I think Imperator is a fight that's harder to judge dps on for a variety of reasons. I have no doubts that your mage can definitely improve greatly on Imperator, but looking at a Butcher log is probably a better idea at this point, if just to find fundamental mistakes in his play.
- His first Prismatic Crystal(PC) is 26 seconds into the fight? I'm not sure what he was waiting for, but he should be using crystal very shortly after the pull.
- Lost a global on PC because he cast frost orb during PC uptime. Frost orb should be cast the global before PC
- Lost another global on PC when he cast MI during PC uptime
- He cast all of his cooldowns approx 1.5 seconds before PC ended, and then started a Frostbolt cast on the dying PC, resulting in a cancelled cast. Waiting till after PC to cast cooldowns is a huge misplay.
- Waited to cast Bloodfury until 1:22
- Cast his second Frost orb ~10 seconds after he cast his second PC
Going to stop there and just say that the biggest thing he needs to work on is proper cooldown usage. It doesn't look to me like he has any real idea of how to use them properly, and is losing a
lot of dps because of it.
EDIT: Forgot to mention that I'm probably going to get corrected by one of the better mages on this forum. I have a pretty good idea what I'm talking about, but take what I said with a grain of salt until another mage says something along the same lines.