The thing with Ray is that the offense tends to stagnate while they wait for him to run off screens or try to set up a double screen for him. The offense is way more complex when he is in, and the Celtics just don't have the mental focus in the regular season to execute consistently. With Avery, he basically goes to the corner and cuts at the right time and gets clean up baskets, and doesn't need great picks (which is why Perk was so valuable). The new guys can run a simpler, easier offense, and don't have their heads on a swivel.
When Ray comes in on the second unit, he goes back to the Seattle Ray where he's the focus, and is way more productive for this version of the Big 3. Back in 2008, we had veterans like Posey and PJ Brown who lubricated the gears of the offense, and Ray was awesome.