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Old 11-17-2006, 05:44 PM   #1
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Default Correlation between Tournament Strength and Points

http://www.tennisone.com/magazine/larson_news.php (November 17, 2006)
Quote:
Tough Enough For You?

You've heard us complain, often enough, about the lack of quality/bonus points on the WTA and ATP. There are a lot of reasons for the complaints -- starting with the fact that quality points are a better predictor of future results than the round points the Tour still awards. But if we had to offer one single reason for why a round-points-only system doesn't work very well, it's that actual tournament strengths bear no necessary relationship to the tournament tier, and hence to the points it awards.

Which raises the question: Just how good or bad is the correlation between tournament strength and the points it awards?

The answer to that depends, unfortunately, on how you define "tournament strength." Which is stronger, a tournament with one Top Ten player who happens to be Roger Federer, or a tournament with four Top Ten players, all ranked between #5 and #10? There is no real answer to this.

We'll try a very simple rule, though: We'll just count up the rankings of the top four players in the field. (Not the top four seeds, note, but the top four players.) So a tournament with the world's top four in the draw will have a strength of 100 (you can think of that as a percent if you like; it's more or less a percent of actual strength). An event with #1, #2, #3, and #5 ranks at 92%, and so on; we set an arbitrary floor of 10%.

Here, then, are how the 67 events on the ATP circuit in 2006 stood in terms of strength (we list them in calendar order). Remember that the higher the strength, the tougher the event.

Event.................ATP Points..Strength
Doha.........................250........24
Adelaide.....................175........15
Chennai......................175........10
Auckland.....................175........16
Sydney.......................175........26
Australian Open.............1000........76
Delray Beach.................175........11
Vina del Mar.................175........10
Zagreb.......................175........19
Marseille....................200........39
Buenos Aires.................175........11
San Jose.....................175........20
Memphis......................250........18
Rotterdam....................250........19
Costa do Sauipe..............175........11
Dubai........................300........65
Acapulco.....................250........12
Las Vegas....................175........16
Indian Wells.................500.......100
Miami........................500.......100
Houston......................175........19
Valencia.....................175........24
Monte Carlo..................500........92
Barcelona....................300........35
Casablanca...................175........10
Estoril......................175........14
Munich.......................175........12
Rome.........................500.......100
Hamburg......................500........35
Portschach...................175........13
Roland Garros...............1000.......100
Queen's......................250........56
Halle........................225........19
's-Hertogenbosch.............175........23
Nottingham...................175........10
Wimbledon...................1000.......100
Gstaad.......................200........13
Bastad.......................175........23
Newport......................175........10
Stuttgart....................250........12
Indianapolis.................200........19
Amersfoort...................175........10
Kitzbuhel....................250........22
Los Angeles..................175........15
Umag.........................175........10
Washington...................200........16
Sopot........................175........18
Canadian Open................500.......100
Cincinnati...................500.......100
New Haven....................200........28
U. S. Open..................1000.......100
Beijing......................175........35
Bucharest....................175........10
Bangkok......................175........22
Mumbai.......................175........18
Palermo......................175........10
Tokyo........................250........29
Metz.........................175........11
Moscow.......................250........12
Vienna.......................250........44
Stockholm....................225........28
Madrid.......................500.......100
Basel........................250........43
St. Petersburg...............250........24
Lyon.........................225........11
Paris........................500........31
Masters Cup..................750.......100

If you want to know which are the strongest tournaments under this system, here they are in descending order:

Event.................ATP Points..Strength
Indian Wells.................500.......100
Miami........................500.......100
Rome.........................500.......100
Roland Garros...............1000.......100
Wimbledon...................1000.......100
Canadian Open................500.......100
Cincinnati...................500.......100
U. S. Open..................1000.......100
Madrid.......................500.......100
Masters Cup..................750.......100
Monte Carlo..................500........92

Australian Open.............1000........76

Dubai........................300........65

Queen's......................250........56

Vienna.......................250........44
Basel........................250........43

Marseille....................200........39
Barcelona....................300........35
Hamburg......................500........35
Beijing......................175........35
Paris........................500........31

Tokyo........................250........29
New Haven....................200........28
Stockholm....................225........28
Sydney.......................175........26
Doha.........................250........24
Valencia.....................175........24
St. Petersburg...............250........24
's-Hertogenbosch.............175........23
Bastad.......................175........23
Kitzbuhel....................250........22
Bangkok......................175........22
San Jose.....................175........20

Zagreb.......................175........19
Rotterdam....................250........19
Houston......................175........19
Halle........................225........19
Indianapolis.................200........19
Memphis......................250........18
Sopot........................175........18
Mumbai.......................175........18
Auckland.....................175........16
Las Vegas....................175........16
Washington...................200........16
Adelaide.....................175........15
Los Angeles..................175........15
Estoril......................175........14
Portschach...................175........13
Gstaad.......................200........13
Acapulco.....................250........12
Munich.......................175........12
Stuttgart....................250........12
Moscow.......................250........12
Delray Beach.................175........11
Buenos Aires.................175........11
Costa do Sauipe..............175........11
Metz.........................175........11
Lyon.........................225........11
Chennai......................175........10
Vina del Mar.................175........10
Casablanca...................175........10
Nottingham...................175........10
Newport......................175........10
Amersfoort...................175........10
Umag.........................175........10
Bucharest....................175........10
Palermo......................175........10

At least part of the system seems to be working right: If you look at the top twelve events, all of them are required. Only two required events (Hamburg and Paris) are weaker than the strongest optional event, and even Paris, at #21 in the list, is stronger than two-thirds of the events on the ATP schedule. And if we look at the top optional events, the one at the very top is Doha, which is a 300 point event (i.e. it awards the maximum possible points for an optional event). Of the events stronger than Paris, only one -- Beijing -- is a bottom-tier 175 point event. And every tournament to earn a last-place ranking of 10 is a 175-point event.

On the other hand, Stuttgart and Moscow and Lyon are high-tier optionals with fields barely above the minimum. By the looks of things, the rules are working pretty well for the required events -- and aren't working at all for the optionals.

But we can test that. There is a formula known as the Correlation Coefficient. We won't explain it -- it's in any halfway-decent statistics book -- but it measures how well two data sets match. The value ranges from 1 (for perfect correlation) to 0 (for no correlation at all) to -1 (meaning perfect correlation except that you've sorted one of the lists upside down).

The result? Correlating tournament strength against tournament points gives us a correlation of .82.

That's really not very good -- not for something that could be done precisely. Speaking based on thumb-fingered-undergraduate-physics lab experience, if you can't get an experiment to yield a correlation coefficient of .97, you don't know what you're doing; if you can't get .95, you are a danger to those around you. A lot of medical trials rely on correlations in the .3 range, but remember, the ATP could get the point values right. This is not a matter of experimentation; it's a matter of looking at who is there and awarding points.

But we already said that the ATP was doing pretty well with the required events. The really interesting correlation is between points and tournament strength for the optional events. You ready for this?

.57

In other words, there is some correlation between tournament strength and points, but it's pretty feeble.

Does that affect the rankings? That is, if we awarded points based on actual tournament strengths, would we get a substantially different rankings list? If by "substantially different" you mean "would someone other than Roger Federer be #1," the answer is certainly "no." If you mean, "Would there be some changes in the ranking list," the answer is... well, the answer is coming in a later column.
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Old 11-18-2006, 07:56 AM   #2
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Default Re: Correlation between Tournament Strength and Points

Very poor way to determine tournament strength.
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Old 11-20-2006, 10:07 AM   #3
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Default Re: Correlation between Tournament Strength and Points

I'd say the cut-off to direct entry, divided by the number of players in a field should also be a factor in determining a tournaments strength (the closer to 1, the stronger the field). This to avois bogus tournaments that pay big bucks for a few top stars and fill the rest of the field with players like Ivo Minar.

Still, I like the idea of this study. Please post the rankings that will be posted ion the next column!
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Old 11-20-2006, 12:06 PM   #4
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Default Re: Correlation between Tournament Strength and Points

Quote:
Originally Posted by Purple Rainbow View Post
I'd say the cut-off to direct entry, divided by the number of players in a field should also be a factor in determining a tournaments strength (the closer to 1, the stronger the field). This to avois bogus tournaments that pay big bucks for a few top stars and fill the rest of the field with players like Ivo Minar.

Still, I like the idea of this study. Please post the rankings that will be posted ion the next column!
I like the idea as well, but indeed a few top players don't make a strong tournament

Such studies are interesting though I like statistics
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Old 10-03-2007, 10:48 AM   #5
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Default Re: Correlation between Tournament Strength and Points

IMHO the tournaments quality is very strange sometimes...
Quote:
For instance Acapulco ($757K) -
Seeds:
1. Juan Carlos Ferrero - 27.
2. Agustin Calleri - 29.
3. Nicolas Almagro - 30.
4. Juan Ignacio Chela - 35.
5. Gaston Gaudio - 37.
6. Nicolas Massu - 39.
7. Jose Acasuso - 41.
8. Carlos Moya - 47.

and Sydney ($436K) -
Seeds:
1. Rafael Nadal - 2.
2. Nikolay Davydenko - 3.
3. James Blake - 4.
4. Marcos Baghdatis - 12.
5. Tomas Berdych - 13.
6. Richard Gasquet - 18.
7. Dmitry Tursunov - 22.
8. Sebastian Grosjean - 28.
best of 7 from Sydney are better of best of 7 in Acapulco, but Acapulco winner earned 250 points, winner in Sydney earned 175 points only! Why?
If u want look at my site >>
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Old 10-03-2007, 10:20 PM   #6
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Default Re: Correlation between Tournament Strength and Points

Quote:
Originally Posted by Purple Rainbow View Post
I'd say the cut-off to direct entry, divided by the number of players in a field should also be a factor in determining a tournaments strength (the closer to 1, the stronger the field). This to avois bogus tournaments that pay big bucks for a few top stars and fill the rest of the field with players like Ivo Minar.

Still, I like the idea of this study. Please post the rankings that will be posted ion the next column!
I agree. It looks like the writers made life easy for themselves, otherwise they should have based their calculations on top 16 or at least top 10 players of a tourney, not top 4. This along with the cut-off should yield a more meaningful result.
And where is that next column anyway?
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