Remember every player doesn't play every game. So it's okay if the numbers come out a little high. Using last year as a baseline and subbing in major additions and subtractions, this is what I see:
Last season:
Isaiah Thomas: 28.9
Avery Bradley: 16.3
Jae Crowder: 13.9
Al Horford: 14
Marcus Smart: 10.6
Kelly Olynyk: 9
Amir Johnson: 6.5
Jaylen Brown: 6.6
Terry Rozier: 5.5
Jonas Jerebko: 3.8
Gerald Green: 5.6
Tyler Zeller: 3.5
James Young: 2.3
Jordan Mickey: 1.5
Demetrius Jackson: 2
So we sub in Hayward for Bradley, but also take 4 points from Thomas to give to Hayward. Also maybe Rozier gets a few more minutes and Thomas gets some more rest as the team now isn't as dependent on Thomas for scoring, so let's take a couple more points from Thomas to give Rozier.
Isaiah Thomas: 28.9 - 4 - 2
Gordon Hayward: 16.3 + 4
Terry Rozier: 5.5 + 2
Similarly subbing in Morris for Olynyk, and Baynes for Amir, but take 2 of Amir's points and give to Morris, because I don't expect Baynes to score much.
Morris: 9 + 2
Baynes: 6.5 - 2
I think Brown's role will increase, while Crowder's decreases:
Jae Crowder: 13.9 - 3
Jaylen Brown: 6.6 + 3
Tatum gets a combination of Jerebko and Greens points and minutes (but Green only played half the time so his ppg is a little inflated). They scored a combined 561 points. Assume Tatum plays 78 games.
Jayson Tatum: 561/78 = 7.2
Horford and Smart probably stay the same.
Now when the team added Horford, they went from scoring 105.7 ppg (5th in the league) to 107 (7th in the league). Warriors adding Durant went from 114.9 (1st) to 115.9 (1st). So maybe there's another point or two we can add in for the team just improving. I'll give it back to Thomas (28.9 - 4 - 2 + 1). So I see:
Isaiah Thomas: 23.9
Gordon Hayward: 20.3
Jae Crowder: 10.9
Al Horford: 14
Marcus Smart: 10.6
Marcus Morris: 11
Aron Baynes: 4.5
Jaylen Brown: 9.6
Terry Rozier: 7.5
Jayson Tatum: 7.2
With everybody else (Yabu, Zizic, Theis, etc.) getting the Zeller, Young, Mickey, etc. production with limited games played.