Could be a whole litany of things, even with perfect form and an effortless swing. Repetitive stress injuries can happen even with moderate physical activities.
And, it could be something unrelated to bowling that the motion of the game exacerbates. His age could be a factor, as we get older tendons and muscles shrink and connective tissue shortens; motions that are effortless in our youth can cause us pain as adults. Just the way it goes.
I have battled some arm and wrist pain from bowling over the years, and found that building muscles through working out helps, also proper stretching before and after bowling can stave off pains. A compression band on my forearm can alleviate stress from long sessions, too.
If he can't figure it out, he needs to see a doctor and find out if there's something going on or an issue he's not aware of.
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