Depends on how much analysis you're actually willing to do. Some of the stats we have right now don't tell the whole story. For instance, demos and soldiers can pad their stats but not necessarily help their team, or a dropped uber does not tell the whole story.
What you could do is go into a demo and look at specific plays and decide whether or not it was a good play, not just judging by damage or k/d. Here are some examples off the top of my head that are easily attainable but require work:
- key plays (dropping/killing/forcing the med, killing the demo, stopped a backcap, etc)
- backcaps that helped their team win the round
- offclass success rate, probably better for seasonal stats (did the spy/sniper get a key pick? did the heavy/engie/pyro stop a last push? etc.)
If you REALLY wanna nerd out, you can tally up useful damage stats, by subtracting useless damage from total damage to see whos actually putting out good damage (ie. two 300 pockets exchanging rockets at gully choke, baiting your team)
If you wanna do analysis similar to some of the existing sports ones like PER and QB rating, you'd have to come up with a formula that quantifies each and every little thing that a player does and multiply that by a factor, whether negative or positive, then totalling that up into a final score. Again, takes time and effort to come up with a formula that's efficiently analyzes a player's performance.