I bowl summer and winter, and have been for 26 years. My summer is more for trying different leagues and working on my game. This year I'm trying out a Sport League.
As for joining a ball league and trading it out, I'd check with the league/pro shop before joining to be sure that is an option.
My Vegas league in the winter has the trip and a ball. We have an option of taking cash for the ball if we want. I have enough bowling balls, so I took the cash last season and this season. See if that is also an option.
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Age is only a state of mind. Since I lost mine years ago, I must be really young