It's 21 games in a league, even if your a sub.
I booked an average as a sub several times now.
If you don't want to book that average, bowl 20 games and stop.
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The league secretary is responsible for uploading book averages and following the rules at the end of the season. But I've seen many cases where I bowled or subbed 1, 3, 6, 9 games in a league and it was uploaded as an average to be reference as part of a composite average.
At my center, we have the book, updated every year. We go to the control desk and we do a lookup on the official USBC book, that has a computer print out of our regions members. There you'll find your name with a book average for league, and if you bowled in a sport shot league, your other sport book. The book is reprinted every tax day.