1. Give us pvp stats. kdr, healing, number of viral matrix nukes number of subnukes. that sort of thing.
2. On a per class basis average those statistics. Use that information to assign pvp tiers. Upon joining open pvp you will be teamed with players of similar skill.
3. Create tournament brackets. 1v1 2v2 3v3 4v4 5v5. Have an entry fee of dilithium or EC to enter the tournaments.
4. Have open brackets where the team or player with the most wins in an allotted time wins a prize.
5. Have elimination brackets where there are a fixed number of slots, and reward the 1st 2nd and third place teams.
6. Shuttle tournaments would be fun as well I would imagine.
This is how you fix pvp.
Noobs do not want to join an open game just to get face rolled 10000000x.
Even experienced pvpers know that if your team is full of morons you lose. And it is not a very enjoyable experience. But even if you have a team of experienced pvpers there is nothing to do atm besides queue up to pwn noobs.
This solves that problem, and creates an atmosphere of competition and fun. Do it.