Nothingness: No you're not. As you said, you play 10 moves, moving instantly when it's your turn. If you make your first move at 1 pm, and your last move at 10pm, and I constantly move one hour after you move, then I move at 11 pm, after which it takes 14 hours before you make your move. Those 14 hours means your average move time is 1h 24m, while my average move time is 1h. That's what average means, one takes into account all move times, not just the once that make you look good.

In such a scenario, I am the faster player.