How many games should the average player be winning?

A good win rate is possible, but the combination of SBMM and multiple, and I mean MULTIPLE factors all go into winning a match. I'd say a 5% win rate is a good ball-park for average players. 

To address if better players win more of their matches, it's a yes and no answer. Multiple factors go into winning a match. The people you play with, the people you play against, the gear you have at every (and I mean EVERY) point in the match, the location you land, the location other people land, how you play, how OTHER people play, do you have comms, do your teammates have comms, are your teammates willing to work with you, do you loot hog, do they loot hog, do you quit early, etc. etc. etc. 

A better player will win more FIGHTS than just your average joe, and yes that technically means they might win more games. But the other factors will influence if said player will win or not. For instance, great players like Aceu, Shroud, Skadoodle, Aculite, we all know they're great players. But they still go down, they still lose games, they still die and need to be respawned. External factors beyond our control will heavily influence a match's determination. It's unfair to say that with SBMM, you should win X percentage of matches because of your skill, when so much of this game is determined by luck rather than skill. However, that's not to say that there's no skill at all in this game. Being good at the game is a great help to winning more and more games, but overall isn't the determining factor in whether or not you win every single game.