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Wuornos
12-02-2007, 01:59 AM
DOT Ratings V3.2 Methodology

This is the first post of the V3.2 DOT Ratings. I will not go into the methodology behind these again as this is already contained within a thread at http://tt.tennis-warehouse.com/showthread.php?t=165420.

The latest revisions incorporate two significant changes and one minor. However before going into these details I need to confess that in making these changes I found a mistake in the algorithm that calculates tournament strength and provides the appropriate weighting for tournaments. This has now been rectified, however, previous rating posts will have contained this error and outputs were distorted. Apologies for this.

1. Following requests from numerous people, the DOT ratings are now calculated over multiple time periods and the results amalgamated with equal weighting to derive an overall rating. On the new overall scale a player could be considered great at 1,100 points and good at 1,000 points. To put this in perspective the womens’ game has produced 49 players in excess of 1,000 points in the open era, which includes 11 players of 1,100+ points and 1 player over 1,200 points. The mens’ game has had 68 players over 1,000 points, 12 in excess of 1,100 points and two players who have exceeded the 1,200 point barrier.

Ratings are calculated by awarding weights to events based upon the strength of competition present. The strength of the competition is based on their overall dominance over the previous 12 months. Points awarded for each event are multiplied by the weighting to derive the points earned by each player.

Once the points have been calculated five primary outputs are produced for each player with a sixth secondary output. The five primary outputs are as follows:

a) Best Single Event for each player which as defined by most points earned. As can be seen from the methodology above this is a reflection of how far the player progressed in the event and the weighting of the event based on the strength of the competitors at the tournament.

b) Best Single Year. Total of all points awarded by DOT within a single rolling horizon year. This of course does not mean most dominant year as the adjuster for the strength of events might make up for lesser dominance by considering the player competed against stronger competition.

c) Best Five Year Period. As Best Single Year but over a longer period. What more can I say.

d) Best Career Achievement. No time limit. Just the total number of DOT points awarded during the lifetime of a player.

e) Current Year. Not really used in the calculations for the overall rating but produced more out of interest than anything else. Shows how many DOT points have been scored by players in the previous 12 months using the same methodology as Best Single Year.

f) This is the secondary output as it requires each of the first four outputs above to calculate a players overall rating. Each of the periods receives equal weighting using the following methodology. The mean for all outputs with a category is calculated along with the Standard Deviation. A players performance with that category is then converted into a form that is + or – a specific number of Standard Deviations from the mean. The outputs from each category are multiplied by 10 (just to make it more user friendly) and added together. Finally 1,000 points are added to avoid negative numbers in the outputs. The resulting figure provides an overall rating which reflects a players performance giving equal weighting to each category.

Finally and more as a fun item, because the Standard deviations balance out the difference in levels of dominance seen in the womens’ and mens’ games the resulting outputs can be directly compared to evaluate whether a particular woman was more or less successful than a man within their individual populations. You can also produce a best players list of the open era across sexes.

2. The second significant change is that previously DOT calculated a players performance via three input criteria. i.e. a players domination, the opposition strength and the tournament status. I have removed the tournament status as this tends to be reflected in the strength of tournaments anyway and it makes things easier to calculate and understand without compromising accuracy to any great extent.

3. In order to accommodate the first change and be able to keep the four primary criteria both comparable and easy to understand the Primary DOT Outputs are no longer standardised to follow an arithmetic pattern but instead are geometric in nature in the same way that the official ATP and WTA ratings are. In fact this is a very food way of understanding each of the four primary outputs. Just imagine the official ratings remaining constant and were implemented at the start of the open era with each event having a variable weight depending on quality of entrants rather than a fixed weight as is the case at the moment.

Finally while I know these ratings won’t resolve any arguments, I hope they provide the statistical evidence to at least provide some background for various debates.

Take care all and I hope you enjoy the outputs.

Regards

Tim

Wuornos
12-02-2007, 02:00 AM
Mens’ DOT Ratings of the Open Era v 3.2


Please remember these are based on performances in the open era only and therefore some early period players will have had a reduced opportunity to achieve the scores of other players particularly within the longer time periods of Five Years and Career. This does subsequently impact on the overall rating as this is an evidence based system and does not compensate for reduced opportunity.

The first list is the Best Single Tournament Performance as defined by a players progression in the tournament and the overall strength of the tournament as indicated by the domination of those players present over the previous 12 months.

1. John McEnroe 1,032 Pts Achieved at US Open of 1984
2. Rod Laver 968 Pts Achieved at US Open of 1969
3. Mats Wilander 952 Pts Achieved at Australian Open of 1988
4. Ivan Lendl 920 Pts Achieved at French Open of 1984
4. Stefan Edberg 920 Pts Achieved at Wimbledon of 1988
6. Roger Federer 888 Pts Achieved at Australian Open of 2007
7. Pete Sampras 856 Pts Achieved at Wimbledon of 1993
7. Pat Cash 856 Pts Achieved at Wimbledon of 1987
9. Björn Borg 848 Pts Achieved at French Open of 1979
10. Rafael Nadal 816 Pts Achieved at French Open of 2007
10. Michael Stich 816 Pts Achieved at Wimbledon of 1991

Other players of interest

13. Jim Courier 800 Pts Achieved at Australian Open of 1992
15. Boris Becker 752 Pts Achieved at Wimbledon of 1989
17. Jimmy Connors 728 Pts Achieved at US Open of 1978
18. Andre Agassi 704 Pts Achieved at Australian Open of 2000


The Best Single Year Performances based upon dominance and strength of opposition.

1. Rod Laver 3,232 Pts Achieved year ending after US Open of 1969
2. Roger Federer 2,984 Pts Achieved year ending after Wimbledon of 2007
3. Mats Wilander 2,459 Pts Achieved year ending after US Open of 1988
4. John McEnroe 2,424 Pts Achieved year ending after US Open of 1984
5. Ivan Lendl 2,234 Pts Achieved year ending after Australian Open of 1988
6. Pete Sampras 2,149 Pts Achieved year ending after French Open of 1994
7. Jim Courier 1,890 Pts Achieved year ending after Australian Open of 1992
8. Björn Borg 1,844 Pts Achieved year ending after French Open of 1979
9. Andre Agassi 1,780 Pts Achieved year ending after Australian Open of 2000
10. Jimmy Connors 1,736 Pts Achieved year ending after US Open of 1974

Other players of interest

11. Boris Becker 1,573 Pts Achieved year ending after Australian Open of 1990
12. Stefan Edberg 1,565 Pts Achieved year ending after Wimbledon of 1993


The Best Five Year Performances based upon dominance and strength of opposition.

1. Roger Federer 9,584 Pts Achieved period ending after US Open of 2007
2. Ivan Lendl 8,224 Pts Achieved period ending after Australian Open of 1989
3. Björn Borg 6,811 Pts Achieved period ending after French Open of 2001
4. Pete Sampras 6,766 Pts Achieved period ending after Wimbledon of 1997
5. Mats Wilander 6,099 Pts Achieved period ending after US Open of 1988
6. John McEnroe 6,052 Pts Achieved period ending after French Open of 1985
7. Stefan Edberg 5,660 Pts Achieved period ending after French Open of 1993
8. Jimmy Connors 4,959 Pts Achieved period ending after US Open of 1978
9. Jim Courier 4,904 Pts Achieved period ending after Australian Open of 1996
10. Boris Becker 4,217 Pts Achieved period ending after French Open 1991

Other players of interest

11. Andre Agassi 3,744 Pts Achieved period ending after Australian Open 2004
12. Rod Laver 3,612 Pts Achieved period ending after Wimbledon 1971


Best Career Performances based upon total achievement and strength of opposition.

1. Ivan Lendl 11,829 Pts
2. Jimmy Connors 10,758 Pts
3. Pete Sampras 10,622 Pts
4. Roger Federer 9,712 Pts
5. Stefan Edberg 8,548 Pts
6. John McEnroe 8,447 Pts
7. Björn Borg 8,335 Pts
8. Andre Agassi 8,275 Pts
9. Mats Wilander 7,216 Pts
10. Boris Becker 6,963 Pts

Other players of interest.

11. Jim Courier 4,970 Pts
14. Rod Laver 3,612 Pts


Overall Rating including all players who make the 1,100 point threshold based upon equal weighting of each of the above four categories after standardisation.

1. Roger Federer 1,214 Pts
2. Ivan Lendl 1,201 Pts
3. Pete Sampras 1,177Pts
4. John McEnroe 1,173 Pts
5. Mats Wilander 1,163 Pts
6. Björn Borg 1,157 Pts
7. Jimmy Connors 1,149 Pts
8. Stefan Edberg 1,147 Pts
9. Rod Laver 1,140Pts
10. Andre Agassi 1,124 Pts
11. Jim Courier 1,121 Pts
12. Boris Becker 1,118 Pts

Wuornos
12-02-2007, 02:01 AM
Womens’ DOT Ratings of the Open Era v 3.2


Please remember these are based on performances in the open era only and therefore some early period players will have had a reduced opportunity to achieve the scores of other players particularly within the longer time periods of Five Years and Career. This does subsequently impact on the overall rating as this is an evidence based system and does not compensate for reduced opportunity.

The first list is the Best Single Tournament Performance as defined by a players progression in the tournament and the overall strength of the tournament as indicated by the domination of those players present over the previous 12 months.

1. Monica Seles 1,064 Pts Achieved at Australian Open of 1993
1. Billie Jean King 1,064 Pts Achieved at Wimbledon of 1973
3. Martina Navratilova 1,040 Pts Achieved at Australian Open of 1986
4. Chris Evert 1,032 Pts Achieved at US Open of 1982
4. Jana Novotná 1,032 Pts Achieved at Wimbledon of 1998
6. Steffi Graf 1,024 Pts Achieved at Australian Open of 1988
7. Venus Williams 1,016 Pts Achieved at US Open of 2001
7. Lindsay Davenport 1,016 Pts Achieved at US Open of 1998
7. Hana Mandlíková 1,016 Pts Achieved at US Open of 1985
10. Serena Williams 1,000 Pts Achieved at Wimbledon of 2003
10. Jennifer Capriati 1,000 Pts Achieved at Australian Open of 2002

Other players of interest

12. Arantxa Sánchez Vicario 984 Pts Achieved at French Open of 1998
16. Margaret Smith Court 896 Pts Achieved at US Open of 1973
18. Justine Henin 832 Pts Achieved at French Open of 2007
21. Martina Hingis 752 Pts Achieved at Australian Open of 1998


The Best Single Year Performances based upon dominance and strength of opposition.

1. Serena Williams 3,600 Pts Achieved year ending after Australian Open of 2001
2. Monica Seles 3,548 Pts Achieved year ending after Australian Open of 1993
3. Steffi Graf 3,456 Pts Achieved year ending after US Open of 1988
4. Martina Navratilova 3,444 Pts Achieved year ending after US Open of 1986
5. Margaret Smith Court 3,192 Pts Achieved year ending after Australian Open of 1971
6. Chris Evert 3,180 Pts Achieved year ending after US Open of 1982
7. Venus Williams 2,489 Pts Achieved year ending after French Open of 2002
8. Martina Hingis 2,488 Pts Achieved year ending after Australian Open of 1998
9. Billie Jean King 2,456 Pts Achieved year ending after US Open of 1972
10. Justine Henin 2,346 Pts Achieved year ending after Australian Open of 2004

Other players of interest

12. Arantxa Sánchez Vicario 2,024 Pts Achieved year ending after US Open of 1994


The Best Five Year Performances based upon dominance and strength of opposition.

1. Martina Navratilova 13,751 Pts Achieved period ending after US Open of 1986
2. Steffi Graf 11,501 Pts Achieved period ending after Wimbledon Open of 1992
3. Chris Evert 11,002 Pts Achieved period ending after French Open of 1986
4. Margaret Smith Court 9,258 Pts Achieved period ending after US of 1973
5. Monica Seles 8,238 Pts Achieved period ending after Australian Open of 1993
6. Martina Hingis 7,016 Pts Achieved period ending after Australian Open of 2002
7. Serena Williams 6,941 Pts Achieved period ending after Wimbledon of 2004
8. Venus Williams 6,860 Pts Achieved period ending after Wimbledon of 2003
9. Justine Henin 6,626 Pts Achieved period ending after US Open of 2007
10. Evonne Goolagong 6,217 Pts Achieved period ending after Australian Open of 1976

Other players of interest

11. Billie Jean King 5,971 Pts Achieved period ending after Wimbledon of 1975
12. Arantxa Sánchez Vicario 5,870 Pts Achieved period ending after Wimbledon of 1995


Best Career Performances based upon total achievement and strength of opposition.

1. Martina Navratilova 24,665 Pts
2. Chris Evert 24,547 Pts
3. Steffi Graf 23,570 Pts
4. Monica Seles 12,140 Pts
5. Arantxa Sánchez Vicario 9,870 Pts
6. Margaret Smith Court 9,771 Pts
7. Venus Williams 9,341 Pts
8. Billie Jean King 9,315 Pts
9. Evonne Goolagong 8,939 Pts
10. Serena Williams 8,446 Pts

Other players of interest.

11. Martina Hingis 7,789 Pts
12. Justine Henin 7,585 Pts


Overall Rating including all players who make the 1,100 point threshold based upon equal weighting of each of the above four categories after standardisation.

1. Martina Navratilova 1,215 Pts
2. Steffi Graf 1,199 Pts
3. Chris Evert 1,196 Pts
4. Monica Seles 1,150 Pts
5. Margaret Smith Court 1,137 Pts
6. Serena Williams 1,131 Pts
7. Venus Williams 1,117 Pts
8. Billie Jean King 1,114 Pts
9. Arantxa Sánchez Vicario 1,106 Pts
10. Martina Hingis 1,103 Pts
11. Justine Henin 1,101 Pts

Wuornos
12-02-2007, 02:02 AM
Finally and just for fun here’s the combined overall ratings list for men and women. I suppose you could say these are the players that DOT would consider to be the greats!

1 Martina Navratilova 1,215 Pts
2 Roger Federer 1,214 Pts
3 Ivan Lendl 1,201 Pts
4 Steffi Graf 1,199 Pts
5 Chris Evert 1,196 Pts
6 Pete Sampras 1,177 Pts
7 John McEnroe 1,173 Pts
8 Mats Wilander 1,163 Pts
9 Björn Borg 1,157 Pts
10 Monica Seles 1,150 Pts
11 Jimmy Connors 1,149 Pts
12 Stefan Edberg 1,147 Pts
13 Rod Laver 1,140 Pts
14 Margaret Smith Court 1,137 Pts
15 Serena Williams 1,131 Pts
16 Andre Agassi 1,124 Pts
17 Jim Courier 1,121 Pts
18 Boris Becker 1,118 Pts
19 Venus Williams 1,117 Pts
20 Billie Jean King 1,114 Pts
21 Arantxa Sánchez Vicario 1,106 Pts
22 Martina Hingis 1,103 Pts
23 Justine Henin 1,101 Pts

Wuornos
12-02-2007, 02:04 AM
All views and comments gratefully accepted.

Regards

Tim

Nickognito
12-02-2007, 02:44 AM
your last ranking is very interesting :)

I don't say anything about this method in general, because I suppose you think it's a good one and you would not change your idea 'in toto'.

Anyway, long-term-rankings seem to be more accurate. Federer australian open 2007 the best Federer result and one of the first six?. Simply impossible, if the ratings are expressed in numbers. (if they are expressed in intervals of numbers, it's possibile, Federer won it without losing a set e played great). Australian open draw was so easy this year. It's the less relevant grand slam torunament of the year. In London Federer had to beat a very tough Nadal, for example.

But i simply think that this is not a right way to make rankings, and I think it's not constructive now to speak on this general argument.

The idea of making a media between 1year-5year-career ratings and so on is great, in my opinion.

Regards,

c.

Wuornos
12-02-2007, 02:59 AM
your last ranking is very interesting :)

I don't say anything about this method in general, because I suppose you think it's a good one and you would not change your idea 'in toto'.

Anyway, long-term-rankings seem to be more accurate. Federer australian open 2007 the best Federer result and one of the first six?. Simply impossible, if the ratings are expressed in numbers. (if they are expressed in intervals of numbers, it's possibile, Federer won it without losing a set e played great). Australian open draw was so easy this year. It's the less relevant grand slam torunament of the year. In London Federer had to beat a very tough Nadal, for example.

But i simply think that this is not a right way to make rankings, and I think it's not constructive now to speak on this general argument.

The idea of making a media between 1year-5year-career ratings and so on is great, in my opinion.

Regards,

c.

Thanks Nick

I have to confess I'm not keen on this either I was really only doing it because others seemed to think this would provide better results. to be honest my own personal view is along siilar lines to yours and this is where I was two months ago, with astandardised rating calculated over a period of four years, with more weight given to the more recent years.

Many people didn't like this though, although to be honest I felt these, while being more complicated to produce were more meaningful.

Please feel free to criticise though as this is the way I improve the ratings. Although I think perhaps I've been listening to feedback that might be a bit off mean recently. :???:

The Top 20s looked as follows for the open era using the methodology from 2 months ago. What do you think?

1 Margaret Smith Court 2880
2 Steffi Graf 2880
3 Martina Navratilova 2878
4 Monica Seles 2837
5 Chris Evert 2823
6 Serena Williams 2797
7 Billie Jean King 2781
8 Arantxa Sánchez Vicario 2769
9 Martina Hingis 2762
10 Evonne Goolagong 2752
11 Venus Williams 2750
12 Justine Henin 2749
13 Hana Mandlíková 2747
14 Lindsay Davenport 2731
15 Gabriela Sabatini 2721
16 Jennifer Capriati 2713
17 Ann Jones 2705
18 Amélie Mauresmo 2701
19 Maria Sharapova 2696
20 Kim Clijsters 2689


1 Roger Federer 2841
2 Rod Laver 2806
3 Ivan Lendl 2786
4 Björn Borg 2771
5 Mats Wilander 2764
6 Pete Sampras 2762
7 John McEnroe 2738
8 Ken Rosewall 2736
9 Jim Courier 2734
10 Boris Becker 2726
11 Stefan Edberg 2716
12 Rafael Nadal 2711
13 John Newcombe 2710
14 Jimmy Connors 2706
15 Andre Agassi 2694
16 Stan Smith 2690
17 Arthur Ashe 2687
18 Guillermo Vilas 2680
19 Tony Roche 2673
20 Ilie Năstase 2672

Thanks for the feedback

Regards

Tim

Nickognito
12-02-2007, 10:30 AM
What I don't like in your rankings (there are a lot of things I like, but I think is more interesting for you what i don't like)

- I didn't understand the importance given to grand slam tournaments
- i didn't undestrastand the relevance given to different surface (beating Sampras at Wimbledon or French Open give you the same points?)
- your ratings are numbers, but a think they must be intervals of numbers
- there's a strange conception of domination: Sampras was very more dominant than Wilander, for example, but in your rankings it seems quite the opposite
-anyway domination is too important in your ranking: if a player has a bad year (whatever reason) loses too many points.
- it doesn't help about the greater question in an all-time ranking: how a champion would have performed with other champions playing in the same times.
Tennis rankings are usually decided by 2-3 match a year in a champions matchup. Other opponents are relevant, but not so relevant. The main question is: Federer can beat a player of Sampras' strenght at Wimbledon? Or Us Open? And viceversa. Tennis has no transitive property, so the best player with normal players is not the best with great players (compare Roddick and Davydenko to Safin or Nalbandian, for example) and the best player with great players is not necessarily the best with champions.

But obviously these are my opinions. And obviously your rankings are very interesting anyway. But unfortunately I don't think that they improve my knowledge about players' strenght and at the moment I don't think that an objective way to make through-times-rankings is not possible.

Regards,

c.

Nickognito
12-02-2007, 01:56 PM
I would like to ask Wuornos and you all a question about a method.

This method can be used in accordance to other rating systems, like Dots or any other.

With your choosen system, you can have some rankings: an 1-year, 2-year 3-year-5year-10year-15year ranking.

The problem often is: wich ranking is more accurate? One? Another? A mix?

I think that the answer is: any player has to chose the best one for him.

So, for Connors is a long-term ranking, for Cash a short one.

How can we do?

I think that anyone can agree with the fact that a long domination is bettere that a short domination, and that, for example, Federer 5-year domination is probably already better than extraordinary career achievements of Agassi and Connors.

So, i suggest this kind of rankings:

We choose the reliability-number of years: for example, that a 7 years ranking has a decent reliability. If a player can have a medium rating x for seven years, we can trust that his rating is fair. If the player have the rating x for just three years, its reliability is poor and it's not the same thing. If he mantains the rating for 12 years, the reliability is greater, or maybe the same, but he deserves a longevity bonus.

So, the method is (if we choose the 7-years system, just for example)

7 years-rating * 100%
6 years-rating * (100-k)%
5 years-rating * (100-2k)%
9 years-rating * (100+2k)%

So any players has many different ratings and he can chose the most convenient

An example based upon atp ranking points.

Federer and Nadal have these end-year-ranking points
2007: 7180 and 5735
2006: 8370 and 4470
2005: 6725 and 4765
2004:6335 and 775
2003: 4375 and 766
2002: 2590 and 165
2001: 1745
2000: 1080
1999: 749

So, let's say that k = 10

These are Federer rankings:

1 year: 3348
2 years: 3887,5
3 years: 4455
4 years: 5006,75
5 years: 5277,6
6 years: 5336.25
7 years: 5331.429
8 years: 5280
9 years: 5219, 867


Nadal's:

1 year: 2294
2 years: 2625
3 years:2994
4 years: 2755.375
5 years; 2545.6

So Federer chooses a 6 years-rating of 5336,35
Nadal chosses a 3 years-rating of 2994

You can apply this method with dots rating too

Regards,

c.

edmondsm
12-02-2007, 05:13 PM
The first list is the Best Single Tournament Performance as defined by a players progression in the tournament and the overall strength of the tournament as indicated by the domination of those players present over the previous 12 months.

1. John McEnroe 1,032 Pts Achieved at US Open of 1984
2. Rod Laver 968 Pts Achieved at US Open of 1969
3. Mats Wilander 952 Pts Achieved at Australian Open of 1988
4. Ivan Lendl 920 Pts Achieved at French Open of 1984
4. Stefan Edberg 920 Pts Achieved at Wimbledon of 1988
6. Roger Federer 888 Pts Achieved at Australian Open of 2007
7. Pete Sampras 856 Pts Achieved at Wimbledon of 1993
7. Pat Cash 856 Pts Achieved at Wimbledon of 1987
9. Björn Borg 848 Pts Achieved at French Open of 1979
10. Rafael Nadal 816 Pts Achieved at French Open of 2007
10. Michael Stich 816 Pts Achieved at Wimbledon of 1991

So the strength of the field is derived not from just the 7 opponents that said player came up against, but the field as a whole?

In 88' Edberg didn't play a single GS winner on his way to the title. To me, this is the equivilant of saying that Ljubicic gave his most dominant performance ever at the 06' FO, even though he didn't beat a single seeded player en route to the semis.

How does Guga Keurten's 97' FO win not make the list, when he went through 3 former champs to win the title?

Nickognito
12-02-2007, 05:35 PM
I don't know. The overall strenght of the tournament is maybe only that Wimbledon is more important than Madrid or New Haven.

But for sure, if I beat Federer and Nadal in the first half of the draw, and in the other half the best player is n.200 in the world, I have to get more points that in the case that i beat only players n. 200 in the world, even if in the draw there are Nadal, Federer, Sampras, McEnroe, Borg and God :)

I cannot get point for 'not winning' a match. In my opinion, it would be a nonsense.

Regards.

c.

Nickognito
12-02-2007, 05:36 PM
Anyway Edberg beated Becker in Wimbledon 88. So.. :)

AndrewD
12-02-2007, 07:47 PM
Tim,

I think the women's rankings look very good. There will always be debate regarding Court, Graf and Navratilova (in my opinion, especially the first two) so, if you're going to have a system, it's good that it shows how there is very little seperating them. Personally, I think that while Graf and Court should be considered on a par there should be more of a buffer between them and Navratilova. Otherwise I have little complaint and appreciate that your ratings place BJK so highly as I do believe no-one ever acknowledges that she sacrificed her career in order to advance the women's pro tour. That and injury denied her at least, in my opinion, the chance to win another 3-4 majors as Court, the one player she couldn't handle, was finished by 74. Evert, on the other hand, was fortunate to come onto the scene at that time and prosper during a long trough in the women's game (post-Court, post-King and pre-Navratilova) without the same stiff opposition as her predecessors faced.

Wuornos
12-02-2007, 11:46 PM
Wow.

There are some great responses so far in this thread.

I really appreciate all the feedback.

I have to pop out to the doctors this morning but will reply to each post when I get back.

Thanks everybody. :)

Tim

Nickognito
12-03-2007, 12:16 AM
if it was possible to have dot rankings for grand slam single tournaments, it would be great.

i.e: Federer at Wimbledon have 300, 800, 700, 750, 830, 700 points, for example

Starting from this data, we could make some interesting rankings apllying two methods.

1)The method that I described before: in this way we can have , i.e. ,a Wimbledon ranking.

Why to do this? Because usually when we make a ranking, we assume that we can compare 'two careers'. If player A has , for example, 12, 15, 14, 16 as ratings for grand slam tournaments and player B has 2, 20, 10, 25 we say that the sum is 57 points for both and the two players have the same ranking. I don't think so. I think we have to create like an ideal year for every player (an year correctly representing his career) and than compare all players in single tournaments.

2)when we have wimbledon rankings of all players (or just of the first 16) we can know the probability of each player of winning a tournament with all of them in the draw. In this way we can have an imaginary atp year, where players are not real players playing in one year, but 'ideal players' represening their career. And we can do this in a mathematical and completely non-subjective way.

It sounds complicate, I suppose, but it's easy.
But we need, first, single tournaments rating for a player in every year. Dots rating is a good one.

Regards,

c.

Wuornos
12-03-2007, 02:35 AM
What I don't like in your rankings (there are a lot of things I like, but I think is more interesting for you what i don't like)

- I didn't understand the importance given to grand slam tournaments
- i didn't undestrastand the relevance given to different surface (beating Sampras at Wimbledon or French Open give you the same points?)
- your ratings are numbers, but a think they must be intervals of numbers
- there's a strange conception of domination: Sampras was very more dominant than Wilander, for example, but in your rankings it seems quite the opposite
-anyway domination is too important in your ranking: if a player has a bad year (whatever reason) loses too many points.
- it doesn't help about the greater question in an all-time ranking: how a champion would have performed with other champions playing in the same times.
Tennis rankings are usually decided by 2-3 match a year in a champions matchup. Other opponents are relevant, but not so relevant. The main question is: Federer can beat a player of Sampras' strenght at Wimbledon? Or Us Open? And viceversa. Tennis has no transitive property, so the best player with normal players is not the best with great players (compare Roddick and Davydenko to Safin or Nalbandian, for example) and the best player with great players is not necessarily the best with champions.

But obviously these are my opinions. And obviously your rankings are very interesting anyway. But unfortunately I don't think that they improve my knowledge about players' strenght and at the moment I don't think that an objective way to make through-times-rankings is not possible.

Regards,

c.

Wow there's alot there. I'll try to answer each point in turn in relation to the methodology used in calculating the ratings posted at #7.

1. I used to calculate on all tournaments but received some quite severe criticism of my work because many believe that the very top players place more emphasis on the majors and treat the lesser events as having secondary importance. People were particularly critical of Sampras in relation to this and felt the methodology of including anything outside the majors was deflating some players scores.

Since then I have calculated majors only. To be honest the difference has been negligible as the weightings DOT was awarding to the minor events and the apparent randomisation within these events due to all top players being present simply flattened the disribution somewhat rather than made any major difference to placings.

Despite this I never switched back to the greater number of tournament methodology as my career in statistcs has taught me to produce models using the simplest methodologies to provide results that are fit for purpose. Therefore without significant differences, I continued on the major only route with a somewhat (!) reduced database and a massively reduced time in providing a system run.

2. There is no evidence placed on different surfaces per se, but there is evidence placed on different tournaments. The weighting of a tournament is based upon the strength of opposition and the historical consistency of the tournament. i.e. how many upsets tend to occur at each event. The overall tournament weighting can therefore be considered as an indication of a tournaments relevance in relation to eing an indicator for the world status of a player. Surface is of course one thing which would impact on this. Again all this is calculated rather based on opinion.

3. I have though about the idea of intervals of numbers but in the end decided against it. By providing the actual output it's left to the reader if they wish to allocate intervals.

4. Sampras was more dominant than Wilander within the #7 posting. It's just these are adjusted for quality of opposition too and DOTconsiders the quality of opposition faced in the mid to late 1980s better than during the Sampras era. Although the difference between them was negligible at 2 points.

5. Yes Domination is the most important factor within my calculation. By taking the peak perfomance of Domination x Opposition x Tournament over a four year period, then a players career is long enough to recover from a bad year. Not if there are regular bad years though.

6. DOT is not meant to say who would have won had two players met in the same era. What it really is, is amore sophisticated form of measuring a players performance against their contemproraries and comparing, e.g. whether the perfomance of Lendl in his time was better or worse than Laver. That's why it's so important that Tournaments have independent weightings to reflect the differing regard people held them in over time.

7. I agree when you say 'Tennis has no transitive property, so the best player with normal players is not the best with great players'. All we can do is look at a players overall success and use that as the best indicator of a combined success against both good and less good players.

8. 'The main question is: Federer can beat a player of Sampras' strenght at Wimbledon? Or Us Open? And viceversa''. 'I don't think that an objective way to make through-times-rankings is not possible'. I agree if your definition is as stated in the first sentance. I disagree if we are simply saying adjusting for the values of the time and allowing for how good the opposition faced were in relation to those values, Federer was more succesful over a four year period than was Lendl.

Sorry if the answers come across as a little bit terse. I just have many posts to answer.

keep posting Nick I really like to read your views.

Regards

Tim

Wuornos
12-03-2007, 02:48 AM
I would like to ask Wuornos and you all a question about a method.

This method can be used in accordance to other rating systems, like Dots or any other.

With your choosen system, you can have some rankings: an 1-year, 2-year 3-year-5year-10year-15year ranking.

The problem often is: wich ranking is more accurate? One? Another? A mix?

I think that the answer is: any player has to chose the best one for him.

So, for Connors is a long-term ranking, for Cash a short one.

How can we do?

I think that anyone can agree with the fact that a long domination is bettere that a short domination, and that, for example, Federer 5-year domination is probably already better than extraordinary career achievements of Agassi and Connors.

So, i suggest this kind of rankings:

We choose the reliability-number of years: for example, that a 7 years ranking has a decent reliability. If a player can have a medium rating x for seven years, we can trust that his rating is fair. If the player have the rating x for just three years, its reliability is poor and it's not the same thing. If he mantains the rating for 12 years, the reliability is greater, or maybe the same, but he deserves a longevity bonus.

So, the method is (if we choose the 7-years system, just for example)

7 years-rating * 100%
6 years-rating * (100-k)%
5 years-rating * (100-2k)%
9 years-rating * (100+2k)%

So any players has many different ratings and he can chose the most convenient

An example based upon atp ranking points.

Federer and Nadal have these end-year-ranking points
2007: 7180 and 5735
2006: 8370 and 4470
2005: 6725 and 4765
2004:6335 and 775
2003: 4375 and 766
2002: 2590 and 165
2001: 1745
2000: 1080
1999: 749

So, let's say that k = 10

These are Federer rankings:

1 year: 3348
2 years: 3887,5
3 years: 4455
4 years: 5006,75
5 years: 5277,6
6 years: 5336.25
7 years: 5331.429
8 years: 5280
9 years: 5219, 867


Nadal's:

1 year: 2294
2 years: 2625
3 years:2994
4 years: 2755.375
5 years; 2545.6

So Federer chooses a 6 years-rating of 5336,35
Nadal chosses a 3 years-rating of 2994

You can apply this method with dots rating too

Regards,

c.

Hi Nick. I like this and I don't like it.

There's nothing wrong with reasoning behind what you are saying, but there are two points, I would make in relation to the methodology.

First of all the K system is interesting but requires human opinion to decide on the K factor. If however you calculate the overall population results for each time band and then calculate the Mean and Standard Deviation. You can calculate a far fairer none human influenced system of comparison between the populations. I will try to do some work on this later to give you some examples using the Data from my abandoned 3.2 methodology. This is essentially what I was doing with my overall ratings in 3.2 methodolgy except with less time nabds and by taking a players place in all bands as an input rather than just their best.

Secondly I feel you need to look at peak 1 year, 2 year, 3 year etc. If we simply take the time periods as starting form the beginning of a players career, players like Martina Navratilova will be disadvantaged purely because despite winning two Wimbledon's it took somewhat longer for her to achieve her true playing level as measured from her first appearance.

All the best

Regards

Tim

Wuornos
12-03-2007, 02:52 AM
So the strength of the field is derived not from just the 7 opponents that said player came up against, but the field as a whole?

In 88' Edberg didn't play a single GS winner on his way to the title. To me, this is the equivilant of saying that Ljubicic gave his most dominant performance ever at the 06' FO, even though he didn't beat a single seeded player en route to the semis.

How does Guga Keurten's 97' FO win not make the list, when he went through 3 former champs to win the title?

I agree this methodology is flawed and it serves me right for making suggested changes to my methodology without thinking them through properly.

Reverting to my old method, results posted at #7, this looks at the quality of opposition actually faced and I feel provides a better quality of overall output for that.

Regards

Tim

Wuornos
12-03-2007, 02:56 AM
I don't know. The overall strenght of the tournament is maybe only that Wimbledon is more important than Madrid or New Haven.

But for sure, if I beat Federer and Nadal in the first half of the draw, and in the other half the best player is n.200 in the world, I have to get more points that in the case that i beat only players n. 200 in the world, even if in the draw there are Nadal, Federer, Sampras, McEnroe, Borg and God :)

I cannot get point for 'not winning' a match. In my opinion, it would be a nonsense.

Regards.

c.

No the overall weighting for a tournament is derived from a combination of the events ability to produce consistent results in recent years. The quality of oppostion competing in the event. Both are calculated independently.

Importance as a separate factor is not used.

Yes your point about beating a better quality player faced is used in methodology #7.

Regards

Tim

Wuornos
12-03-2007, 03:18 AM
Tim,

I think the women's rankings look very good. There will always be debate regarding Court, Graf and Navratilova (in my opinion, especially the first two) so, if you're going to have a system, it's good that it shows how there is very little seperating them. Personally, I think that while Graf and Court should be considered on a par there should be more of a buffer between them and Navratilova. Otherwise I have little complaint and appreciate that your ratings place BJK so highly as I do believe no-one ever acknowledges that she sacrificed her career in order to advance the women's pro tour. That and injury denied her at least, in my opinion, the chance to win another 3-4 majors as Court, the one player she couldn't handle, was finished by 74. Evert, on the other hand, was fortunate to come onto the scene at that time and prosper during a long trough in the women's game (post-Court, post-King and pre-Navratilova) without the same stiff opposition as her predecessors faced.


Thanks Andrew

I agree with everything you say although the DOT ratings draw their conclusions for slightly different reasons.

I take your point about BJK but of course this factor is not built into DOT which is only concerned with measuring the quality of results. the fact that DOT rates BJK, so highly is I would hope a credit to the methodology in the added value it provides to the raw data.

I agree about Evert. DOT calculates her results as being much inferior to her later career when she faced the challenge from Navratilova. Essentially the first five years of her career she was coasting and because of the lesser competition was winning slams. DOT indicates she raised her game with the challenge from Navratilova.

I would just like to post Evert's Post US Open Rankings here, as one criticism I constantly get when a players DOT rating reduces in the face of a serious challenger to their domination is that its because they have reduced success due to the the challenge. This is not true as DOT has been carefully cllibrated to balance the success of other players in the calculations and it has no effect on the overall DOT rating. Success goes down and opposition adjuster goes up. Chris is a great example of how a player does not nesessarily decrease in the face of big challenge. Chris actually did the opposite and improved.

Anyway here's the DOT Output showing what I mean.

1972 2613
1973 2675
1974 2763
1975 2763
1976 2772
1977 2736
1978 2716
1979 2715
1980 2738
1981 2729
1982 2752
1983 2782
1984 2770
1985 2812
1986 2811
1987 2746
1988 2726
1989 2677

I have been told on other threads that the reduction in Graf's performance as shown by DOT ratings was because of her reduced success as a result of the challenge from Seles. I hope the above goes some way to showing the callibration of DOT as being correct and the opposition adjuster used is sufficient to compensate for the appearence of a better player.

Regards

Tim

CyBorg
12-03-2007, 09:51 AM
Ratings are calculated by awarding weights to events based upon the strength of competition present. The strength of the competition is based on their overall dominance over the previous 12 months. Points awarded for each event are multiplied by the weighting to derive the points earned by each player.

aha .. I have a problem with this, particularly in regards to surfaces. Perhaps you've accounted for this, so correct me if I'm wrong.

Let's take a hypothetical year and consider a particular player - let's say Thomas Muster. Let's assume that half of Muster's year is played on clay and the other half is played on grass (for simplicity's sake). If we account for his strength as an opponent to a certain player in a particular event on a particular surface do we attempt to weed out a rating based on average or cumulative success based on the 12 months or do we look specifically at the surface and his success on that surface?

Let's say that Muster is the top player on clay, but lost in the first round at Wimbledon on grass (which makes him, let's say, at least 65th in the world on grass). If we average this out we may still conclude that Muster is a top-10 player overall. But how good of an opponent is he to Sergi Bruguera in the final of a French Open? How do we account for these surface differences?

Wuornos
12-04-2007, 03:47 AM
aha .. I have a problem with this, particularly in regards to surfaces. Perhaps you've accounted for this, so correct me if I'm wrong.

Let's take a hypothetical year and consider a particular player - let's say Thomas Muster. Let's assume that half of Muster's year is played on clay and the other half is played on grass (for simplicity's sake). If we account for his strength as an opponent to a certain player in a particular event on a particular surface do we attempt to weed out a rating based on average or cumulative success based on the 12 months or do we look specifically at the surface and his success on that surface?

Let's say that Muster is the top player on clay, but lost in the first round at Wimbledon on grass (which makes him, let's say, at least 65th in the world on grass). If we average this out we may still conclude that Muster is a top-10 player overall. But how good of an opponent is he to Sergi Bruguera in the final of a French Open? How do we account for these surface differences?

No Cyborg. You're absolutely correct in saying this isn't being adjusted for within the DOT Ratings.

No calculation is made for players for each individual surface. They only hold an overall rating for all surfaces which is taken into each respective event and used to derive their new overall rating.

However the devalutaion of ratings against past results is not smooth but stepped by year. Therefore each event should be represented equally within each players rating. Therefore technically the rating is actually a hybrid rating based on the same proportions at any point in time that appear within the majors. Therefore current ratings are one quarter clay, one quarter grass and half hard court influenced.

Well spotted though.

Regards

Tim

PS my comments here are based on the DOT ratings I have reverted to following the debacle of the 3.2.

Bolt
12-04-2007, 05:34 AM
The Best Five Year Performances based upon dominance and strength of opposition.

1. Roger Federer 9,584 Pts Achieved period ending after US Open of 2007
2. Ivan Lendl 8,224 Pts Achieved period ending after Australian Open of 1989
3. Björn Borg 6,811 Pts Achieved period ending after French Open of 2001


Is there a typo for the year in Borg's entry?

Wuornos
12-04-2007, 07:00 AM
Is there a typo for the year in Borg's entry?

No, I don't hink so. What did you have in mind.

To be honest I have largely abandoned this methodology now and reverted to type 2.3 methodology from two months ago. 2.3 was probaly the best version of the DOT Ratings and I think I have been heading up a dead end with the past two months development.

Regards

Tim

CyBorg
12-04-2007, 09:13 AM
No, I don't hink so. What did you have in mind.

To be honest I have largely abandoned this methodology now and reverted to type 2.3 methodology from two months ago. 2.3 was probaly the best version of the DOT Ratings and I think I have been heading up a dead end with the past two months development.

Regards

Tim

He probably means the year being '2001'.

Bolt
12-04-2007, 09:54 AM
He probably means the year being '2001'.

Indeed ...

Wuornos
12-05-2007, 04:25 AM
Indeed ...

I'm sorry I'm not with you at all. Why shouldn't his best period end at the French Open of 2001? I know he lost the next two majors and then retired, but before that he had the oppurtunity of dominating with both McEnroe and Connors active on the scene and his results up to and including the French of 2001 were just as good. That means his rating goes up. Is there some reason to think his standard of play went down at this point and the period immediately precededing it. Sorry if I'm being Dim

Regards

Tim

Steve132
12-05-2007, 04:48 AM
I'm sorry I'm not with you at all. Why shouldn't his best period end at the French Open of 2001? I know he lost the next two majors and then retired, but before that he had the oppurtunity of dominating with both McEnroe and Connors active on the scene and his results up to and including the French of 2001 were just as good. That means his rating goes up. Is there some reason to think his standard of play went down at this point and the period immediately precededing it. Sorry if I'm being Dim

Regards

Tim

The year should be 1981, not 2001.

Wuornos
12-05-2007, 05:00 AM
The year should be 1981, not 2001.

Oh god of course it should. Just goes to show sometimes you can look at things for an age and still not see what is right under your nose.

See I was being dim !! :)

Thanks

Tim

Bolt
12-05-2007, 05:09 AM
Oh god of course it should. Just goes to show sometimes you can look at things for an age and still not see what is right under your nose.

See I was being dim !! :)

Thanks

Tim

Giggle ... :)

Wuornos
12-07-2007, 02:40 AM
Giggle ... :)

It's not funny !!!! ;)

Nickognito
12-07-2007, 07:01 AM
I think that the best method is the one that makes better forecastings.

So i think there is an objective way to determine if elo system or dot or other method are better than others.

What do you think?

c.

Wuornos
12-07-2007, 07:18 AM
I think that the best method is the one that makes better forecastings.

So i think there is an objective way to determine if elo system or dot or other method are better than others.

What do you think?

c.

Interesting Nick. It cerainly a way forward. I'll think about how I might approach the analysis.

Thanks again

Take care

Tim