I prefer to wear the Patagonia 9Trails shorts and can fit 2 balls in each pocket. If I feel like I need more room, I have some of the Patagonia Baggies shorts, I can fit 6-7 balls in each pocket of those, but typically just fill the left pocket due to the weight of a dozen tennis balls dragging down my shorts and the fact that I'm right handed keep my racket in my right hand a majority of the time that I'm on the court.
"You lose some, you win some. Nothing wrong with that at all." Stefan Edberg