Tennis score average

[mxh]

In a best of 3 tennis match, player A wins 6-2, 6-2 against player B

You can clearly see that player B has won 4 of the 16 games played, ie 1/4 of the games.

And if you work out the average score of the sets, it would be "(2/8 + 2/8) / 2" = 1/4, which works out at a 6-2 scoreline

If Player A wins 6-1, 6-3 then again Player B wins 4 of the 16 matches, and you'd assume that the average of the set scores would again be 6-2. But if you work it out, it's not.

(1/7 + 3/9) / 2 = ( 9/63 + 21/63 ) / 2 = 30/63 / 2 = 15/63 = 5/21

Can someone explain where the logic goes wrong.

 

[tkhunny]

First, "work it out" doesn't mean anything.

Combining averages to make a total average requires (All of one thing)/(all of every thing)

2/8 and 2/8 requires (2+2)/(8+8) = 4/16 = 1/4 -- Since both sets are the same size, that "work it out" thing happens to give the correct answer.

1/7 and 3/9 requires (1+3)/(7+9) = 4/16 = 1/4 -- Different size sets make the "/2" thing invalid.

 

[mxh]

Ah yes, that makes sense. Sorry, but it was bugging me!