I voted for 'Combination of various factors.' Centers are rare, Ainge doesn't seem very excited about developing them, and we haven't had very solid draft position for getting anyone who could stick.
I think that's true, though it's an important position and at some point you have to invest in it, project or not, early pick or not. I wonder if his standards for the position are too high (insert Fab Melo joke here) and he just doesn't want to bother with projects who have high stiff potential.
OK, it's clear I'm going to have to look at every draft so here goes:
2003: Banks and Perkins, no center of note besides ZaZa Pachulia in the 2nd round.
2004: Jefferson, West, and Allen. This was the year of the oft-rumored Robert Swift fascination, who ended up being a bust. Anderson Varejao ended up being a nice pick as 31st pick overall, 2nd round.
2005: Gerald Green. Mahimni goes 28th overall. Ainge takes Orien Greene and Gomes over Marcin Gortat and Amir Johnson in 2nd round (he could also be a PF, but I remember he was a lauded "project" big man so mentioning him here).
2006: Ainge trades down to take Rajon Rondo. This was a pretty bad draft overall, actually the Celtics ended up with some of the noted failures from this year such as Shelden Williams (5th) and Patrick O'Bryant (9th).
2007: Traded pick (Jeff Green) for Ray Allen. Obviously this deal was necessary for the Garnett deal so no complaints here, though Joakim Noah would obviously have been a great Celtic! In the 2nd round they take Pruitt and Big Baby. 4 picks before Pruitt, Splitter was taken by the Spurs, and way down in the 2nd round Marc Gasol was taken.
2008: The first post Garnett draft. Celtics memorably take bust JR Giddens with Pekovic, DeAndre Jordan, and Omer Asik taken 1, 4, and 5 picks later (this is probably the biggest obvious miss).
2009: No first rounder here, this pick was traded to the Wolves. They take Lester Hudson late in the 2nd.
2010: Avery Bradley 19th overall (right after Blesode, ouch!) and Harangody in the 2nd. No good centers picked around there.
2011: Celtics trade back slightly to take JaJuan Johnson and E'Twuan (sp?) Moore in the 2nd. No real obvious good center picks this year either.
2012: Celtics take Sullinger and Fab Melo 21 and 22nd and Kris Joseph in the 2nd round. Miles Plumlee only C of note, taken 26th overall.
2013: Celtics trade up to take Kelly Olynyk and get Colton Iverson in the 2nd. Some centers of note are Gorgui Dieng and Mason Plumlee (21st and 22nd overall, respectively).
2014: Celtics take Smart 6th and Young 17th. Would they have taken Jusuf Nuric if he hadn't gone 16th? Did they ever consider Clint Capela at 17th (he went 25th).
Looking at this list, my first conclusion is that besides a few exceptions there weren't a host of options where they were picking. My second conclusion is that the Celtics really, really hate foreign players for some reason, but that's a subject for another post. The fact that they never taken foreign players who are often the kind of hidden gems you need to take later in the draft bothers me to no end. This past draft was the same, with the Celtics not seeming to show much interest in Nuric, Capela, or Walter Tavares. Not saying those guys are any good, but other teams have successfully mined the foreign leagues for talent in the past 15 years and the Celtics seem allergic to it. Is it all Jerome Moiso's fault?