "classy" is most often applied to horses who run winning races in the higher purse levels at the track, or circuit where they compete - but that doesn't really help.
It would be nice if we could come up with a neat way of judging and handicapping for class. The reality of the situation though is often puzzling.
Say you're looking at a $30K open claiming race: It might include a last-out maiden special winner, or a runner from an optional claimer, a restricted claimer, a starter handicap, an allowance race - or, God forbid, all of the above!
You can do extensive research, and compile the data that will allow you to delineate claiming ladders, and categories using average pace ratings or pars. I certainly applaud that kind of research and do some of it myself. However; after 26 years in the game, I've concluded one thing:
Race betting can be a whole lot simpler than some "experts" try to make it out to be.