I asked my darling husband, who’s an avid tennis player and fan. Paul says that there’s really no science to it. All three balls look and feel the same.

If you’ve ever been to a professional tennis tournament, you’ve seen that a ball knocked into the stands gets retrieved. That’s because all 3 balls must have the same wear and “bounciness,” and all 3 are retired and replaced at the same time.

So, when a player tosses the ball to the ballboy/ballgirl, there really isn’t an evaluation process. Keep two; toss one; play.

@PaulSadieMartin But why not just throw two and none gets thrown back?

^^^ If I’m understanding your question, it’s because the serving player needs to have two tennis balls on hand. If the first serve lands outside of the lines, the player gets a second chance.

The longer a ball is used the fluffier it becomes. The fluffier it becomes the slower it travels through the air, especially if it is humid. They generally choose the newest and tightest ball from the ones in play. They want the second best to keep in their pocket for a second serve if needed. Some players don’t keep a second in pocket or pants, they take one from the ball person. Others feel this interrupts their concentration. There are however probably as many reasons as there are tennis players.

What @rooeytoo said, there’s also the occasional “rogue” ball which has a hairline tear in it, making the ball useless, humidity/moisture in the air also can affect a ball’s performance.
It’s like the towel thing, Greg Rusedski started this off in the late nineties, look back on any tennis coverage prior to then & no one did this, aside from at the change of ends.
I think it’s more of a habit now, used for a variety of reasons, not least to compose themselves before a crucial point is played.

@ucme – I forgot about that, Rusedski was the first with the towel. And I think Courier was the guy who started the baseball cap, before that if anyone wore a cap it was usually a bucket hat.

@rooeytoo I can only imagine how hilarious Borg & McEnroe would have looked with a baseball cap atop their huge hair…wow!

Greg Rusedski was one frood who really knew where his towel was…