How many golden sets have been dished out in the history of our sport on the highest level? A golden set is of course a set where a player wins a set 6/0 without conceding a point neither on serve or return. 24 straight points.

samanosuke

09-02-2009, 06:29 PM

I am pretty sure that neither one

Purple Rainbow

09-03-2009, 12:02 PM

To answer the original question: Only one player in the history of professional tennis has ever achieved this, Bill Scanlon. It was against Marcos Hocevar in the first round of the WCT Gold Coast Classic at Delray Beach on February 22, 1983. Scanlon won the match 6–2, 6–0.

I was bored, so I did a little math.
Suppose both players have an equal chance of winning each point. That means the chance of any set being a golden set is 0.5^23, which is 1 in 8,388,608, which is negligible.

However, suppose a player is much better than his opponent and is likely to win 80% of his own serve points and 60% on his opponents serve, then the odds increase to 1 in 6684 sets.

I am making an educated guess, but this might be in the range of the number of sets played on ATP level every year.

Now, I understand that there's more than sheer probablity going on in tennis, eg. players might be more error prone when they have a big lead in a set, but still, with so many matches being played, often with one player much more capable than his opponent, you would expect golden sets to happen more often than they do.

Blarghman

09-05-2009, 09:20 AM

However, suppose a player is much better than his opponent and is likely to win 80% of his own serve points and 60% on his opponents serve, then the odds increase to 1 in 6684 sets.

I am making an educated guess, but this might be in the range of the number of sets played on ATP level every year.

Now, I understand that there's more than sheer probablity going on in tennis, eg. players might be more error prone when they have a big lead in a set, but still, with so many matches being played, often with one player much more capable than his opponent, you would expect golden sets to happen more often than they do.

I think that your analysis is good, but your conclusion somewhat underestimates how rare really huge mismatches are. Of 2034 ATP matches so far this year, just 7 have been on the level you calculated for; 80% on serve and 60% on return. While there are often match-ups where one player is superior to another, those levels are major beat-down territory.

Even if we extend the assumptions a bit, and assume there would be 50 such matches a year, that would be 100 sets a year, or one golden set every 66 years. So I don't think it's too much of a surprise that they're so rare.

BodyServe

09-05-2009, 02:23 PM

I was bored, so I did a little math.
Suppose both players have an equal chance of winning each point. That means the chance of any set being a golden set is 0.5^23, which is 1 in 8,388,608, which is negligible.

The probability of winning a point on serve and on return ain't the same.

Lets say .65 on serve and .35 on return, that leads to a 1 to 11835990 which is even more negligible.

Purple Rainbow

09-05-2009, 08:30 PM

I figured I was pretty nerdish to do a little math on the topic, but thankfully I'm not the only one interested. :)
Thanks for your input, both of you come up with good points.
Blarghman, how did you get the number of matches with the 80/60 win ratio? Do you have access to the ATP database? If do, it might be nice to know how many sets are "near golden" in a given year, e.g. player winning 5 or less points to 24.

BodyServe

09-06-2009, 12:54 PM

I can't let it like that, we made a mistake: it's .5^24 and not .5^23 :o
So it's 1 out of 16777216 for you and 1 out of 52026330 for me.

Purple Rainbow

09-06-2009, 05:17 PM

I can't let it like that, we made a mistake: it's .5^24 and not .5^23 :o
So it's 1 out of 16777216 for you and 1 out of 52026330 for me.

This is not a mistake.
If both players have equal chance of winning a point, it doesn't matter who wins the first point. All that matters is that the player winning the first point makes the next 23 points as well. So, 0.5^23 is the correct odds for this situation. :p

Blarghman

09-06-2009, 11:03 PM

Blarghman, how did you get the number of matches with the 80/60 win ratio? Do you have access to the ATP database? If do, it might be nice to know how many sets are "near golden" in a given year, e.g. player winning 5 or less points to 24.

I just have my own data I collect from the ATP match summaries; unfortunately I only have the data at match level, not set-by-set. Thinking about the issue of sets v. matches actually changes my original response somewhat; it's more likely to have a single blow-out set at the 80/60 level than an entire match, so the frequency is probably higher then I said, though I'd think it's still pretty small. :shrug:

HKz

09-07-2009, 04:35 AM

Now, I understand that there's more than sheer probablity going on in tennis, eg. players might be more error prone when they have a big lead in a set, but still, with so many matches being played, often with one player much more capable than his opponent, you would expect golden sets to happen more often than they do.

Well it is the same reason why bagels aren't handed out as often as they should seem to be even by the top 10 players in the world against under-100-200 ranked players.

The fact is, it is tough to break serve and it is tough to NOT make a mistake.

Good analysis though.

BodyServe

09-08-2009, 12:43 PM

This is not a mistake.
If both players have equal chance of winning a point, it doesn't matter who wins the first point. All that matters is that the player winning the first point makes the next 23 points as well. So, 0.5^23 is the correct odds for this situation. :p

Yeah correct, i was more in a "given player" perspective not "one player" :o
My point still stands though.

stebs

09-11-2009, 02:26 PM

Maybe if Santoro was playing one more year and got drawn vs Nadal on clay we could see this happen. Very low chance of any free points on serve for Fab, feasibility of Fab making no big shots in 24 points, reasonable chance that Nadal may not make an error. Still it would be hugely, hugely unlikely but more possible than most matchups with Fab's unorthodox style. Truth is, most players in the top 200 should be winning several points with a big serve/big shit combo.

Archer16

09-12-2009, 06:20 AM

I figured I was pretty nerdish to do a little math on the topic, but thankfully I'm not the only one interested. :)
Thanks for your input, both of you come up with good points.
Blarghman, how did you get the number of matches with the 80/60 win ratio? Do you have access to the ATP database? If do, it might be nice to know how many sets are "near golden" in a given year, e.g. player winning 5 or less points to 24.
I'd also love to see stats on that.
The most well-known example, I guess, is the fastest set that I know of, Henman-Ivanisevic, Wimbledon SF 2001, with Henman winning the 3rd set in 14 minutes for the loss of four points (http://www.independent.co.uk/sport/tennis/henman-must-make-history-the-hard-way-752853.html), before rain interrupted and changed the course of tennis history :sad:
In the quickest match in ATP history, Rusedski d. Arriens 6-0, 6-0 in 29 minutes (Sydney 1996), the winner lost just six points in each set (edit: Voo has the match at 58 points total which would be maximum 10 points lost for the entire match, but I found an article [link now broken] from after the match stating the above information).

BTW, although I think the women tend to have more bagel sets than the men, there never been a golden set on the WTA Tour. The closest have been im Memphis 2006 when Yaroslava Shvedova (18 y.o. qualifier, then #228) led Amy Frazier (33 y.o. and #54) 5-0 40-0 without conceding a point. Amazingly Frazier won the match 1-6 6-0 6-0!!