Which rankings are best?

[Wuornos]

As some of you know my hobby is in developing statistical ratings and rankings for past players.

I have over the years developed various systems. Some more complex than others. But I now find myself having doubts about my latest and by far most complex project.

As a result I was seeking some feedback. Below I am going to post the outputs from four of the ranking sytems I have previously developed without saying how each was calculated or how complex the calculations were. However, I will say they are all purely evidence based and free from personal opinion and are restricted in that they only consider results from the open era. Therefore, please take this into account as Rod Laver's ranking will not take take into account any results from prior to 1968.

All that differs between each ranking is what criteria are used in the calculations.

What I would like to know, is which rankings you believe is the best indicator of 'greatness' and why.

At the end of a week I will let those posting know what ramkings were more or less complex and what criteria were used in compiling each list.

Thanks

Tim

List 1

1. Roger Federer
2. Ivan Lendl
3. Rod Laver
4. Pete Sampras
5. Björn Borg
6. Mats Wilander
7. John McEnroe
8. Stefan Edberg
9. Boris Becker
10. Jim Courier
11. Ken Rosewall
12. Jimmy Connors


List 2

1. Ivan Lendl
2. Pete Sampras
3. Jimmy Connors
4. Andre Agassi
5. John McEnroe
6. Stefan Edberg
7. Björn Borg
8. Boris Becker
9. Mats Wilander
10. Ken Rosewall
11. Rod Laver
12. Jim Courier


List 3

1. Pete Sampras
2. Bjorn Borg
3. Roger Federer
4. Jimmy Connors
5. Mats Wilander
6. Andre Agassi
7. Ivan Lendl
8. John McEnroe
9. Boris Becker
10. Rod Laver
11. Jim Courier
12. Ken Rosewall

List 4

1. Roger Federer
2. Jimmy Connors
3. Pete Sampras
4. Mats Wilander
5. Bjorn Borg
6. Rod Laver
7. Ivan Lendl
8. John McEnroe
9. Andre Agassi
10. Boris Becker
11. John Newcombe
12. Jim Courier

 

[superman1]

If you don't have Sampras/Federer/Laver/Borg in the top 4, in some order, then your list isn't any good.

I also don't know why Jim Courier is in all of these lists. Or why Wilander is above Agassi who he admitted was better than him, or why Lendl is above Sampras, and other things like that.

 

[Wuornos]

If you don't have Sampras/Federer/Laver/Borg in the top 4, in some order, then your list isn't any good.

I also don't know why Jim Courier is in all of these lists. Or why Wilander is above Agassi who he admitted was better than him, or why Lendl is above Sampras, and other things like that.

Ok that's good feedback. Justa quick couple of questions.

Why not Jim Courier? and Who instead of Jim Courier?

Thanks

Tim

 

[pabloJD]

This topic is very debatable and there are handfuls of threads on this board about this, so I will just point a couple of things that I don't understand how could happen:

List 2:
6. Stefan Edberg
7. Björn Borg

List 4:
4. Mats Wilander
5. Bjorn Borg

Edberg was my favourite player for awhile but I don't think he accomplished more than Borg, who won more slam titles, more tour titles, was more dominant during a period of time... the same with Wilander and Borg
There's also something weird with Connors being #12 on List 1. Connors was #1 for 5 years in a row, 8 slams and 7 other finals, and won more overall tournaments than anybody else.

 

[vive le beau jeu !]

Why not Jim Courier? and Who instead of Jim Courier?

vilas, for instance.

 

[Wuornos]

This topic is very debatable and there are handfuls of threads on this board about this, so I will just point a couple of things that I don't understand how could happen:

List 2:
6. Stefan Edberg
7. Björn Borg

List 4:
4. Mats Wilander
5. Bjorn Borg

Edberg was my favourite player for awhile but I don't think he accomplished more than Borg, who won more slam titles, more tour titles, was more dominant during a period of time... the same with Wilander and Borg
There's also something weird with Connors being #12 on List 1. Connors was #1 for 5 years in a row, 8 slams and 7 other finals, and won more overall tournaments than anybody else.

That's great thanks and makes a great point of the very issues that are at the heart of this. However, I don't agree that there are a handful of threads onm this board about this. This topic is concerned with what are the most imporatnt criteria in an evdentially based system while the other threads are concerned with who were the better players.

I am not at this stage stating what the criteria are, as I believe this might introduce error into the results of this survey.

You are of course correct in what you say relating to the two lists and in justifying your answers you tell me what criteria you consider most important in measuring 'greatness'. Great, that's exactly what I wanted to hear.

I am not going to state here which the following statements relate to, but I will make a couple of points that might provide reasons as to how what you consider to be anomalies might occur.

First a have read a number of times on this forum how it is impossible to judge or measure the standard of opposition over an extended time period. However, if we start with an assumption that the overall population is a constant rather than as some people believe a gradually improving standard we can go some way towards this.

Ratings of players can then be calculated as a function of a players dominance over the elite group (the top players in the world at that time) and the distance the elite group lies from the population mean. Hence a player receives credit depending on the quality of other players active during their era. Therefore to simply refer to a players major count can sometimes be misleading. Yes it is the most basic proxy of success but it does have a moving value.

Apart from major win having a moving value depending on who was active at that time, it is also dependent on the status of the tournament and how many top players were attracted to it at that time. This so far has always been a judgement call but it need not be. Events are weighted according to their status at the individual point in time at which they influence a players rating, i.e. the point in time at which they were played. The status (weighting) is calculated by examining recent years performance of the top players within each event. Tournaments where the top players have been absent score lower than events where all top players have been present. Events which more consistently produce results that reflect the current overall rankings also receive additional weighting when compared with those tournaments where results appear more random. This type of weighting of course devalues French titles in the 1970s and while Borg was still undoubted No 1 in the late 70s it might deflate his modified levels of achievement.

I won’t at this stage say which of the above two points relate to any or all of the lists, but it illustrates how a rating system might be developed that takes more than simple major wins and time spent at number 1 into account. However, you can see that such things which up until now have been considered subjective might be calculated and incorporated into a rating system with self adjusting variable criteria and therefore remain free from personal opinion.

If you then consider that many pundits and fans take a more basic approach in evaluating players it would be reasonable to assume that while the majority of individuals rankings within such a system might be consistent with current opinion, the new data might shed some light evidentially to support a couple of surprises.

I am not saying at this stage whether those items you identified might be because of this or not.

Thanks for your time in looking at my rankings.

I appreciate your thoughts and will let you know what lists incorporate what criteria by next weekend

Tim

PS Glad to see you took into account Jimmy Connors achievements at majors other than his wins. I believe this is important and is not something everyone considers.

PPS Connors also played in 31 major semi finals !

 

[noeledmonds]

If we look at the most dominant players in each opne-era decade we have Laver over Rosewall in th 60s, Borg over Connors in the 70s, Lendl over McEnroe in the 80s, Sampras over Agassi in the 90s and what will likely be Federer over Nadal in the 00s. I think the dominant players in their decade should be the ones at the top of the list. I also agree that Wilander and Edberg should never be above Borg. I believe Laver should be consistantly higher even if we look at Open-era results only. His Grand Slam alone should put him above the likes of Wilander IMO. Personally I would proabably put Ash on the list over Courier.

 

[pabloJD]

Well, I can tell you're putting a great deal of hard work into this project. It's very interesting stuff.
I think it's very difficult to establish the criteria for best player over a long period of time and that's what the arguments were always really about. Once you establish the criteria there's not much left to discuss.
When you say "Events which more consistently produce results that reflect the current overall rankings also receive additional weighting when compared with those tournaments where results appear more random." I don't think that's fair to very fast or slow surfaces. It would mean that what you do on clay doesn't represent you as a tennis player as faithfully as what you do on hardcourts, because clay has its own specialists and the results are expected to be surprising rankings-wise. And there's the availability of points issue too: suppose there was one unbeatable player on hardcourts and one unbeatable player on clay. The HC player could get 5250 points from grand slams, masters series and masters cup, and there'd be 2500 for the clay expert. Who will end more likely as #1? So the latest player would not only have a lesser chance to get more points (because of the structure of the tour) but his accomplishments will be diminished in your ratings just because of that same factor! I know it's an extereme example but it illustrates what I'm trying to say. It's a circular reasoning and adds a variable that is not needed and I think it's detrimental to what you're trying to do. And there's also an undesirable retroactive effect: what a player does at a certain time will be affected if there are some surprise winners ten years from then.
Hope this is useful to you.
Great effort and I really like the objective approach you're having on this

 

[JW10S]

I do not agree with any of lists posted here. There is no 'best' one among them.

 

[boredone3456]

I do not agree with any of lists posted here. There is no 'best' one among them.

I agree. One list doesnt even have federer...which to me throws out that list considering all he has acheived. and the others just dont look right...but that is just my opinion

 

[Wuornos]

Well, I can tell you're putting a great deal of hard work into this project. It's very interesting stuff.
I think it's very difficult to establish the criteria for best player over a long period of time and that's what the arguments were always really about. Once you establish the criteria there's not much left to discuss.
When you say "Events which more consistently produce results that reflect the current overall rankings also receive additional weighting when compared with those tournaments where results appear more random." I don't think that's fair to very fast or slow surfaces. It would mean that what you do on clay doesn't represent you as a tennis player as faithfully as what you do on hardcourts, because clay has it own specialist and the results are expected to be surprising rankings-wise. And there's the availability of points issue too: suppose there was one unbeatable player on hardcourts and one unbeatable player on clay. The HC player colud get 5250 points from grand slams, masters series and masters cup, and there'd be 2500 for the clay expert. Who will end more likely as #1? So the latest player would not only have a lesser chance to get more points (because of the structure of the tour) but his accomplishments will be diminished in your ratings just because of that same factor! I know it's an extereme example but it illustrates what I'm trying to say. It's a circular reasoning and adds a variable that is not needed and I think it's detrimental to what you're trying to do. And there's also an undesirable retroactive effect: what a player does at a certain time will be affected if there are some surprise winners ten years from then.
Hope this is useful to you.
Great effort and I really like the objective approach you're having on this

Thanks Pablo

I appreciate your lengthy reply and I think you have made some good points. The point you make about clay is interesting and the point about the system being self referencing is excellent.

Thanks you so much

Regards

Tim

 

[Wuornos]

I agree. One list doesnt even have federer...which to me throws out that list considering all he has acheived. and the others just dont look right...but that is just my opinion

Thanks Boredone.

Your opinion is as valid as one elses, so your input is just fine. The list you refer to that excludes federer is based on career achievement as defined by time based ratings being graphed and the area under the line of performance to date being used for the rankings. And you are of course right, that list is never going to be representative for a player who is only half way through his career.


In fact Federer holds the highest peak rating of any player at 3,509 points, so if you assume the pattern of his career performance remains typical, we would expect him one day to top this list. He currently has an area under his performance curve of 7,770 Rating Point Years which puts him 15th on the list but I would expect his rank to climb rapidly as he nears the end of his career.

Jimmy Connors is one of the most interesting players in relation to this type of rating system. He only ranks 12th with 1,778 points at his peak as he lost out in the majors when both Borg and McEnroe were at their peak, but his career was so long that he achieved 21,874 Rating Point Years in career that was defined by a low (for a great) but long career curve.

Thanks for the feedback.

Tim

 

[Wuornos]

If you don't have Sampras/Federer/Laver/Borg in the top 4, in some order, then your list isn't any good.

I also don't know why Jim Courier is in all of these lists. Or why Wilander is above Agassi who he admitted was better than him, or why Lendl is above Sampras, and other things like that.

Actually on your top point they are in list 1 in the top 5. We only seem to disagree on the kudos due to Lendl. That's pretty good given a subject which provokes such diverse opinions, don't you think.

Thanks for the help

Tim

 

[Wuornos]

If we look at the most dominant players in each opne-era decade we have Laver over Rosewall in th 60s, Borg over Connors in the 70s, Lendl over McEnroe in the 80s, Sampras over Agassi in the 90s and what will likely be Federer over Nadal in the 00s. I think the dominant players in their decade should be the ones at the top of the list. I also agree that Wilander and Edberg should never be above Borg. I believe Laver should be consistantly higher even if we look at Open-era results only. His Grand Slam alone should put him above the likes of Wilander IMO. Personally I would proabably put Ash on the list over Courier.

Thanks Noel. Interesting to note that exactly as you described the 5 top players from each of the decades in your first sentence so the top 5 in list 1 appear.

I take the point you make about Laver and this would certainly be true if we take into account his achievements prior to the open era, then he would be a monster of the game. Unfortunately the system uses a slinding scale for domination rather than a rigid one of having achieved a Grand Slam or not and 5 major wins is tough to prove evidentially that you are significantly better than anyone else who has played the game in the open era. I think the list 1 system does damn well to identify Laver as one of the absolute greats of such a limited open record as it is. I consider this an achievement of the system along with the top 5 players you previously mentioned.

Your point about Wilander is noted and is one I have already examined time and time again. No matter what I do I cannot deflate Mats Wilander's achievements within List 1 without compromising it's validity in other areas. At the moment it is a self adjusting variable parameter system independent of human interference in weighting or emphasis. So it's very strength in creating it's own scales rather than artificially subjective human ones are what adds even more validity to your opinion of the top 5, the laver issue, but highlights the fact that Wilander may be underrated given his achievements at which events and against which players.

Your point about Ashe is noted instead of Courier. It is I think inevitable that as we move down the list the selections will become more varied. The list 1 system has calculated a peak rating for Jim Courier of 2,099 which was achieved at Wimbledon in 1993. Arthur Ashe made his peak rating of 1,546 at the French of 1972. Again it's another good call by you as had list 1 have gone down to 13 instead of 12, Arthur Ashe would have been included. The most significant difference between Jim Courier and Arthur Ashe as identified by the software algorithm that generated list 1 is the issue of dominance. Jim Courier having achieved more in a shorter time frame.

Take care and thanks for your feedback

Regards

Tim

PS Are you really Noel Edmonds?

 

[Wuornos]

If we look at the most dominant players in each opne-era decade we have Laver over Rosewall in th 60s, Borg over Connors in the 70s, Lendl over McEnroe in the 80s, Sampras over Agassi in the 90s and what will likely be Federer over Nadal in the 00s. I think the dominant players in their decade should be the ones at the top of the list. I also agree that Wilander and Edberg should never be above Borg. I believe Laver should be consistantly higher even if we look at Open-era results only. His Grand Slam alone should put him above the likes of Wilander IMO. Personally I would proabably put Ash on the list over Courier.

Thanks Noel. Interesting to note that exactly as you described the 5 top players from each of the decades you desribe in your first sentance are the top 5 in list 1.

I take the point you make about Laver and this would certainly be true if we take into account his achievements prior to the open era, then he would be a monster of the game. Unfortunately the system uses a slinding scale for domination rather than a rigid one of having achieved a Grand Slam or not and 5 major wins is tough to prove evidentially that you are significantly better than anyone else who has played the game in the open era. I think the list 1 system does damn well to identify Laver as one of the absolute greats of such a limited open record as it is. I consider this an achievement of the system along with the top 5 players you previously mentioned.

Your point about Wilander is noted and is one I have already examined time and time again. No matter what I do I cannot deflate Mats Wilander's achievements within List 1 without compromising it's validity in other areas. At the moment it is a self adjusting variable parameter system independent of human interference in weighting or emphasis. So it's very strength in creating it's own scales rather than artificially subjective human ones are what adds even more validity to your opinion of the top 5, the laver issue, but highlights the fact that Wilander may be underrated given his achievements at which events and against which players.

Your point about Ashe is noted instead of Courier. It is I think inevitable that as we move down the list the selections will become more varied. The list 1 system has calculated a peak rating for Jim Courier of 2,099 which was achieved at Wimbledon in 1993. Arthur Ashe made his peak rating of 1,546 at the French of 1972. Again it's another good call by you as had list 1 have gone down to 13 instead of 12, Arthur Ashe would have been included. The most significant difference between Jim Courier and Arthur Ashe as identified by the software algorithm that generated list 1 is the issue of dominance. Jim Courier having achieved more in a shorter time frame.

Take care and thanks for your feedback

Regards

Tim

 

[rjkardo]

I do not agree with any of lists posted here. There is no 'best' one among them.

I agree. All of the lists have major flaws.

Rod

 

[Wuornos]

I agree. All of the lists have major flaws.

Rod

Thanks Rod.

Could you give me some ideas of what the flaws are? I am seeking to improve the objective rating systems I am creating and any feedback would be appreciated especially if there are major flaws.

I am sure you guess from the previous two posts by me that my favourite system is list 1 and it has so far not been to far removed from some of the opinions posted. Of course nothing is going to be perfect given a subject matter that instills such diverse opinion. If, however, you believe list 1 has some one in the top 5 who shouldn't even be in the top 10 or there is someone in the top 10 who shouldn't be in the top 20 and you can say why you think this, it would be of significant interest to me.

Thanks for posting.

Tim

 

[superman1]

List 1 shows promise, but you've got Lendl (8 Slams) above Sampras (14 Slams), you've got Courier in there and you don't have Agassi, and you have Wilander above McEnroe and Connors.

List 3 seems more balanced.

 

[Wuornos]

List 1 shows promise, but you've got Lendl (8 Slams) above Sampras (14 Slams), you've got Courier in there and you don't have Agassi, and you have Wilander above McEnroe and Connors.

List 3 seems more balanced.

Thanks Superman. I think your opinion is quite representative of experts views at the moment so I appreciate your comments.

Looking at whats going on in the system that generated list 1, Lendl seems to get the nod over Sampras for two reasons.

Firstly, while Lendl won 6 less majors, he played in more finals, 19-18, and more semi finals 28 - 23, and I think some credit for this consistency is being given.

Also the algorithm involved sees Lendl's peak being at the Australian in 1988 when it saw the elite group of mens tennis as being 13,316 points removed from the constant population mean while Samras' peak was after Wimbledon in 1997 when the elite group was 12,025 points removed from the constant population mean. What this all means is that Lendl receives some extra credit for playing at a time when the game at its highest level was probably more competitive than when Sampras was at his peak. Don't misinterpret this though, the asumption within the system is that the standard of tennis for the population as a whole remains constant.

Neither of these two point alone would bring Lendl up to the level of Sampras but when combined they are sufficient for him to just overtake.

I would really value your views on whether these calculations seem reasonable, not from the mathematical sense but from the tennis experts point of view. i.e. Should Lendl's additional achievements be allowed to narrow the gap between his level of achievement and Sampras based purely on major count and does it seem reasonable for the late 1980s to be rgarded as more competitive at the very top of the game than the late 1990s.

Forgive me if I don't provide similar analysis for your other excellent points but I felt the posting might become to long.

Many thanks for your help and advice.

All the best

Tim

 

[Zimbo]

List 1 shows promise, but you've got Lendl (8 Slams) above Sampras (14 Slams), you've got Courier in there and you don't have Agassi, and you have Wilander above McEnroe and Connors.

List 3 seems more balanced.

Agreed.

There are major flaws is all the lists. I can't wait to see your criteria, cause I just don't understand how Wilander could be ranked so high in 3 of the lists. Also, I'm betting that Connors longivity hurt him in list 1, and that Agassi's up and down career hurt him. As for Mac's not being highly ranked, most of it probably had to do with his career post '85. As for Lendl in list 3 and 4, he's probably low in the ranking due to his career post '91 but in list 2 he was number 1 due to his domination in the mid '80's and the fact that he made it to 19 slam finals.

 

[Rafa freak]

List 3 for me.

 

[Zimbo]

If you don't have Sampras/Federer/Laver/Borg in the top 4, in some order, then your list isn't any good.

I also don't know why Jim Courier is in all of these lists. Or why Wilander is above Agassi who he admitted was better than him, or why Lendl is above Sampras, and other things like that.

Good point on Wilander admitting that Agassi's was better then him. Rightly so. However, how come when Mac time and time again would admit Agassi was better then him alot of people on the board would still say Mac was greater. I just don't get it. Can someone explain this to me? Superman1, do you think Mac was better then Agassi? I know I'm revisiting an old thread here.

 

[Rafa freak]

Good point on Wilander admitting that Agassi's was better then him. Rightly so. However, how come when Mac time and time again would admit Agassi was better then him alot of people on the board would still say Mac was greater. I just don't get it. Can someone explain this to me? Superman1, do you think Mac was better then Agassi? I know I'm revisiting an old thread here.

I don't........

 

[Zimbo]

Also the algorithm involved sees Lendl's peak being at the Australian in 1988 when it saw the elite group of mens tennis as being 13,316 points removed from the constant population mean while Samras' peak was after Wimbledon in 1997 when the elite group was 12,025 points removed from the constant population mean. What this all means is that Lendl receives some extra credit for playing at a time when the game at its highest level was probably more competitive than when Sampras was at his peak. Don't misinterpret this though, the asumption within the system is that the standard of tennis for the population as a whole remains constant.

Neither of these two point alone would bring Lendl up to the level of Sampras but when combined they are sufficient for him to just overtake.

I would really value your views on whether these calculations seem reasonable, not from the mathematical sense but from the tennis experts point of view. i.e. Should Lendl's additional achievements be allowed to narrow the gap between his level of achievement and Sampras based purely on major count and does it seem reasonable for the late 1980s to be rgarded as more competitive at the very top of the game than the late 1990s.

Tim

How did you decide statistically that the late 80s was more competitive then the Sampras peak? Though I agree with it I was just wondering how you came up with the 13,316 points and 12,025 points.

 

[Wuornos]

How did you decide statistically that the late 80s was more competitive then the Sampras peak? Though I agree with it I was just wondering how you came up with the 13,316 points and 12,025 points.

Gosh this is such a difficult question to answer within the confines of a single post, but here it goes.

If you take a numerical evaluation of results, e.g. the current world ranking system, and then plot the results on a graph, you will obtain a curve of population performance. What system is chosen for the points is largely an irrelevance as long as it is kept constant over time. Remember we are looking to evaluate how the populations elite group’s strength moves and not absolute strength or individuals performance at this stage.

Again the actual shape of the curve that is created is largely irrelevant. What is relevant is how this pattern changes overtime. If the pattern becomes elongated we would be seeing a greater range in performance distribution. It is unlikely that the entire population has suddenly become weaker and therefore the most probable explanation is that the higher levels are performances which are more distant from the mean of the population than is usual. Likewise if the curve becomes taller and shorter the most likely explanation is that the top performers are not reaching the normal margin that is present between themselves and the population mean.

In reality there is no real need to draw the lines on paper as there are statistical measures of spread which work equally as well. Standard Deviation is the square root of variance. The figures quoted here representative of the variance.

This indicator of Elite Strength is then used as part of the weightings within the system to give additional or less credit to basic calculations on achievement and domination etc.

Finally I must stress that all of this is dependent upon the population mean being a constant. I can’t stress that enough.

I hope this helps.

Regards

Tim

 

[Wuornos]

As some of you know my hobby is in developing statistical ratings and rankings for past players.

I have over the years developed various systems. Some more complex than others. But I now find myself having doubts about my latest and by far most complex project.

As a result I was seeking some feedback. Below I am going to post the outputs from four of the ranking sytems I have previously developed without saying how each was calculated or how complex the calculations were. However, I will say they are all purely evidence based and free from personal opinion and are restricted in that they only consider results from the open era. Therefore, please take this into account as Rod Laver's ranking will not take take into account any results from prior to 1968.

All that differs between each ranking is what criteria are used in the calculations.

What I would like to know, is which rankings you believe is the best indicator of 'greatness' and why.

At the end of a week I will let those posting know what ramkings were more or less complex and what criteria were used in compiling each list.

Thanks

Tim

List 1

1. Roger Federer
2. Ivan Lendl
3. Rod Laver
4. Pete Sampras
5. Björn Borg
6. Mats Wilander
7. John McEnroe
8. Stefan Edberg
9. Boris Becker
10. Jim Courier
11. Ken Rosewall
12. Jimmy Connors


List 2

1. Ivan Lendl
2. Pete Sampras
3. Jimmy Connors
4. Andre Agassi
5. John McEnroe
6. Stefan Edberg
7. Björn Borg
8. Boris Becker
9. Mats Wilander
10. Ken Rosewall
11. Rod Laver
12. Jim Courier


List 3

1. Pete Sampras
2. Bjorn Borg
3. Roger Federer
4. Jimmy Connors
5. Mats Wilander
6. Andre Agassi
7. Ivan Lendl
8. John McEnroe
9. Boris Becker
10. Rod Laver
11. Jim Courier
12. Ken Rosewall

List 4

1. Roger Federer
2. Jimmy Connors
3. Pete Sampras
4. Mats Wilander
5. Bjorn Borg
6. Rod Laver
7. Ivan Lendl
8. John McEnroe
9. Andre Agassi
10. Boris Becker
11. John Newcombe
12. Jim Courier

As promised. How each list was compiled.

List 1 and List 2 were both decribed in length as part of the above posts.

List 3 is a hybrid list with weightings for majors won coupled with duration of reign as number 1. This list was started when I was about 12 and is put together because I didn't know all the results other than winners for each major.

List 4. Is a weighted list calculated by the number of majors won in a calendar year with the best year receiving most weighting and subsequent weaker years receiving less weighting down to a players 6th best year. Like list 3 this is a simple methodology which can be calculated in 5 minutes, but unlike list 3 which is dependent on total achievement, this list is more concerned with short term dominance.

Thanks for everyone who provided feedback.

Regards

Tim