But, of course, there isn't. The group is complete, all $ORDER points are reachable by multiplying the generator from 1..$ORDER-1. Some points _can't_ be more likely than others as a property of the curve with a uniform input, or otherwise some points would be unreachable (obvious by the pigeonhole principle) and the order would be less.
OK - that's a solid statement.
But he only makes the stats for the least 32 bits, and not for the entire numbers - it doesn't matter?