Author Topic: Full Open Era Rankings (RESEARCH PHASE)  (Read 7075 times)

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Offline JonG

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #120 on: August 14, 2013, 06:16:44 PM »
This time I started from the bottom up.

I think that is the right way to go.

Maybe try some who played GP only to nail GP points, then some who played GP+Mediterranean, then some GP+US indoor and leave WCT players til last.

Offline JonG

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #121 on: August 14, 2013, 06:18:09 PM »
By the way, do you use the ATP database for your results or do you have a better source?

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #122 on: August 19, 2013, 01:27:14 AM »
By the way, do you use the ATP database for your results or do you have a better source?

ATP database and ITF database. I don't have any other source for draw results.

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #123 on: August 19, 2013, 01:55:58 AM »
Well, until now, it was all an unknown. I had some free time to do some clear thinking, and the way I see this, it can be solved with some interesting high degree numerical methods. Juggle into the unknown with tournament prize point values and there will probably always be some player with a different point value.

But, I will try to create an equation system, where each player is an equation and tournament type results for that player are the unknown variables. I have managed to identify 23 unknown variables, meaning that I will be using 23 players to solve the equation system. Normally, such a mathematical system has one single solution. Anything that would vary beyond .5 precision would either be an ATP error or a system error. If it is a system error, the equation can probably be adjusted (see how the entire system would behave once a tournament prize points are modified). Gonna see if I can use MATLAB to simulate it all.

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #124 on: August 19, 2013, 02:29:53 AM »
Here are the equations entering the system:

Code: [Select]
Nastase: TC_W + TC_64 + 2*A_W + 2*A_SF + A_QF + A_16 + 4*B_W + 2*B_F + B_SF + 6*C_W + C_F + C_QF + C_16 = 239.5
Kodes: TC_F + TC_QF + A_SF + A_QF + B_W + B_F + B_SF + 2*B_QF + 4*B_16 + C_F = 101
Connors: TC_QF + A_W + A_SF + B_W + 4*B_SF + B_16 + 3*C_W + C_F + C_16 = 125
Okker: TC_QF + TC_16 + 2*A_W + 2*A_F + 3*A_SF + A_16 + A_32 + 3*B_W + 2*B_SF + 4*B_QF + 5*B_16 + 2*C_W = 202.5
Rosewall: TC_SF + A_QF + 2*A_16 + A_32 + 4*B_W + 5*B_SF + 3*B_QF + B_16 + C_W = 122
Laver: TC_32 + A_SF + A_QF + 2*A_16 + 4*B_W + 3*B_F + 2*B_SF + 2*B_QF + C_W + C_QF = 115
Orantes: TC_32 + TC_64 + A_W + 3*A_F + A_QF + 2*A_16 + A_32 + B_W + 2*B_F + B_16 + 2*C_W + C_F + 2*C_SF + C_16 = 145.5
Ashe: TC_16 + TC_32 + A_W + 2*A_F + 2*A_QF + A_16 + A_32 + B_W + 4*B_F + 2*B_SF + 3*B_QF + 3*B_16 + C_QF + C_16 = 148.5
Gorman: TC_F + TC_QF + 4*A_QF + A_16 + A_32 + 3*B_SF + 9*B_16 + C_SF + C_16 = 105.5
Emerson: 2*A_16 + B_W + 3*B_F + 2*B_SF + 2*B_QF + 2*B_16 + C_16 = 61.5
Riessen: TC_64 + 2*A_QF + 2*A_16 + B_W + 2*B_F + 2*B_SF + 7*B_QF + 3*B_16 = 82
Panatta: TC_SF + TC_32 + A_16 + 2*A_32 + B_W + 3*B_16 + 5*C_F + C_QF = 64
Gerken: TC_16 + TC_64 + A_QF + A_16 + 2*B_QF + 2*B_16 + C_F + 2*C_SF + 4*C_QF + 4*C_16 = 34.5
Dent: 2*TC_32 + A_16 + 2*A_32 + B_SF + 3*B_QF + 12*B_16 + C_16 = 39
Hrebec: 2*TC_64 + A_QF + 2*A_32 + B_QF + C_W + 2*C_QF + C_16 = 24.5
Jauffret: TC_16 + A_32 + B_QF + B_16 + 2*C_SF + C_QF + C_16 = 15.5
Pasarell: 2*TC_32 + A_QF + 4*A_16 + 10*B_16 + 2*C_F + C_16 = 39
Vilas: TC_32 + A_SF + 2*A_16 + 2*A_32 + B_W + B_QF + 2*B_16 + C_16 = 33
Mottram: A_SF + A_QF + B_QF + B_16 + 2*C_16 = 21
Metreveli: TC_64 + A_QF + A_32 + B_SF + 2*B_QF + 7*B_16 + C_SF = 28
Lutz: B_F + B_SF + 4*B_QF + 2*B_16 = 27
Stolle: 2*A_16 + B_F + 2*B_QF + 4*B_16 + C_W + C_SF = 29
Pohmann: TC_32 + A_QF + B_SF + C_W + C_QF = 18.5
« Last Edit: August 19, 2013, 03:21:57 AM by Slasher1985 »

Offline Swish

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #125 on: August 19, 2013, 05:36:21 PM »
Here are the equations entering the system:

Code: [Select]
Nastase:    TC_W + TC_64 + 2*A_W + 2*A_SF + A_QF + A_16 + 4*B_W + 2*B_F + B_SF + 6*C_W + C_F + C_QF + C_16 = 239.5
Kodes:       TC_F + TC_QF + A_SF + A_QF + B_W + B_F + B_SF + 2*B_QF + 4*B_16 + C_F = 101
Connors:    TC_QF + A_W + A_SF + B_W + 4*B_SF + B_16 + 3*C_W + C_F + C_16 = 125
Okker:      TC_QF + TC_16 + 2*A_W + 2*A_F + 3*A_SF + A_16 + A_32 + 3*B_W + 2*B_SF + 4*B_QF + 5*B_16 + 2*C_W = 202.5
Rosewall:   TC_SF + A_QF + 2*A_16 + A_32 + 4*B_W + 5*B_SF + 3*B_QF + B_16 + C_W = 122
Laver:      TC_32 + A_SF + A_QF + 2*A_16 + 4*B_W + 3*B_F + 2*B_SF + 2*B_QF + C_W + C_QF = 115
Orantes:   TC_32 + TC_64 + A_W + 3*A_F + A_QF + 2*A_16 + A_32 + B_W + 2*B_F + B_16 + 2*C_W + C_F + 2*C_SF + C_16 = 145.5
Ashe:      TC_16 + TC_32 + A_W + 2*A_F + 2*A_QF + A_16 + A_32 + B_W + 4*B_F + 2*B_SF + 3*B_QF + 3*B_16 + C_QF + C_16 = 148.5
Gorman:      TC_F + TC_QF + 4*A_QF + A_16 + A_32 + 3*B_SF + 9*B_16 + C_SF + C_16 = 105.5
Emerson:   2*A_16 + B_W + 3*B_F + 2*B_SF + 2*B_QF + 2*B_16 + C_16 = 61.5
Riessen:   TC_64 + 2*A_QF + 2*A_16 + B_W + 2*B_F + 2*B_SF + 7*B_QF + 3*B_16 = 82
Panatta:   TC_SF + TC_32 + A_16 + 2*A_32 + B_W + 3*B_16 + 5*C_F + C_QF = 64
Gerken:      TC_16 + TC_64 + A_QF + A_16 + 2*B_QF + 2*B_16 + C_F + 2*C_SF + 4*C_QF + 4*C_16 = 34.5
Dent:      2*TC_32 + A_16 + 2*A_32 + B_SF + 3*B_QF + 12*B_16 + C_16 = 39
Hrebec:      2*TC_64 + A_QF + 2*A_32 + B_QF + C_W + 2*C_QF + C_16 = 24.5
Jauffret:   TC_16 + A_32 + B_QF + B_16 + 2*C_SF + C_QF + C_16 = 15.5
Pasarell:   2*TC_32 + A_QF + 4*A_16 + 10*B_16 + 2*C_F + C_16 = 39
Vilas:      TC_32 + A_SF + 2*A_16 + 2*A_32 + B_W + B_QF + 2*B_16 + C_16 = 33
Mottram:   A_SF + A_QF + B_QF + B_16 + 2*C_16 = 21
Metreveli:   TC_64 + A_QF + A_32 + B_SF + 2*B_QF + 7*B_16 + C_SF = 28
Lutz:      B_F + B_SF + 4*B_QF + 2*B_16 = 27
Stolle:      2*A_16 + B_F + 2*B_QF + 4*B_16 + C_W + C_SF = 29
Pohmann:   TC_32 + A_QF + B_SF + C_W + C_QF = 18.5

 
Try putting this:
 
TC_W + TC_64 + 2*A_W + 2*A_SF + A_QF + A_16 + 4*B_W + 2*B_F + B_SF + 6*C_W + C_F + C_QF + C_16 = 239.5
TC_F + TC_QF + A_SF + A_QF + B_W + B_F + B_SF + 2*B_QF + 4*B_16 + C_F = 101
TC_QF + A_W + A_SF + B_W + 4*B_SF + B_16 + 3*C_W + C_F + C_16 = 125
TC_QF + TC_16 + 2*A_W + 2*A_F + 3*A_SF + A_16 + A_32 + 3*B_W + 2*B_SF + 4*B_QF + 5*B_16 + 2*C_W = 202.5
TC_SF + A_QF + 2*A_16 + A_32 + 4*B_W + 5*B_SF + 3*B_QF + B_16 + C_W = 122
TC_32 + A_SF + A_QF + 2*A_16 + 4*B_W + 3*B_F + 2*B_SF + 2*B_QF + C_W + C_QF = 115
TC_32 + TC_64 + A_W + 3*A_F + A_QF + 2*A_16 + A_32 + B_W + 2*B_F + B_16 + 2*C_W + C_F + 2*C_SF + C_16 = 145.5
TC_16 + TC_32 + A_W + 2*A_F + 2*A_QF + A_16 + A_32 + B_W + 4*B_F + 2*B_SF + 3*B_QF + 3*B_16 + C_QF + C_16 = 148.5
TC_F + TC_QF + 4*A_QF + A_16 + A_32 + 3*B_SF + 9*B_16 + C_SF + C_16 = 105.5
2*A_16 + B_W + 3*B_F + 2*B_SF + 2*B_QF + 2*B_16 + C_16 = 61.5
TC_64 + 2*A_QF + 2*A_16 + B_W + 2*B_F + 2*B_SF + 7*B_QF + 3*B_16 = 82
TC_SF + TC_32 + A_16 + 2*A_32 + B_W + 3*B_16 + 5*C_F + C_QF = 64
TC_16 + TC_64 + A_QF + A_16 + 2*B_QF + 2*B_16 + C_F + 2*C_SF + 4*C_QF + 4*C_16 = 34.5
2*TC_32 + A_16 + 2*A_32 + B_SF + 3*B_QF + 12*B_16 + C_16 = 39
2*TC_64 + A_QF + 2*A_32 + B_QF + C_W + 2*C_QF + C_16 = 24.5
TC_16 + A_32 + B_QF + B_16 + 2*C_SF + C_QF + C_16 = 15.5
2*TC_32 + A_QF + 4*A_16 + 10*B_16 + 2*C_F + C_16 = 39
TC_32 + A_SF + 2*A_16 + 2*A_32 + B_W + B_QF + 2*B_16 + C_16 = 33
A_SF + A_QF + B_QF + B_16 + 2*C_16 = 21
TC_64 + A_QF + A_32 + B_SF + 2*B_QF + 7*B_16 + C_SF = 28
B_F + B_SF + 4*B_QF + 2*B_16 = 27
2*A_16 + B_F + 2*B_QF + 4*B_16 + C_W + C_SF = 29
TC_32 + A_QF + B_SF + C_W + C_QF = 18.5
 
 
Into this: http://wims.unice.fr/wims/en_tool~linear~linsolver.en.html
 
 
I tried for you but there was an error, possibly a typo is indicated.
 
It may work if you have enough data to solve the variables.
 
 
Another thing you can try is to download C++ code to do it and then just compile it if that's what kind of compiler you have handy. You may have to modify the code for the number of variables you have???
 
Good luck in your endeavers.
 
 

Offline Swish

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #126 on: August 19, 2013, 06:53:18 PM »
You can also try to pick players who didn't play much at all, less variables then in their equation.
You might get lucky and solve a few variables that way.
 
Take the result of the solved variables and put that in the bigger equations to reduce the number of variables there.
 
Good luck again.  :rofl_2:
 
 
 
 

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #127 on: August 20, 2013, 12:55:08 AM »
Thanks for the help. I actually solved the equation with MATLAB.

The results were incredible. There were even some negative solutions. Either the player's tournaments are not in their right categories or there's something fishy here. :rofl_2:

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #128 on: August 20, 2013, 02:28:44 AM »
If you're wondering, this is the solution I got:

Code: [Select]
TC_W = -766356/190565
TC_F = 8154748/190565
TC_SF = 2225558/190565
TC_QF = 1952077/190565
TC_16 = 859846/190565
TC_32 = 814919/190565
TC_64 = 523040/190565
A_W = 8631978/190565
A_F = 996047/190565
A_SF = -360568/190565
A_QF = 1296272/190565
A_16 = -7122/190565
A_32 = 411704/190565
B_W = 3010078/190565
B_F = 1564979/190565
B_SF = 666254/190565
B_QF = 681417/190565
B_16 = 94177/190565
C_W = 1819633/190565
C_F = 1223683/190565
C_SF = 416477/190565
C_QF = -1071626/190565
C_16 = 1145283/190565

Offline Swish

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #129 on: August 20, 2013, 04:45:14 AM »
It looks like different values were used for the variables or the totals were not calculated correctly.
 
For example:
TC_16 = 5 in one equation and 4 in another.
 
Or the totals may be from tournaments not shown.
 
In that case you can add the variable x to every equation. It will represent missing points.
example: x = tournament a + tournament b ....
 
Then when you get a number for x you have to find those tournaments.
 
Not sure if this will work. It's still early for me
:dunno:
 
 
Sorry, that won't work. It's highly unlikely they all missed the same points. I told you it's early.  :)
 
« Last Edit: August 20, 2013, 04:52:32 AM by Swish »

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #130 on: August 20, 2013, 05:51:49 AM »
It does not make any sense really.

I have calculated the amount of negative solutions and input into a special feature of MATLAB which plots an error curve. If you adjust any equation to fit the points, other will not. It's like the entire rankings of 1973 were incorrect because the points calculated for each players were attributed in different manners although they played the same type of tournament.

The error I am getting is 43.5%. :scared:

It could mean that there were bonus points which would factor in the differences, but at the same time, the differences exist in bottom ranked players as well, where it's still extremely difficult to make rankings agree.
« Last Edit: August 20, 2013, 05:53:22 AM by Slasher1985 »

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #131 on: August 20, 2013, 07:20:19 AM »
I reached some stable point where adjusting values for some players heavily modifies others, but some players match the official points, some are very close, yet some are quite far.

This example and calculation shows just what I said earlier, that ATP didn't calculate the points for players uniformly, but individually, and some players ended up calculating a tournament with a different value than another player.

These are the players from the Top 50 (the difference shown is official vs. the corrected values). You will see the paradoxes for yourselves. Many players have incorrect tournament counts in the official rankings. Some players count a tournament that others don't. Some players score for a tournament more than other players for the same tournament. Most importantly, this shows the rankings for uniformly calculated values, and the players with large differences are in that category.

Some changes in the calendar too. Had to put AO at 25K (which is correct), but also the first and last WCT event (Miami, Gothenberg) at 25K to fit it Laver and Smith close to their exact values (although Smith's tournament count is incorrect, or, judging by the points, is in no database we can access - but, if it is a 25K, you can add 6p to his total of 157.5 and get his official score of 163.5).



This is the ranking system I calculated:

« Last Edit: August 20, 2013, 07:25:47 AM by Slasher1985 »

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #132 on: August 20, 2013, 09:07:23 AM »
The more I think about this, the more I realize that it's actually normal to see so many errors done by ATP.

Think 1973. So, we come up with this ranking system. OK, when should we start using it? How about before US Open, so we can use it for seeding. Seems right. So, we're in August 1973 and suddenly decide to rank players according to their performance in the last 52 weeks. To do that, we take each player and add them points according to tournament types, but we do it all at once and individually for each player. Do we use one person to do the calculations? Of course not, it's A LOT of work, there's no actual computer involved. So, multiple people calculate, some people rank a tournament as 50K for a player, others rank it as 25K for another player, some people count a specific tournament, some people do not. It's so much hard work, that most of the rankings are well calculated individually for the tournament types each "calculator" used, but "calculators" ranked some tournaments differently and counted some extra tournaments or failed to count some other tournaments. With the exception of Wimbledon, of course, which is general knowledge. And why should they verify it, let's not forget the purpose of these rankings. They were meant to provide only seeding information, not determine World Number 1. They were just for information. As months went by, ATP realized their importance, and recreated the system into a better one for 1974, also adding bonus points.

So, I say, that this HUGE error ratio is quite logical given the circumstances.


Offline JonG

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #134 on: August 20, 2013, 02:49:40 PM »
I don't think that the ATP decided to come up with a ranking list in August 1973.

Legend has it that the ATP was formed at the 1972 US Open which started on August 27.

You can't really "back date" a points system, so my guess is that players started accruing points at the US Open. It would then take a year for players to build up a year's worth of points - meaning the first list would come out just before the 1973 US Open.

The first ATP list was NOT used at the 1973 US Open. The seedings were quite different from the ATP list. Smith and Nastase were named as joint no. 1 seed!

I do think that  the ATP computer rankings would really have been compiled by a computer. Computers were used to make football and cricket fixture lists from about 1970. I can clearly remember in the early 70s there were a huge amount of "computer all-time sporting contests" - pitching boxers, cricketers and whatever from various eras against each other using a computer. I haven't a clue how sophisticated the inputs and outputs were - probably not anywhere near as clever as we all believed at the time. But it shows computers were used in sport in the early 70s - and I would not be at all surprised if the ATP had one. 

Offline JonG

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #135 on: August 20, 2013, 02:51:44 PM »
If you're wondering, this is the solution I got:

TC_W = -766356

Kodes would be relieved that they did not count Wimbledon then. It would have cost him 766,356 points! :)

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #136 on: August 21, 2013, 01:05:57 AM »
I do think that  the ATP computer rankings would really have been compiled by a computer. Computers were used to make football and cricket fixture lists from about 1970. I can clearly remember in the early 70s there were a huge amount of "computer all-time sporting contests" - pitching boxers, cricketers and whatever from various eras against each other using a computer. I haven't a clue how sophisticated the inputs and outputs were - probably not anywhere near as clever as we all believed at the time. But it shows computers were used in sport in the early 70s - and I would not be at all surprised if the ATP had one.

Alright, but even so, they were heavily dependent on operator input, and operators may have used different tournament type values for the same tournament across different players. Although, the tip about when they started calculations is convincing me that maybe there is another parameter I'm missing. Maybe bonus points? But they could only have used those starting with US Open 1973.

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #137 on: August 21, 2013, 01:44:14 AM »
From the start, Connors goes off the charts with a bonus system, something like 150+. He beat Okker 3 times, Smith, Ashe, Orantes, and a few 9-16 ranked players. The same system applied to the other Top 10 players is filled with desire. None match the exact points they had, and outside it, Pilic is even better ranked than with this system. I say again that it seems to me that this system is the best approximation I can recreate for now. Only a slight variation to a variable will increase accuracy to some players but damage many more.

Offline Slasher1985

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #138 on: August 21, 2013, 02:07:14 AM »
JonG, if possible, can you get me the prize money for GP, WCT and other events from 1974 and 1975? Is it all in the World of Tennis magazines? Thanks a lot in advance. :)

Offline JonG

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Re: Full Open Era Rankings (RESEARCH PHASE)
« Reply #139 on: August 21, 2013, 06:35:29 PM »
JonG, if possible, can you get me the prize money for GP, WCT and other events from 1974 and 1975? Is it all in the World of Tennis magazines? Thanks a lot in advance. :)

These  were the GP grades in 1974

Roland Garros   TC
Wimbledon   TC
US Open   TC
Rome   AA
Nottingham   AA
Washington   AA
Indianapolis   AA
Louisville   AA
Montreal / Toronto   AA
Boston   AA
Los Angeles   AA
San Francisco   AA
Tehran   AA
Stockholm   AA
Johannesburg   AA
Madrid   A
Tokyo   A
Barcelona   A
Sydney Indoor   A
London   A
Buenos Aires   A
Australian Open   B
Hamburg   B
Bournemouth   B
Bastad   B
Gstaad   B
Kitzbuehel   B
Chicago   B
Bretton Woods   B
Columbus   B
South Orange   B
Cedar Grove   B
Maui   B
Paris Indoor   B
Jakarta   B
Hong Kong   B
Bombay   B
Manila   B
Florence   C
Munich   C
Dublin   C
Hilversum   C
Cincinnati   C
Merion   C
Adelaide   C
Christchurch   C
Vienna   C
Oslo   C

The WOT book says AA is $100k+ , A $75k+ and B $50k + but doessn't mention C - so these could be the 75 levels.

Philadelphia was $100k, other WCT were $50k.

The two ATP events at Tucson and Las Vegas were $150k each.

No mention in the book at all of US Indoor or Spring Mediterranean.