A couple things:
Firstly, the odds that we pick 13th are very low. That means that a) we somehow pass Phoenix or New Orleans in the standings while missing the playoffs, or that the one of the 13th or 14th teams jumps in the lottery. Given that we're 6.5 games behind Phoenix and 7 games behind New Orleans, but 1.5 games out of the playoffs, it seems quite unlikely that occurs. Meanwhile the odds of one of those teams jumping up in the lottery is less than 4%. Accordingly, if we miss the playoffs, we're likely to finish no worse than 12th. I think it's a virtual certainty we can get someone at 12 who's got star potential.
So the real question is can we get someone good at 15 or 16? One name that gets knocked down on this board is Frank Kaminsky. There are valid concerns about his athleticism and the fact he's a college senior -- in some sense he feels like Kelly Olynyk round 2. But Kaminsky is a great example of the modern NBA center. He can stretch the defense to the perimeter on offense and is a good passer out of the high post, but at the same time is a capable interior defender (which is how he is significantly different than Olynyk,) and also a very good rebounder (#1 in the Big 10 in defensive rebounding). He's not Willie Cauley-Stein defensively, but he's not a liability either on that end. It wouldn't surprise me at all if he winds up going in the 10-12 range for the reasons I just mentioned, which would push a Celticsblog favorite down a spot, but if he's there at 15, he's a very good choice.
Another college senior who could push an underclassmen down a peg is Jerian Grant, a PG from Notre Dame. Given his position, I'm less interested in him as a Celtic, although he hails from Silver Spring, MD, of which I'm a proud resident, so I guess he's got that going. He's a passing PG who can also get his own points, and gets to the line with some frequency. His outside shot is not a true weapon, although good enough to keep defenses honest. He's solid defensively as well. He's arguably the best PG in the draft, depending what position you think Mudiay and Russell will end up as pros. (Probably #2 PG behind Mudaiy is how most would rate him.) He doesn't have the ceiling of some of the other draftees, but if you were handicapping which player could be ROY next year, Grant should be one of your first choices. Grant could be one of only two PG taken in the first round (Mudaiy being the other), which means he a) could come off the board a little earlier than projected, and/or b) be the type of player a team is willing to trade up to get, especially since he's the most NBA-ready at his position. He seems like a player Houston would be interested in at 13 or 14, for instance, given that Beverley is a restricted free agent. Indiana, if they pick at the end of the lottery, is another viable destination.
Anyway, I think there are definitely viable options going down to 15, and it is very easy to imagine that the player the Celtics would draft at 12 could still be there at 15. #Team8thSeed