# Probabilities of winning as a function of sets played

In tennis, what are the probabilities of winning a player has as a function of sets played? Examples:

• 1-0 in a 3 set game
• 2-1 in a 5 set game

However, if you include psychology (such as winning the last set may give you an edge) and conditional probabilities (the best player may have a better chance of winning the second set than the first) the state is a bit more detailed. Examples:

• Player A won the first set in a 3 set game
• AB in a 3 set game
• AABB in a 5 set game
• etc

Do you know (a subset of) these statistics?

• 1-0 in a 3 set game would be 67% vs 33% then? Pretty much like they run the math in Poker... Or what exactly are you looking for? Also if you want to include psychology and other conditions this would be beyond any math. There are always things you can't display with numbers.
– dly
Jun 25, 2018 at 12:56

It is called a match.

If you assume you have a 50% chance of winning each set.

For up 1-0 in a 3 sets
Take 1 - chance of losing the rest
1 - (.5 x .5) = .75

If you think they are better or worse than .5 then plug in any number you want.

Up 2-1 in 5 set match is the same math.

• Down vote care to comment? This is correct. Look me up on Poker.StackExchange.com. Jul 4, 2018 at 13:04
• I think the question is asking for answers based on a more sophisticated set of assumptions than "the chance of winning a set is a constant". Jul 4, 2018 at 13:26
• @PhilipKendall That is why I said plug in the number you want. But that is how you run the math. 1 - the chance of losing both. Even at 50% up 2-1 the player is better than 2/3. Jul 4, 2018 at 13:40