avmoghe

06-05-2006, 07:24 PM

I realize there have been quite a few threads about the "depth" of the men's and the women's fields. However, the French Open is ongoing, and it would be appropriate to conduct a little experiment.

Too often, people say "Federer wins everything, and on the women's we have different winners for the past X grandslams. (At this point, I belive X is 8.) Therefore the women's field has more depth"

It should be pointed out that simply looking at the winner of the tournament is an unfair measure of the depth of the men's/women's field.

For this post, I define the "depth" of a field as the "probability that a lower ranked player can defeat a higher ranked player". Yes, this is a very, very rough definition since it ignores the closeness of the matches played, and only looks at the winner.

So, given that definition, it is trivial to find a numerical value for the depth.

depth of a field = (number of matches where a lower ranked player defeated a higher ranked player) / (total number of matches).

It would be very interesting (I feel) to see the depth for the French Open for the women's and men's fields.

If anyone has a lot of time on their hands - and by posting on this forum, I assume you do - please calculate the numerical value of the depth for the French Open. It seems like a very tedious task since there are a total of 64 + 32 + 16 + 8 + 4 + 2 + 1 matches = 2^7 -1 matches.

Comments about the definition or method?

PS - Yes, I'm too lazy to do it myself.

Too often, people say "Federer wins everything, and on the women's we have different winners for the past X grandslams. (At this point, I belive X is 8.) Therefore the women's field has more depth"

It should be pointed out that simply looking at the winner of the tournament is an unfair measure of the depth of the men's/women's field.

For this post, I define the "depth" of a field as the "probability that a lower ranked player can defeat a higher ranked player". Yes, this is a very, very rough definition since it ignores the closeness of the matches played, and only looks at the winner.

So, given that definition, it is trivial to find a numerical value for the depth.

depth of a field = (number of matches where a lower ranked player defeated a higher ranked player) / (total number of matches).

It would be very interesting (I feel) to see the depth for the French Open for the women's and men's fields.

If anyone has a lot of time on their hands - and by posting on this forum, I assume you do - please calculate the numerical value of the depth for the French Open. It seems like a very tedious task since there are a total of 64 + 32 + 16 + 8 + 4 + 2 + 1 matches = 2^7 -1 matches.

Comments about the definition or method?

PS - Yes, I'm too lazy to do it myself.