[Someone]

Adding some math: assume player 1 has a probability of p of winning a game, and therefore, player 2 having a probability of 1-p.

Then, the probability of player 1 winning a set 6-0 is p⁶; the probability of player 2 doing that is (1-p)⁶.

Let’s assume a fairly evenly matched game, where p=0.6. Then, those probabilities are about 4.7% and 0.4%. Combined, that’s about 1 in 5,000, or 1:2500 to get either of 6:0;0:6 or 0:6;6:0.

Doesn’t sound too bad but in real life, that number will be a lot lower because of the server advantage in tennis. Especially in men’s tennis, the server has a big advantage, making even single set 6-0 scores highly unlikely.

[jedberg]

Your math assumes each game is fair, but we know they aren't, because different players have different skill levels, and skill is an important factor.

And if the first set is 6-0, that indicates one side has exceptionally better skills.

[Someone]

> And if the first set is 6-0, that indicates one side has exceptionally better skills.

In the model I proposed, it doesn’t. Even if the players are perfectly balanced, there’s a 1:64 probability of getting 6-0 and a 1:64 probability of getting 0-6. Combined, that’s a 3% chance of getting a bagel.

But as I said, there’s a huge server’s advantage in men’s tennis. That makes ‘bagels’ (https://en.wikipedia.org/wiki/Bagel_(tennis)) less likely there, and means a player winning a set 6:0 indeed statistically is much better than their opponent.

They’re fairly common in women’s tennis, though, even ones with the side losing that set winning the match.