24-07-2002 04:21									#241
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Well I never..... There is one floor in this entire debate.... The rankings are no longer being updated..... So the argument is kind of academic... It is over three months since the results were last calculated...

Keygen the Formula for the new system is at the start of every new rating thread...Calling it new is a misrepresentaion however, it started with Gameleague, apart from the stake was reduced from 20% of your points to 10%, to take into account that in PBEM there are more results per game.

I actually do not think it matters all that much which system is used... I only started using the Gameleague system because I was too thick to understand the other system . BUT I do prefer it because it is easier, and seems to represent ability better...

I think the biggest issue is the players that only want to be rated in games they will score positive at... this kind of defeats the object of having a ratings system... I appreciate the Blackice comments about bad land... But any game creator with 30 minutes of effort can equalise the land, and make the game more enjoyable, fairer, and longer lasting... when games can run for years the 30 minutes should be a worthy investment... SO maybe rules for game creation should be applied too.

But to reiterate, this is just all gibberish unless someone takes the mantle of updating the rankings onboard , and I would strongly suggest you forget about holding a vote as to what system to use, and instead let someone take over the ratings, and use whatever system they see fit.

Oh and by the way, hello everyone!

	24-07-2002 08:37									#242
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Hello Gary! You're right about current updates... But why update unless it is backed by a concensus of voters? You, Blackice, and I have all updated the ratings at one time or another. Without a good solid vote to stand on, we were just sort of spinning our wheels. While many appreciated our work, many were not happy with the system for various reasons. At least with a good 51% or more vote, whoever takes over doing the ratings will know that the majority is in support of their work.

Personally, I will be happy to support whatever the vote turns out to be. Though I think that the "Chess-like Points Differential" system is better than the "GameLeague Wagering Points" system, I will fully support whichever one is voted in.

And Keygen... thanks for creating the link to the documentation for the old "points differential" system we used to use!

	24-07-2002 09:54									#243
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Keygen the formula is in the first page of this thread.
The rest has been stated if you now have the formulas add it up.
Add new rules or keep the system that needs none.
I also think you see people just want to play add a rule of manditory ranking and lose people.
It is not gavrushka/blackice system gavrushka did the PBEM and I did the online take note they are TWO different systems. It is the new system keep it genetic not personal as I have been requested to do Thanks.

Rankings were being updated until I decided to end it rather than being bumped after volunteering.

This is not chess, games here are rated at the finish more important they are rated per 9 turns chess is not.

That obviously changes the facts and how the system works. The based on GL Not GL system is tried and true for CTP.

It may work in chess too but who cares this is CTP and the new system not only works. It is more fair more to the reality of PBEM CTP. It also does not need more negative rules to make it adapt to a game it was designed for.

So show some people some examples Quinn show them side by side the difference. Show us all why your system for chess is better. Use some examples of current random players. It is your system explain to us all by side by side examples of why your system is better.

That is only fair for an informed vote. Besides you solver and me are probably the only ones who could figure out your system. The new is quite easy and self explanitory ( user friendly ). On that note I think people should fully understand what your system is explain it to us in full detail with examples please.

	24-07-2002 11:04									#244
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I got a neuatral suggestion... You are discussing two rating systems which all people see as having Merits and DeMerits... Maybe it is time to devise a NEW system for Apolyton, if everyone (that is interested) posts their ideas of what they would like from a system, then PERHAPS a new, universally accepted Formula can be created.. We do have some Maths capable people here..

I guess in outline a rating system would:



Reward Players more for beating Players with a Higher Score.

Give Higher Rewards the More Players in the Game.

Give diminishing Returns for consecutive Victories.

Reward the Player more for Volume of Games they are in.

Be sufficiently Volatile that a WIN is likely to move them up the Rankings, without a massive change in their score.

Not cripple a player for having one or two bad games.

Have a very marginal impact for gaming against opponents with far lesser scores (but never negative).

Be Transparant and easy to calculate by all.



Can't be that difficult can it??

	24-07-2002 11:24									#245
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You just described the new system

	24-07-2002 16:52									#246
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The formula can clearly be built, except for this:

quote: Be Transparant and easy to calculate by all.

But since I already got a program, I'll just have to change the calculation bits should a new formula be presented. That is, of course, what we want. I'm just eager to do an update now, and am only waiting for this formula the, eh?

	24-07-2002 17:34									#247
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Reward the Player more for Volume of Games they are in.
WHY? WHY? WHY?

No inflation points, please!

	24-07-2002 19:39									#248
	Support Apolyton or Terrorists Win

quote: Originally posted by blackice So show some people some examples Quinn show them side by side the difference. Show us all why your system for chess is better. Use some examples of current random players. It is your system explain to us all by side by side examples of why your system is better. That is only fair for an informed vote. Besides you solver and me are probably the only ones who could figure out your system. The new is quite easy and self explanitory ( user friendly ). On that note I think people should fully understand what your system is explain it to us in full detail with examples please.

Okay.

Here is the example:

Albert rated 20.
Bob rated 15.
Charlie rated 15.
Dallas rated 15.

GameLeague Based Ratings Calculation:

Power Graph order at turn 9 = Albert, Bob, Charlie, Dallas.

Wagers:
Albert = 10% of 20 = 2 points
Bob = 10% of 15 = 1.5 points
Charlie = 10% of 15 = 1.5 points
Dallas = 10% of 15 = 1.5 points

Total Wagered = 6.5 points.
Percent Distribution = 46%, 29%, 17%, 8%
Wagered Points Distribution = 3.0, 1.9, 1.1, 0.5

After Turn 9 ratings:
Albert = 18 + 3.0 = 21.0 (net change + 1.0 rating points)
Bob = 13.5 + 1.9 = 15.4
Charlie = 13.5 + 1.1 = 14.6
Dallas = 13.5 + 0.5 = 14.0

Albert is playing in four other games exactly similar to the one above, where he plays against 3 much weaker players than himself. So that now, after the first 9 turns of all of his games,

Albert has a new rating = 25 (GameLeague Based)

(20 + 1.0 + 1.0 + 1.0 + 1.0 + 1.0 = 25)

--------------------------------------------------------
Differential Based Ratings Calculation:

Power Graph order at turn 9 = Albert, Bob, Charlie, Dallas.

Albert (20) defeats Bob (15) -- Ratings Points Differential = 20 - 15 = 5

Probability of Lower Player Winning = 1/[2 + Differential**2] (Note: **2 means squared)

Probability = 1/[2 + (5)**2] = 1/27 = 0.04

Because Albert is higher rated than Bob,

Change = 0.04 / 2 = 0.02 points.

[Note: If Bob had defeated Albert then the change would have been (1- 0.04) / 2 = 0.48]

So that Albert gains 0.02 points and Bob loses 0.02 points.

The calculations are the same for Albert defeating Charlie and Dallas. So Albert gains 0.02 points for defeating Charlie and 0.02 points for defeating Dallas.

The total calculations done are: Albert defeats (d.) Bob, Abert d. Charlie, Albert d. Dallas, Bob d. Charlie, Bob d. Dallas, Charlie d. Dallas. We are highlighting on Albert so I will just focus on Albert's rating change.

*** Edit *** (I think this is what Blackice meant about the "loss ratio"):

After Turn 9 ratings:

Albert = 20 + .06 = 20.06
Bob = 15 - .02 + .25 + .25 = 15.48
Charlie = 15 - .02 - .25 + .25 = 14.98
Dallas = 15 -.02 - .25 - .25 = 14.48
*** End Edit ***

In total, Albert gains 0.06 ratings points for defeating the much weaker players in the turn 9 power graph for a new rating of 20.06.

Albert is playing in four other games exactly similar to the one above, where he plays against 3 much weaker players than himself. So that now, after the first 9 turns of all of his games,

Albert has a new rating = 20.30 (Differential Based)

(20 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 20.30)

Edit: Without doing the exact calculations for the other players, I can estimate their new ratings assuming that order of the 5 games
-----------------------------

Conclusion:

In the first example with GameLeague Based calculations, Albert has managed to go from a rating of 20 to a rating of 25 by playing in 5 games against players with ratings no higher than 15. This is unfair in my opinion.

In the second example with Differential Based calculations, Albert has gone from a rating of 20 to a rating of 20.30 by playing the mass number of weaker players. This is fair in my opinion.

	24-07-2002 21:02									#249
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Aaargh! Doesn't everyone see that everyone has an opinion on which system is best, therefore neither system can work! a new one is required based on the consensus of what everyone (who is interested ) thinks... If you vote for one system or the other, people who lose the vote will see it as a defeat and may refuse to be rated.. So why not get MAd Maths Man J Bytheway to devise a new system, which everyone has input into... There are no absolutes here, just subjectivity, and differences are irreconcilable - so just create a new system.. It really is the only way all people will be at least moderately happy.

Anyone see that awful news bulletin yesterday about the cat that was force fed Petrol by some kids and then thrown into a Barrel?? It ran round and round the barrel like a thing possessed until it just suddenly stopped...

Was it dead I here you all shout?

Nope.... it had just ran out of petrol.....

	24-07-2002 21:21									#250
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He won them he should be rewarded quinn. It is fair.
You will note even the losers in the first example gain points for playing a stronger opponent. This in effect off sets the win of Albert doesn't it? Of course it does...

Albert's new scores would also go up each game before the calculations. So would the pot then. While Albert gained more per turn so would his opponents. The losers playing stronger players are in a win win scanerio. They too would go up again off setting Alberts gains. Take note too it is doubtfull three players will ever have the same score.

Albert has a new rating = from 20 to 25
Bob 1.5 x 5= 7.5 from 15 to 22.5
Charlie 1.1 x 5= 5.5 from 15 to 20.5
Dallas .05 x 5= 2.5 from 15 to 17.5

It is win win scenario the rankings are ever moving this has been proven with the new system.

Quinn could you show what the lossers lost in the second example please. Then show Albert losing to weaker players.

After all that has been the complaint not the points gained in either system for winning. Now does everyone see why Klair may have never moved from first place over all? At least in our life time no one made enough points per turn to do it. And she only played ONE GAME!

Here is Albert losing to weaker players in the new system. Notice the points distribution is the same. The higher ranked player always helps the lower ranked in a game by adding more to the pot. This is why this system is fair and promotes higher ranked playing lower ranked.

After Turn 9 ratings Albert losing:

Dallas = 13.5 + 3.0 = 16.5 (net change + 1.5 rating points)
Bob = 13.5 + 1.9 = 15.4 (net change + .4 rating points)
Charlie = 13.5 + 1.1 = 14.6 (net change - .4 rating points)
Albert = 18 + .5 = 18.5 (net change - 1.5 rating points)

Note Albert lost to lower ranked players and pays the price. Because Albert put so much in the pot most all the weaker players gain points. Win win scenerio.

Except for the losers Charlie a mear .4 loss for being beaten by same ranked players. Albert as it should be he lost to weaker players. He would more than likely go down in the rankings for this one loss but gain on his next five wins. Also note this system tells people to play more games to gain more points. This is the way it should be it also does this without the need for a play three games minmum rule. Less rules is good right? I say so. This way you do not force people to play more games if they do not have he time or the inclination to do so.

This system moves players if Albert won his next 4 games the rankings would be very close Albert would still be ahead in the rankings but so would the other players. Win Win scenerio.

Now lets see an example of the old system and the losses each player takes...Sorry for the request but that is the whole point here...

As said the ratio as with the blackice example is 2 to 1 or better. You win two and lose one you drop like a lead balloon...As you can see in the new system that is simply not the case. You lose big time for losing to lower ranked players. You would then gain on the rest of your games for winning them.

It is not so with the old system your loss is so great even if you win the next two games because they are weaker players you would drop 4 ranking spots or more for winning! It did not promote playing weaker players the new system does...
The reality of the situation is you will more than likely have weaker players playing in a game in PBEM.

That is the way it should be you should be awarded for winning. Albert playing weaker players will gain points but the points he gains are limited because he plays weaker players. He still wins though! just not as much...

gav

This is a new system and it works great! the whole Idea here is to compare them side by side and let people vote with an informed vote.

Last edited by blackice on 24-07-2002 at 21:35

	24-07-2002 22:37									#251
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I cannot convince you Ice, and I never will. All the logic in the world will not matter to you. You know and love GameLeague's system, and that is that. The above explanation was not really meant for you, Blackice, but for the others who may want to vote on the issue.

I would agree with Gavrushka, though, about another system if one is presented. Yes, J Bytheway is the most qualified of all of us. But I do not know if he is willing to do it. Are you able to find time to do this Mad Maths Man JBTW?

	25-07-2002 01:04									#252
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why won't you post the loss ratio quinn?

quote: The above explanation was not really meant for you, Blackice, but for the others who may want to vote on the issue.

It is only fair people get a complete view of the two systems not half. Post the whole situation...I find it highly suspect when you do not post what people complained the most about the unfair win loss ratio...Complete the example you did it for the new system why did you not for the old one? At best is misleading the people here... nothing personal it was probably an oversight...

It is not gameleague's system it is a variation of it adapted specifically to pbem

I like it because it is better others do too obviously. It rewards winning. It is fair for all players including losers of games.

What if Paulino1 or Yoda joined here. They would be ranked as lower players. We all know they are not that at all. So why should a higher ranked player get wiped out in the rankings by a couple of turn 9 rounds playing better lower ranked players? The old system did just that. The new ones accounts for newer good players and does not heavy handedly wipe out higher ranked ones that lose to better lower ranked players.

The idea here quinn is to have a honest display of both systems to convince others here that your system or the new one is better. Not to convince me that will never happen. The key differences between these systems is the loss factor of the old system. I want the other players to see that, they need to see that in order to get the complete picture.

I really see no need to have a Third system as stated. This system is fair and new.

Lets just post the actual facts and let people decide so how about it Quinn post the loss ratio in these examples so people can see the whole picture and decide.

Lets get on with it shall we...

	25-07-2002 01:27									#253
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Blackice, half of post about ladder system is yours and you'll only one promoting Gavrushka/Blackice system. You make your point.
JBTW can you came out with third solution?

	25-07-2002 01:45									#254
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Kralj and? What are you telling me to shut up? That is not going to happen sorry...

I am trying to inform the people here so they can make an informed descision. What have you posted for details so people can make an informed decision?

Last time It is not my system

I find it odd you have read everything but missed that again?

JBTW can you came out with third solution?

Why do you need a third system you have not seen the comparision of these two yet?

It is getting clear a few of you do not want people to see the comparison at all let alone vote on it. Humm wonder why?

On top of that we could see them side by side and start a new thread with the complete story of the two rankings and then offer the choices.

New
Old
Third system to be designed yet

Give the people the chance to see the true pictures then the chance to vote. There are a lot more people here than us five...let them have a chance to vote on all three options. Some people seem to want to just over rule the rest with a third option. Get the true picture out and give the others and opportunity to see them and vote...

Too much politics just get on the the full picture that was omitted. Well whats wrong why not post it Quinn?
You did not offer a complete picture of your system you did of the new one.

Be fair post it lets go...

Last edited by blackice on 25-07-2002 at 03:35

	25-07-2002 01:58									#255
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I've been thinking, believe me, but I can concieve of no system which will fulfill many of the requirements stated.

Personally I think the fact that in the wagering system winners can lose points and losers gain them is a much more serious flaw than the problem with the old system (which I still don't understand, frankly...).

I'm going to look up the rules on the differential system and get back to you - I think for a start the power used might be reduced to offset the problem. The calculations as described above make no sense since if the two players had the same score the probability of one winning would be 1/(2+0)^2 = 1/4, it should be 1/2...

	25-07-2002 01:58									#256
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*deleted*

	25-07-2002 02:35									#257
	Remove this text

The example shown is missleading no one will have the same score or rarely. The small amount of points given to the second and rarely third place person is to reflect the fact they did beat at least one opponent in the game. This does not happen on every ranking it depends on the rank of the players in the game and the points wagered. This is to reflect the fact that the score is calculated every 9th turn. It should not be that "the winner only" scores points every ninth turn. That would simply be unfair and would not promote players playing or beiing ranked. I hope that helps.

It is also incentive to play and be ranked. By doing this their was no need to impose upon people the rule of having to be ranked.

Quinn post the win loss so people can get on with this why the delay?

	25-07-2002 02:55									#258
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Well, after some research I find that the actual formula is 1/(2+d^2) where d is the difference and ^ denotes exponentation - which makes more sense.

*Here begins the heavy maths *

But it's still a very strange formula - I can't imagine what probabalistic assumtions would give rise to it. Basically if A and B have scores a and b and d=a-b this formula claims that the probability of B beating A is:

1/(2+d^2) for d>=0
and 1-1/(2+d^2) for d<0

this has zero gradient at d=0 which seems exceptionally peculiar. I would have expected a formula more along the lines of:

(1+tanh(d))/2

or:

(pi/2 + atan(d))/pi

Since these have maximal gradient at the origin, but again, these are unlikely to be derived from theory.

Probably you'd actually end up with some formula involving the phi function (phi(d) being the integral from -infinity to d of 1/(sqr(2pi))*e^((d^2)/2), which unfortunately cannot be expressed in closed form) but that's of little use to us.

* Here ends the heavy maths *

But, after some thought I do understand and approve of the application of the probabilities to the manipulation of the scores as described (scores move by half the probability of the observed outcome) since this should award/penalise most for play where the low-ranked beats the high-ranked.

However, the introduction of probabilities is an unnecessary obfuscation of the relevant process, except insofar as it explains the otherwise arbitrary introduction of the '1-' to the defenition of the function used. It might be more sensible, perhaps, to manipulate the function and use it directly to deduce the change made to the scores, rather than including an intermediate step. In this case a function such as that used has some benefits which perhaps explain its use rather than any probability theory.

I can see the Klair-syndrome hidden in this system - it arises from the fact that results on consucutive *9 turns are not independant. Without further study I can't place a cure, but my instict says that it might be a good idea to use a reduced power (change 2 to 1.5 or 1.6), as I suggested above, so that the function decays less quickly - but that might in fact exacerbate the problem. I believe Gav recommended diminishing returns (i.e. you get less for leading if you've been leading for a long time), and that might also help if applied judiciously but my gut warns me off, if only because of the increased administrative burden. Perhaps if a suitable program were written to store the information then it would be plausible.

All in all it's a knotty problem - I'll give it thought as I lie in bed this evening and get back to you tomorrow with any insights I have.

Last edited by J Bytheway on 25-07-2002 at 17:59

	25-07-2002 03:21									#259
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1. Kralj Matjaz 23.2532 10% wagered=2.3-3.9= 1.6 new ranking 24.8532
2. Faded Glory 22.2950 10% wagered=2.2-2.619= 0.419 new ranking 22.714
3. Darth Viper 10.6760 10% wagered=1.0-1.649= 0.649 new ranking 11.325
4. Nuke Boy 15.0358 10% wagered=1.5-0.97= -0.53 new ranking 14.5058
5. TheBirdMan 27.8815 10% wagered=2.7-0.485= -2.6515 new ranking 25.23

9.7 points wagered total divided by the forumula below:

5..1ST..41%..2nd..27%..3rd..17%..4th..10%..5th..5%

This game is waiting to be ranked so I used it as an example. 1st 2nd and 3rd receive some points be it token points for 2nd and 3rd. 4th and 5th negative points. As you can see award/penalise most for play where the low-ranked beats the high-ranked. Is built into this system also. But unlike the old system the new one may or may not award points to the bottom ranked players. They did not win.

Again here we go making new rules to make a system work maybe. The new system works and awards points for winning. No new rules are needed and you do not have to have a math degree to understand the formula.

John the old system also awards points for second and third and forth if they beat a higher ranked player. I guess that means it is flawed too even more so...Bottom line is I don't get your flawed reasoning since both do it the old system more so...In a five player game with the bottom position being the highest ranked player. Every person above them will get points it guess I am missing the logic here? You dismissed the new system for something the old one does more of?
Maybe you could explain why?

It also awards way more points for doing so and way more negative points for the loser. Look at the blackice example.

The difference is the ease of the new system and the built in no need for rules to create balance and fairness.

Last edited by blackice on 25-07-2002 at 03:50

	25-07-2002 03:55									#260
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quote: Originally posted by blackice But unlike the old system the new one may or may not award points to the bottom ranked players. They did not win.

Eh? The old system would never have awarded points to the bottom player, but the new one might if they were ranked sufficiently lowly.

quote: The new system works and awards points for winning.

Unless the winner is far ahead already in which case they lose points for winning...

quote: John the old system also awards points for second and third and forth if they beat a higher ranked player. I guess that means it is flawed too even more so...

But that's a good thing, isn't it?

quote: It also awards way more points for doing so and way more negative points for the loser. Look at the blackice example.

Is that the one where he wins 2 games, loses 1 and drops in score? That is primarily due to the falloff speed of the formula used (I presume). If that situation continued then an equilibrium would have been reached with Blackice at some lower score, but still higher than all his competitors, just as it should be. The details of the formula will dictate the position of this equilibrium. I don't see the problem.

quote: The difference is the ease of the new system and the built in no need for rules to create balance and fairness.

Ease is nice, but I'd rather have fairness (Naturally, I would say that). I'm fairly sure an appropriate system of a similar sort can be devised without recourse to additional rules like a 3-game minimum.

	25-07-2002 04:26									#261
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quote: Eh? The old system would never have awarded points to the bottom player, but the new one might if they were ranked sufficiently lowly.

Oh so it does not award players for beating a higher ranked player?
Or is it only the first placed player that beats a higher ranked player that gets points? If the higher ranked player is last of five players. fourth place gets no points for beating them? they do in fact get points. J. They are awarded one win over the last place player and then three losses for being in fourth. So in each and every 9th ranked turn someone takes 3 losses and one win for fouth place. They also lose points for beating a higher ranked player. The reality is 1st and 2nd get all the awards for beating the Higher ranked player. In the new system 1,2 maybe three and maybe four will get points for beating the higher ranked player. More fair.

quote: Unless the winner is far ahead already in which case they lose points for winning

Are you refering to LUNG? if so then yes you have top spot you have to play games to keep it. on top of that you have to play at least one higher ranked player to gain points. In Lungs case his remaining game he is way ahead of his opponents so no he will not be rewarded big for beating far lower ranked players.

quote: But that's a good thing, isn't it?

You mean it is flawed if the new system does it but not if the old one does? Makes no sense still...

quote: Is that the one where he wins 2 games, loses 1 and drops in score? That is primarily due to the falloff speed of the formula used (I presume). If that situation continued then an equilibrium would have been reached with Blackice at some lower score, but still higher than all his competitors, just as it should be. The details of the formula will dictate the position of this equilibrium. I don't see the problem.

Really the other players would be going up and he down so what you are saying is they meet and all stay the same? How would blackice stay ahead if he losses points for one loss and two wins? Makes no sense.

quote: Ease is nice, but I'd rather have fairness

The new system is fair the winner gets points as do second and third sometimes. The losers lose points(sometimes depends on the rank of the players)what is not fair about that? makes no sense again.

Quinn where is that complete example? You are not going to post it or what? Do you not think the people should see the two systems side by side in an equal and fair comparision?

This is all talk until we see a clear example of the old system J. could you take the example I just gave and use the old system to show how it works to the other players here? We can see them side by side with the same players as an example. Would that be possible?

	25-07-2002 04:38									#262
	Increase the size of your Attachments

Thanks for the very reasoned response J Bytheway! You are right about the above formula... I will fix it in the above post (i.e. it is the differential alone squared, without the +2). Regarding "probablity", it was a stretch to use that term because it is an imperical number, but I thought it might help to understand what the formula was doing. Also, I had considered using an exponent of 1.5 or 1.6 instead of 2, but thought it would make the formula too messy. But maybe your right. It would level out the curve somewhat.

Blackice, I would be happy to post the "loss ratio" but I don't know exactly what you mean by that. For example? You mean the number of ratings points that the losers lose? Or the ratio of winner gain points to loser loss points? That ratio is always 1. That is, if Albert gains .02 then Bob loses .02. The ratio = .02/.02 = 1. This is always true. I don't think that is what you meant though when you said "loss ratio". Edit: Ice, I added what I think you meant by "loss ratio". Take a look at my previous post where I show the ratings of Bob, Charlie, and Dallas after the first *9 turn.

Obviously, JBTW has much more knowledge about this subject than I. I await his thoughts on this tomorrow.

Last edited by quinns on 25-07-2002 at 04:59

	25-07-2002 05:00									#263
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Thanks Quinn

What I mean is take the birdman game example I gave above:
http://apolyton.net/forums/showthre...0&pagenumber=26
and with the old system do the calculations. That way we have a real example of the two systems rankings side by side. That it easy really then people can see in a real game scenerio how they both would work.

In this example given the losser is the highest ranked player.
This has been the complaint in the past and the real difference between the two systems. The fact that Albert gains so little playing lower ranked players is one very good reason NOT to play lower ranked players.

The new system promotes playing with lower ranked players, primarily because in 9 out of ten games you play lower ranked players here. The loss for playing lower ranked players is even more important to show as that is the big difference between the systems.

Quite frankly most can not do the math required to make you calculations.

If we can do that we can talk apples and apples go to a vote and offer the third solution a new ranking system all together. Should not take you more than a few minutes. Thanks :d:

Last edited by blackice on 25-07-2002 at 05:24

	25-07-2002 07:56									#264
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Ice, it isn't really apples to apples to use the Birdman example you mentioned. At this point, the PBEM ratings are already way out of skew as compared to the old system. In my opinion, there is no possible way that Birdman should be 17 points higher than Darth Viper. I have played both players and know both of their relative playing abilities. At most Darth Viper and Birdman should be within 1 to 3 points of each other.... not 17! See, I would have to use an example BEFORE the GameLeague based system took over in order to compare apples to apples. However, if you really feel it would clarify things for you and everyone else, I can do the calculations if you like. But as I said, I would be using the old system to calculate the already heavily skewed GameLeague based rating numbers. It would not be apples to apples.

	25-07-2002 08:12									#265
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Old
BLACKICE 21.342

New
Blackice 26.301

Thanks it will do an number is a number looking at my old score compare to the new one? 5.041 difference. I do not get the skewing part but lets move on and use the example and compare the difference ok?

This will show a lower ranked person winning over a higher ranked. That is the whole point here.

Darth has lost more games than Birdy has won and played far less.

Thanks Quinn

	25-07-2002 17:53									#266
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quote: Originally posted by blackice quote: Eh? The old system would never have awarded points to the bottom player, but the new one might if they were ranked sufficiently lowly. Oh so it does not award players for beating a higher ranked player? Or is it only the first placed player that beats a higher ranked player that gets points? If the higher ranked player is last of five players. fourth place gets no points for beating them? they do in fact get points. J. They are awarded one win over the last place player and then three losses for being in fourth. So in each and every 9th ranked turn someone takes 3 losses and one win for fouth place. They also lose points for beating a higher ranked player. The reality is 1st and 2nd get all the awards for beating the Higher ranked player. In the new system 1,2 maybe three and maybe four will get points for beating the higher ranked player. More fair.

Sorry, I misunderstood you - I thought you meant the bottom player, not just one near the bottom. It is indeed true that If a few low-ranked players beat a sufficiently highly ranked one then all of them will gain, and the highly ranked player will lose a lot. Surely the highly ranked player should lose a lot in this situation, and since the system is conservative (total rank of all players constant) it is inevitable that the other players will rise. Is your concern that too much of this rise is allocated to the lower amongst those lowly ranked players - I can see that this might be a problem.

quote: quote: Unless the winner is far ahead already in which case they lose points for winning Are you refering to LUNG? if so then yes you have top spot you have to play games to keep it. on top of that you have to play at least one higher ranked player to gain points. In Lungs case his remaining game he is way ahead of his opponents so no he will not be rewarded big for beating far lower ranked players.

This I view as a bad thing - I think you should be rewarded for every victory, no matter how apparently trivial, but that those rewards should be small. If this is what you want then certainly the new system (or something like it) is appropriate.

quote: quote: But that's a good thing, isn't it? You mean it is flawed if the new system does it but not if the old one does? Makes no sense still...

No, the flaw in the new system to which I was referring in this context was that the very last player (5th of 5, or whatever) can gain points if losing to sufficiently highly ranked players, not the awards to those near the bottom for beating a player who is highly ranked and last.

quote: quote: Is that the one where he wins 2 games, loses 1 and drops in score? That is primarily due to the falloff speed of the formula used (I presume). If that situation continued then an equilibrium would have been reached with Blackice at some lower score, but still higher than all his competitors, just as it should be. The details of the formula will dictate the position of this equilibrium. I don't see the problem. Really the other players would be going up and he down so what you are saying is they meet and all stay the same? How would blackice stay ahead if he losses points for one loss and two wins? Makes no sense.

No, I mean that he will drop and they will rise until they are a certain distance apart appropriate to this win/loss ratio. The fact that he is losing points for 2 wins/1 loss is essentially because - according to the system - someone with a 2/3 chance of victory should not be so far ahead of his opponents as he is. As his score drops the aqmount by which it drops will slow.

quote: quote: Ease is nice, but I'd rather have fairness The new system is fair the winner gets points as do second and third sometimes. The losers lose points(sometimes depends on the rank of the players)what is not fair about that? makes no sense again.

If you don't mind situations like that in which Lung found himself (and the converse for very lowly ranked players) then there is nothing wrong with that. That is the only obvious flaw to me (but that doesn't mean there aren't others). If you can live with that then the ease of use almost certainly outweighs any other problems. I'm certainly not going to volunteer to maintain the rankings and so I don't think my opinion carries very much weight, but it was requested and so I give it.

quote: This is all talk until we see a clear example of the old system J. could you take the example I just gave and use the old system to show how it works to the other players here? We can see them side by side with the same players as an example. Would that be possible?

Yes, but I won't because I don't have a spreadsheet to hand and my graphical calculator is out of batteries . This system does need a calculational aid in excess of Windows calculator to do in any sensible time, which I'll be the first to admit.

The best recommendation I can come up with so far is this:

Use a differential system as before, so if A beats B and d=a-b then increase a by f(d) and decrease b by f(d) where f is the function:


f(d) = { (1/(2+d))/n if d>=0
.......{ (1-1/(2-d))/n if d<0


where n could be 2 for simplicity, but if you wish to avoid Klair syndrome then it might be better to use n equal to the number of times A has beaten B in this game so far (including this one) - but that does of course require storing additional data and I don't think it would be worth it.

I reduced the power all the way to 1, rather than stopping at 1.5 since this avoids the 'messiness' quinns mentions, and simplifies things further.

Though it's purely gut instinct, I think that you should indeed calculate all changes before applying any of them as someone (blackice?) recommended a couple of pages ago - but it probably won't make that much difference so if it would be simpler not to then I wouldn't worry.

In any case, I believe that this is a fascinating subject (ranking theory?) and I think I'll do some additional research into it, though probably not in time to be of any use to you.

I've noticed a mistake in the above post - I confused the probability of A beating B with that of B beating A - I'll fix that.

	25-07-2002 19:20									#267
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2..1ST..67%..2nd..33%
3..1ST..54%..2nd..31%..3rd..15%
4..1ST..46%..2nd..29%..3rd..17%..4th..8%
5..1ST..41%..2nd..27%..3rd..17%..4th..10%..5th..5%
6..1ST..36%..2nd..25%..3rd..17%..4th..11%..5th..7%..6th..4%
7..1ST..33%..2nd..23%..3rd..16%..4th..12%..5th..8%..6th..5%..7th..3%
8..1ST..30%..2nd..22%..3rd..16%..4th..12%..5th..8%..6th..6%..7th..4%..8th..2%

quote: No, the flaw in the new system to which I was referring in this context was that the very last player (5th of 5, or whatever) can gain points if losing to sufficiently highly ranked players, not the awards to those near the bottom for beating a player who is highly ranked and last.

As you can see the odds of that happening beyond a two player game are extremely rare. you put 10% of your points into the pot and gain 8% or less. We have not allowed a two player game to be ranked as yet nor should we. The two and three player points are to reflect the fact that a 5 or 6 player game is down to 3 or 2 players. People should be awarded point for sticking out a game and especially for beating out the other players. Mind you like the old system if the last two people where one is high ranked and the other way lower points will be small.
IMHO if a 5 player game has only 2 or 3 players that want to be ranked. The game should still be ranked out as a 5 or 6 player game. Until there are 3 or 2 players left.

quote: Is your concern that too much of this rise is allocated to the lower amongst those lowly ranked players - I can see that this might be a problem.

Mine and a pile of others too. this was the biggest problem with the old system. We are just waiting for quinn to post this senerio so we can move on.

quote: I think you should be rewarded for every victory, no matter how apparently trivial, but that those rewards should be small.

Lung senerio is the fact he has one game and the opponent is lower ranked. If you have first place you have to work to keep it. Lung will also win points when he wins this game. no system should allow a 1st ranked player to play but one game against a weaker opponent and remain in the top spot while others have several and against better opponents.
The Klair factor will not happen in this new system.

quote: As his score drops the aqmount by which it drops will slow.

Correct be if I am wrong but that depends on his opponents winning. if the opponents are losing games at a faster rate this player will continue to drop in the rankings by large amounts. This also would depend on how many games the player is playing. If only one game it could put them down huge. It also depends on the other games they are in. If they are winning other games they are gaining less than they are losing. Back to the 2 wins mean less than one loss.

quote: I don't think my opinion carries very much weight, but it was requested and so I give it.

Everyone's opinion should count here I hope! Thanks for your input we need more people to speak up.

quote: This system does need a calculational aid in excess of Windows calculator to do in any sensible time, which I'll be the first to admit.

The average person does not have the calculator or the knowlegde to make these formulas work. That is a nessessity in order to maximize ones wins with the old system. That was the other problem because of the huge wins vs loss difference. With the old system you would want to play a game with less or no players way down the rankings to maximize your win vs loss on the ranking board.

The new system does the same thing but with less of a hit both ways, winning or losing. This is more friendly to PBEM as the chances of playing lower ranked players are great. The fact less damage is done promotes games with lower ranked players. This is needed without the need for rules. This also eases the "bad land" scenario that is a huge factor. You are playing lessor ranked opponents you have tundra they have rivers and mountains. Like gary said we should take the time each and every game to balance the land factors.
Any volunteers?

	25-07-2002 19:22									#268
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Alright Blackice, here is the old way of calculating your example (rounding to two decimal places). It took me about an hour of manual work, but in the past the program did all of the work once the *9 finish orders were entered. I hope this clarifies things.

Differential Based Calculation Example

*9 Finish Order:

1. Kralj Matjaz 23.30 (K)
2. Faded Glory 22.30 (F)
3. Darth Viper 10.70 (D)
4. Nuke Boy 15.00 (N)
5. BirdMan 27.90 (B)

K d. F: Prob = 1/(2 + 1.0**2) = .33 --- K is higher than F so Change = .33/2 = 0.17.
K d. D: Prob = 1/(2 + 12.6**2) = .01 --- K is higher than D so Change = .01/2 = 0.01.
K d. N: Prob = 1/(2 + 8.3**2) = . 01 --- K is higher than N so Change = .01/2 = 0.01.
K d. B: Prob = 1/(2 + 4.6**2) = .04 --- K is lower than B so Change = (1 - .04)/2 = 0.48.
F d. D: Prob = 1/(2 + 11.6**2) = . 01 --- F is higher than D so Change = .01/2 = 0.01.
F d. N: Prob = 1/(2 + 7.3**2) = . 02 --- F is higher than N so Change = .02/2 = 0.01.
F d. B: Prob = 1/(2 + 5.6**2) = .03 --- F is lower than B so Change = (1 - .03)/2 = 0.49.
D d. N: Prob = 1/(2 + 4.3**2) = . 05 --- D is lower than N so Change = (1 - .05)/2 = 0.48.
D d. B: Prob = 1/(2 + 17.2**2) = . 01 --- D is lower than B so Change = (1 - .01)/2 = 0.49.
N d. B: Prob = 1/(2 + 12.9**2) = . 01 --- N is lower than B so Change = (1 - .01)/2 = 0.48.

Net Change:

Kralj Matjaz: +.17 + .01 + .01 + .48 = +0.67
Faded Glory: -.17 + .01 + .01 + .49 = +0.34
Darth Viper: -.01 - .01 + .48 + .49 = +0.95
Nuke Boy: -.01 - .01 - .48 + .48 = -0.02
Bird Man: -.48 - .49 - .49 - .48 = -1.96

New Ratings (Differential Based):

1. Kralj Matjaz 23.30 (K) +0.67 = 23.97
2. Faded Glory 22.30 (F) +0.34 = 22.64
3. Darth Viper 10.70 (D) + 0.95 = 11.65
4. Nuke Boy 15.00 (N) - 0.02 = 14.98
5. Bird Man 27.90 (B) -1.96 = 25.94

Last edited by quinns on 25-07-2002 at 21:43

	25-07-2002 20:23									#269
	Lose 30 kilos (of popups)

quote: In my opinion, there is no possible way that Birdman should be 17 points higher than Darth Viper. I have played both players and know both of their relative playing abilities.

Just because you have all the Gods, the luck, the terrain and all the babarians (so I feel it ) on your side in our challenge-game .

You might even have ME on your site. It took ages before I noticed what you were doing . Outnumbering me in populationsize/number of cities at a rate of 1:3 or even 1:4. And now it's TOO LATE - soon your PG will be more 4 times mine and I am without doubt going to LOOSE .

	25-07-2002 21:30									#270
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quote: Originally posted by TheBirdMan Just because you have all the Gods, the luck, the terrain and all the babarians (so I feel it ) on your side in our challenge-game . You might even have ME on your site. It took ages before I noticed what you were doing . Outnumbering me in populationsize/number of cities at a rate of 1:3 or even 1:4. And now it's TOO LATE - soon your PG will be more 4 times mine and I am without doubt going to LOOSE .

Sorry Bird, I didn't mean it that way. I think you are a very good player, but Darth is good too. A 17 point relative difference essentially means that you are "Beyond Grand Master of CTP" and Darth is "Way Below Beginner Level". That is not exactly true!

Regarding our current PBEM challenge game, I would be happy to grant you a rematch! You are right about your terrain and bad luck with Barbarians. Let's start afresh. PBEM is the most reasonable way to play CTP IMHO. We play when we can without having to commit many hours at designated times and places. It is the best! Internet play is for those who have GADS of free time. Lucky them.