Let's start with the guarenteed contracts for next year:
PG: Isaiah Thomas, Marcus Smart, Terry Rozier
SG: Avery Bradley, R.J. Hunter
SF: Jae Crowder, James Young
PF: Jordan Mickey
C: Kelly Olynyk
I'm going to assume that Young's contract will be eaten or he'll be traded to a team with the money to pay for his contract. The Celtics have options on three players - Amir Johnson ($12M), Jonas Jerebko ($5M) and John Holland (<$1M). I'm going to assume that the Celtics will pick up Jerebko's option, decline Holland's and think hard about Johnson's. The Celtics can make qualifying offers to Tyler Zeller ($3,695,169) and Jared Sullinger ($4,433,683). I'm going to assume neither gets offers. Evan Turner is an unrestricted free agent. That means the roster is at:
PG: Isaiah Thomas, Marcus Smart, Terry Rozier
SG: Avery Bradley, R.J. Hunter
SF: Jae Crowder
PF: Jonas Jerebko, Jordan Mickey
C: Kelly Olynyk
?? - Amir Johnson, Evan Turner
Now, I'm going to add in the draft picks. Brown I'll put in at backup SF. There's been a lot of chatter about Guerschon Yabusele and Ante Zizic playing in Europe next season, but I'm not sure. There's no room for Demetrius Jackson at PG, but he's too good of a steal to let walk. I'll put Ben Bentil as a third string PF. I'm going to leave Abdel Nader off of the roster. That takes us to:
PG: Isaiah Thomas, Marcus Smart, Terry Rozier, Demetrius Jackson
SG: Avery Bradley, R.J. Hunter
SF: Jae Crowder, Jaylen Brown
PF: Jonas Jerebko, Jordan Mickey, Ben Bentil
C: Kelly Olynyk
?? - Amir Johnson, Evan Turner, Guerschon Yabusele, Ante Zizic
The Celtics seem well stocked for 1-3, but need help at PF and C. So I think they'll pick up the option on Johnson and let Turner walk. Zizic is of the size and age that it would be better to develop in Europe at least another year. Yabusele is less clear cut. If the Celtics sign a free agent big, then probably should play in Europe. If all he has to do to get playing time is to beat out Mickey and Bentil, bringing him over makes sense:
PG: Isaiah Thomas, Marcus Smart, Terry Rozier, Demetrius Jackson
SG: Avery Bradley, R.J. Hunter
SF: Jae Crowder, Jaylen Brown
PF: Jonas Jerebko, Jordan Mickey, Ben Bentil
C: Amir Johnson, Kelly Olynyk
?? - Guerschon Yabusele
That's 13 without Yabusele and 14 with. Looking at that roster, the Celtics need to one or preferably two free agent bigs.