Scratch leagues are not a dime a dozen.  Those are handicap leagues.  Most houses if they have one scratch league you are lucky.  And if its an open scratch league (not draft or invitational) you are even luckier.  If you find one that wants bowlers under 210 even more lucky.  Given that, you have one day a week.  So most 200+ average bowlers I know bowl in handicap leagues.  Most are not high enough for the 650 scratch trio type leagues or the Classic drafts.  Today's league environments is a catch all in handicap, or high end scratch leagues.  If you are at 200 you are kind of caught in the middle.  Centers cannot really afford to limit handicap leagues to a minimum average, nor will they cap it at a maximum average.  So there's a wide range of bowlers.  

But most 180 to 200 average bowlers are not going make drastic moves in improvement.  While the beginning bowler will.  One year we had a bowler join and establish at 67 average.  Of course she got better, I think ending the league at over 100.  So that's a 30+ pin improvement.  I don't think you are going to find many 180 to 200 average bowlers that will be able to improve 30 pins in one season.  This team had a huge advantage as she increased her average.  It was years ago, so I cannot remember the end championships.  But I do remember their team was in the roll offs.