Simple enough for a tournament, you just divide all of your scores by the amount of games you play. If you bowl a league you can usually find your total pinfall somewhere on the league sheet. If you add your series for this week plus your total pinfall and divide by the total games including this week you get your average.
Bowling averges are calculated by dividing total pins by number or games bowled.
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Your bowling handicap depends on what league you're in. My handicap went from a 12 to a 33 when I switched leagues.