Four points is the most that can be held by a NR, who began applying four years ago when Utah first announced its intention of issuing a NR tag. Following the 2006 draw, there are 341 NR applicants with four points.
There are twenty NR's with more than four points, including two with twelve points. These are all former Utah residents, who accummulated their points as residents, but who subsequently moved away from Utah, taking their points with them.
IMO, unless Utah substantially increases its NR Rocky allocation, the odds of your drawing a permit in your lifetime are no better than lottery type odds. The maximum number of points that a Utah resident can have is fourteen, and there will probably be a never ending stream of Utah residents transferring into the NR draw by moving out of state. I'm not saying that a person would leave Utah simply to beat the permit draw system... it will just happen, because people move around, and the Utah system allows a departing resident to take their points with them when they leave.
One or two NR Rocky permits a year in Utah... and you likely will never draw. But if the herds keep growing, and Utah ever gets up to issuing say, ten NR permits a year, then... you might stand a chance.
Good luck.