The Pete Newell Big Man of the Year Award began in 2000 and is given to the top low-post player in the country, as determined by the National Association of Basketball Coaches.
(More after the Jump)
Former recipients include, courtesy of wikipedia (you guys should really check this website out):
A quick look at the list shows that it is in Greg Monroe's best interest to stay another year, because all underclassmen winners that went to the NBA the following year have had injury problems or failed to live up to the lofty expectations.
Interestingly, according to Draft Express, there are six other low post players that are currently projected to be drafted higher than Greg Monroe. I think this is another sign.
Finally, there has never been a two time recipient of the Pete Newell Big Man Award.
Thus, Greg Monroe should stay another year. I am pretty sure this is what the coaches had in mind when they gave him the award.