It could be a higher or lower thing. Usually if its lower, its referred to as a "drop", like a 10 pin drop for people who's book average is 175 and they are averaging say 160, their average can't drop below 165. The 15 pin rule would be to prevent anyone who is new to bowling who had a low average in their first season and is bowling much better now from using the lower average.
I bowled in a tourney back in 1995 and it was after my first full year in bowling and my winter average was 140 and I was running a 170ish average in the summer league, but we had to use the winter average, so I bowled with the 140 and it was a 10 game tourney. I was running about a 205 (scratch) average through the first 5 games and everyone was up in arms (and frankly I don't blame them) and I had a massive lead. I came back down to earth for the last 5 but won the tourney by a decent margain. I felt bad that I won, but it was how the rules were then, so it would prevent that kind of thing.
High Game: 279 (twice)
Series: 737 2/25/10
Average: Mixed:185 Mens: 197
15# Brunswick Power Groove Dry R
15# Global 900 Creature S40
14# Faball Purple Hammer (spare ball)
15# Rotogrip Mars Pearl