Can I also asked when was the last time Danny have drafted in the top 10 lottery prior to 2014?
Since you can get all-star players while picking outside of the top 10 (about 6 or 7 players on this year's all star teams fit that list, for example), your question isn't particularly relevant to what I asked, but Ainge has had 4 chances to draft in the top 10.
Trade #5 for Ray Allen (Great move)
Trade #7 (as Randy Foye) for Sebastian Telfair (Freakin' disaster)
Drafted Marcus Smart (Jury out)
Drafted Jaylen Brown (jury out)