so this effect can be easily eliminated by submitting score if one played at least 100 or 50 games
I think RootRanger's point still stands. Even if there was only a theoretical hard cap (like 100 battles scoring whatever the maximum per game would be) that no one could ever actually reach, I think the high scores (assuming there is a leaderboard, which I would hope/assume there would be, because otherwise what fun is that?) would be dominated by people that created new accounts until they got a high score and then left them stagnant.
Your system of dividing by the number of games means that there is a certain score per game you have to hit, and if you can do that, you can maintain your high score forever by no longer battling. A system similar to what we have now without a hard cap would be much better, in my opinion. You would discourage PVP if even winning could lower your score, which is the system you described.
A simple PVP win -> score increase, PVP loss -> score decrease system would work better than one where winning could lower your score. Basically, the exact system we have now, except separate from your main score is what I would like to see.
Plus, RootRanger is right about the AI. its 35 score for an EM against AI3 (and I believe 50 for T50, not the "maximally 20" you described). I just clicked PVP and it would have been 10 (not the "at least 20" you described) if I won. More for an EM (I'm not sure how much more, for PVP). But regardless, since EMs are so much easier against the computer, grinding AI would still be the way to go. But this is really quite trivial, to me. The important thing is, a system that divides your score by number of games would discourage PVP because all losses and some victories would lower your score. It would still encourage people to make new accounts and try to game it, rather than just playing and playing and playing