Claudius

05-24-2010, 12:27 PM

http://cheeptalk.wordpress.com/2010/05/24/two-ways-tennis-scoring-helps-stronger-playersdeu/

Any of you math people understand his reasoning?

Any of you math people understand his reasoning?

View Full Version : Tennis scoring helps stronger players?

Claudius

05-24-2010, 12:27 PM

http://cheeptalk.wordpress.com/2010/05/24/two-ways-tennis-scoring-helps-stronger-playersdeu/

Any of you math people understand his reasoning?

Any of you math people understand his reasoning?

Steady Eddy

05-24-2010, 03:53 PM

The scoring system "amplifies" the superiority of the better player. Suppose a player wins 51% of the points, but wins 55% of the games. The scoring system has amplified his performance.

This continues, the player who wins 55% of the games, might have something like a 70% advantage in winning a set, and it gets even high for winning the match, more so if it's a best of 5 match than best of 3.

This should all be common sense. The part where he talks about winning the big points more often is confusion, IMO. We've seen that a player with a constant chance of 51% per point has a huge advantage of winning a match because of amplification. Some people posit that the huge advantage comes from winning "the big points" instead. I think it's unnecessary to propose this, as amplification explains how a small per point advantage turns into such a large match advantage.

BTW, if your chance of winning a point is "p" and losing a point is "q", then your chance of winning the game is: p^4 + 4p^4 q + 10p^4 q^2 / (p^2 q^2). There's a shortcut way to estimate your chances, though. Suppose the score is deuce, and p = 2/3, q = 1/3. The ratio in your favor is 2:1, so your chance of winning when it's deuce is 2^2 / (2^2 + 1^2) or 4/5. So it amplifies from 67% to 80%. That's just for when it's deuce, but it's about the same thing when it's love-love. Yep, you might think at the beginning of a game that there's lots of points to spare, but there aren't. Always pretend it's deuce at the beginning of each game. (That's why double partners who net two consecutive easy volleys bug me, it should be 30-0, but it's 0-30 and we'll lose because they're thinking, "Well, there's so many points, it doesn't matter that I'm not paying attention for the first few points." They are so wrong!)

This continues, the player who wins 55% of the games, might have something like a 70% advantage in winning a set, and it gets even high for winning the match, more so if it's a best of 5 match than best of 3.

This should all be common sense. The part where he talks about winning the big points more often is confusion, IMO. We've seen that a player with a constant chance of 51% per point has a huge advantage of winning a match because of amplification. Some people posit that the huge advantage comes from winning "the big points" instead. I think it's unnecessary to propose this, as amplification explains how a small per point advantage turns into such a large match advantage.

BTW, if your chance of winning a point is "p" and losing a point is "q", then your chance of winning the game is: p^4 + 4p^4 q + 10p^4 q^2 / (p^2 q^2). There's a shortcut way to estimate your chances, though. Suppose the score is deuce, and p = 2/3, q = 1/3. The ratio in your favor is 2:1, so your chance of winning when it's deuce is 2^2 / (2^2 + 1^2) or 4/5. So it amplifies from 67% to 80%. That's just for when it's deuce, but it's about the same thing when it's love-love. Yep, you might think at the beginning of a game that there's lots of points to spare, but there aren't. Always pretend it's deuce at the beginning of each game. (That's why double partners who net two consecutive easy volleys bug me, it should be 30-0, but it's 0-30 and we'll lose because they're thinking, "Well, there's so many points, it doesn't matter that I'm not paying attention for the first few points." They are so wrong!)

ubermeyer

05-25-2010, 11:08 PM

I've always thought this, but never thought about applying math to it. Deceptively simple.

fed_the_savior

05-26-2010, 01:35 AM

Tennis isn't about just one point. So I don't think skill is "amplified" in that sense.

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