Chuck, has any stats been done on what the ratings average is for any division to be won?
Nothing formal. There are too many permutations for the number of players and their mix of ratings to produce something that might be useful. The stats I posted on the 2008 Competition thread might be helpful. You can also just look at the division stats for events that are posted with ratings online. For example, usually the cash line for well attended A-tiers and NTs usually requires the player to shoot 1000 rated average. Unless the player is a shooting star, an established 970 player will shoot 1000 on average for four rounds less than 1 in 6 times based on the typical standard deviation for players at that level.
Taking that further, a 900 player might beat a 930 player about once every six times that the 930 player shoots their rating.