17-07-2003 19:11									#31
	Increase Your PM Length

quote: Originally posted by Solver Mathe, the thing I was disliked was exactly that, the losing players loses the amount of points the winner gets with a minus sign. That is, |lost| = |won| , isn't correct, IMHO. A player rated 1700 beats a 1610 player and both get the same adjustment to their ratings. It works fine, but in 1v1 games. In a 7 player CtP game, one player has 6 wins essentially, the next one 5 wins and 1 loss, and so on. Won't this formula give the winning player too big of an advantage over the others?

no,
because not the winning player gets all the points of all other players, but rather, as an example, considering 5 players:

player 1 takes 6 points
player 2 takes 3 points
player 3 takes 1 point
player 4 loses 4 points
player 5 loses 6 points

+6
+3
+1
-4
-6
=====
= 0

	17-07-2003 19:13									#32
	Suffering from ads?

the system doesnt count first place in a 7 player game as 6 wins, it just counts it as one first place in a 7 player game.

	17-07-2003 19:21									#33
	Tired of ads?

quote: Originally posted by Mathemagician solver, could you please tell me more about this tennis system ? was it the one gavrushka used that needed a hell of a lot of tables ? did i mention my system, apart from more or less complicated equations , needs only the results, previous scores and number of players as input and directly puts it into the formula ?

No, no, Gavrushka was running the system using the 10% formulas, and yes, those needed also a referrence table, not only the formulas themselves.

Tennis system does, as well as the ELO one, needs only the results and players' ratings, same as you.

Now hmm, where is the tennis system formula, gee, let me look. Here it as, as agreed to establish in November 2000.

quote: CtP PBEM Ratings Formulae, Oct 2000 The ratings would change using the formula: Probability of Lower Rated Player Defeating Higher Rated Player = Prob = 1 /(2 + (player1 - player2)^2). If the higher rated player defeats the lower rated player, then the Change in Rating = Prob./2 If the lower rated player defeats the higher rated player, then the Change in Rating = (1 - Prob.)/2.

Apparently you are rather good with maths, so that should not be hard to understand, but for anyone who isn't a math wizard , here's an example.

quote: Before Game After Game Player Rating Finish Order Joseph 17.000 2 Michael 20.000 1 Samuel 22.000 3 The above formula is applied each time a player is defeated or resigns, using the CURRENT ratings. 1st Pass ----- Samuel was ejected first, so the first pass calculation goes as follows: Joseph Defeated Samuel: Prob. = 1/(2 +(22 - 17)^2) = 0.037 Change = (1 - 0.037)/2 = 0.482 Joseph's new rating is 17.000 + 0.482 = 17.482 Samuel's new rating is 22.000 - 0.482 = 21.518 Michael Defeated Samuel: Prob. = 1/(2 + (21.518 - 20.000)^2) = 0.232 Change = (1 - 0.232)/2 = 0.384 Michael's new rating is 20.000 + 0.384 = 20.384 Samuel's new rating is 21.518 - 0.384 = 21.134 2nd Pass --- Michael Defeated Josesph: Prob. = 1/(2 +(20.384 - 17.482)^2) = 0.114 Change = (0.114)/2 = 0.057 Michael's new rating is 20.384 + 0.057 = 20.441 Joseph's new rating is 17.482 - 0.057 = 17.425 ---- End of Calculation After Game Player Ratings Joseph 17.425 Michael 20.441 Samuel 21.134

	17-07-2003 19:24									#34
	Enter the AD-FREE zone

quote: the system doesnt count first place in a 7 player game as 6 wins, it just counts it as one first place in a 7 player game.

That's not good, IMO. Both the previous systems we have had were based on the opposite - counting that situation as 6 wins. I think your system would be too much of a change, while not working much better than tennis or 10% did - for now, I'd still rather go with either of these two, minor changes applied.

Now, could we maybe get some feedback from other people who were around in time of the system founding? Mathe, I wish you'd know how non-enthusiastic people were, and what a success it was later .

	17-07-2003 19:28									#35
	Support Apolyton buy from Amazon

you're funny, solver.
that system, too, doesnt take away or give any points. the point total also remains the same.

besides, in your example, i think counting josephs win over samuel first or not first makes a difference. i believe it would be best to use the original ratings for all point adjustments, and only then adjust the score.

btw, the ELO system i was building my proposal on is just a different approach to estimate the probability of one player defeating the other.

	17-07-2003 19:33									#36
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

quote: Originally posted by Solver quote: the system doesnt count first place in a 7 player game as 6 wins, it just counts it as one first place in a 7 player game. That's not good, IMO. Both the previous systems we have had were based on the opposite - counting that situation as 6 wins. I think your system would be too much of a change, while not working much better than tennis or 10% did - for now, I'd still rather go with either of these two, minor changes applied.

what do you mean by "too much of a change" ?

too much change in score ?
that definitely depends on the values of K, r(i) and s(i) and isnt fix yet.

for people to get used to ?
well, most people wouldnt need to do the math anyway.

---

now, can you tell me a little more about gav's 10% system please.

	17-07-2003 19:34									#37
	Increase the size of your Attachments

quote: Originally posted by Mathemagician besides, in your example, i think counting josephs win over samuel first or not first makes a difference. i believe it would be best to use the original ratings for all point adjustments, and only then adjust the score.

True!

I like Math's proposal, it is more simple. I've also seen it used on other ladders, so it seems to have some street cred.

	17-07-2003 19:39									#38
	Support Apolyton, buy Civilization 2

quote: Originally posted by ricketyclik I like Math's proposal, it is more simple. I've also seen it used on other ladders, so it seems to have some street cred.

where have you seen MY system being used ?
plagiarism ! plagiarism !

	17-07-2003 19:41									#39
	Support Apolyton, buy Galactic Civilizations

i'd love to continue this thrilling discussion, but i think i will go to the fitness center soon.
you never know who you run into when applying for a new job or practicum.

	17-07-2003 19:45									#40
	Support Apolyton, buy Call to Power 2

I know point totals remain the same... but the actual numbers are better.

quote: besides, in your example, i think counting josephs win over samuel first or not first makes a difference.

Correct. That's how it's supposed to be. In a 5 player game, you'd calculate ratings adjustements in order: 1 beat 5, 2 beat 5, 3 beat 5, 4 beat 5, 1 beat 4, 2 beat 4, and so on. That's how it's supposed to work .

quote: i believe it would be best to use the original ratings for all point adjustments, and only then adjust the score.

An arguable point. Look above. Say, Michael gets +0.441 to his previous rating.

Now, let's use ratings before the game for all calculations in between as you say.

Pass 1.

Joseph beat Samuel

prob = 1/(2+(22-17)&2)=0.037
change = (1-0.037)/2 = 0.482

Ratings stay the same, but changes taken in account.

Michael beat Samuel.

Prob = 1/(2+ (22-20) ^2) = 0.167
Change = (1-0.167)/2 = 0.417

Pass 2.

Michael beat Joseph.

Prob = 1/(2 + (20-17)^2) = 0.091
Change = 0.091 / 2 = 0.045

Now, all the changes. Michael for his two wins, initial rating of 20, gets + 0.417 and + 0.045, so his rating is 20+0.417+0.045 = 20.462 .

Samuel's rating is 22-0.482-0.417=21.101

Joseph's is 17 + 0.482 - 0.045 = 17.437.

As you see, this approach generally makes the players lose/get a bit more points than it would otherwise be, not that it's too great a difference, but it grows if there are more players. I think that this part about the old formulas was definitely not broken, so I can not see any reason to attempt and change it.

	17-07-2003 19:54									#41
	Tired of ads?

quote: what do you mean by "too much of a change" ? too much change in score ? that definitely depends on the values of K, r(i) and s(i) and isnt fix yet. for people to get used to ? well, most people wouldnt need to do the math anyway.

Too much a change for ME to get used for . If we are to resume the system using the tennis or 10% stuff, I would be rather happy to also resume running it myself - would be just about the time.

I'll tell you more about the 10% system soon, need to take a break from this for a moment.

Rickety - I highly doubt that this system is already used anywhere . Besides, most people shouldn't care for how simple it is, essentially, because it is, after all, only one or maybe two persons who have to do all the maths and calculations in the end.

Now, please, where are some more old-timers? I need support .

	17-07-2003 20:11									#42
	Support Apolyton

The following is copied fromt theladder.com: http://www.theladder.com/glicko.asp

quote: Skill Rating Formula A higher number indicates a better rating. Skill rating is calculation is based upon the following formula: NR = OR + C(W-We) NR = The new rating for the player OR = The player's old rating C = Numerical constant (30 for established players with over 50 games played, 50 otherwise) W = If the player won the match, this value is equal to 1, otherwise it is zero. We= The expected result of the game based on the following formula: We = 1/ (10 (-RD/400) + 1 RD is equal to the difference of the players' ratings New players start with a rating of 1500.

Now, this is Math's:

quote: new score = old score + K-factor * {result - 1 / (1 + 10^((own old score - opponents old score)/400)) }

Actually, now that you mention it, they are quite different aren't they

Edit: But I still like the idea of each player being assessed against each other player only once, using the score before the comparison to other players on that turn.

	17-07-2003 20:14									#43
	Get a bigger avatar today!

Quite different, apparently, it's just that this one is also based on the ELO system.

	17-07-2003 21:58									#44
	Lose 30 kilos (of popups)

quote: Originally posted by ricketyclik Actually, now that you mention it, they are quite different aren't they

quote: Originally posted by Solver Quite different, apparently, it's just that this one is also based on the ELO system.

are you kidding ???
its exactly the SAME !

the writer probably just forgot the "to the power of" symbol "^" before that one bracket.
then it is exactly the SAME system...

C would have to be the same for both players though to maintain the characteristic of no points getting created or lost, so the rule you mentioned there would have to understood somehow differently.

	18-07-2003 09:33									#45
	Support Apolyton, buy Civilization 2

quote: Originally posted by Mathemagician are you kidding ??? its exactly the SAME ! the writer probably just forgot the "to the power of" symbol "^" before that one bracket. then it is exactly the SAME system...

I tested the formula when I firstr saw it years ago and it seemed to work without the "^", but I never checked it against actual ladder results though.

	18-07-2003 14:45									#46
	Browse Apolyton AD-FREE

double posted - deleted

	18-07-2003 14:58									#47
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

quote: Originally posted by ricketyclik I tested the formula when I firstr saw it years ago and it seemed to work without the "^", but I never checked it against actual ladder results though.

im sure it was meant with the "^" as the formula loses some important characteristics without the "^", for example, points taken by the winner are not equal to the points lose by the loser anymore. also, for equally scored players BOTH of them would take points and that doesnt seem to make sense to me.

	18-07-2003 15:36									#48
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

quote: Originally posted by Mathemagician quote: Originally posted by Solver In this regard, you better trust me. Excel does not work good enough, and I say that as someone who has been doing that stuff with Excel. i see that as a challenge to prove you wrong.

while i must agree with Solver that his proposed ranking system is probably superior to mine (i tested some and just cant get all desired characteristics under one hat), i must say im pretty sure i proved him wrong on the Excel issue.

ladies and gentlemen,
i present the almost completely automatic Excel sheet for ranking games (attached).
since i was using a german version, i hope the commands are auto-translated when loading the file.

please disregard the precise formulas, as i just admitted they are not as good as desired.

all the work you'll have with this sort of Excel sheet is:

for a newly started game
copy the template from above in table 2 to the end and modify player names and player numbers as well as delete the surplus fields (delete the whole lines, not just the content !).

for a finished game
add the scores from the game to the 'fix score' column in table 1 and delete the game.

for ranking updates
just change the numbers 1 - n in the power graph column of that game in table 2.

try it out !
i'll gladly program a similar excel sheet for any system we come up with to use for the PBEM rankings.

	18-07-2003 21:23									#49
	Increase the size of your Attachments

Mathe - yes, if the power symbol was forgotten, systems are the same. Testing your sheet out now.

And, I say, it's not as good as an automated program would be, although surely feasible. It's good, yet I see ways how a program could work better. For instance, you would have an easier time adding new games, etc. I agree though, that you have done a very good job, but I still remain confident that a program would do it even quicker.

A question... can you explain s(i) to me?

	19-07-2003 05:00									#50
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

CtP PBEM Ratings Formulae, Oct 2000
The ratings would change using the formula: Probability of Lower Rated Player Defeating Higher Rated Player =
Prob = 1 /(2 + (player1 - player2)^2).

If the higher rated player defeats the lower rated player, then the Change in Rating = Prob./2

If the lower rated player defeats the higher rated player, then the Change in Rating = (1 - Prob.)/2.

-----

This is not a tennis formula. It was used to calculate tennis ratings but it had nothing to do with tennis. I created these formulas. Thanks for "credits" Solver!

	19-07-2003 12:38									#51
	Support Apolyton, buy Civilization III: Complete

@Solver
sure, an automated program would always require less manual input.
just programming a real program is much more work (and requires more knowledge) than programming an excel sheet. if you want to do that, its fine with me.

the s(i) resulted from several attempts to appromixate the
1 / (10^(RD/400) + 1) part from the ELO formula for 2 player games, and thus make them fit the multiplayer requirements.
they were meant to approximate the points an average ranked player would gain in the game (since you cannot easily pack the probability for a player 'winning' the game in one value.)

i could get almost all characteristics of the original (exponential) formula in in the non-exponential one, but not all. thats why i gave up.

i had to cut back on either or several of the following:

- point change totals of all players adding up to zero
- winning player never losing points
- all participating players rankings being accounted for
- proportionality of ranking points, finishing position and gained/lost points being reasonable
- probably some more i forgot now...

@quinns
thanks for the formula
but still, i'd prefer combining the exponential ELO formula with Solver's suggestion to count a multi-player game as several 2 player games and use the ELO formula for the seperate rating adjustments instead of yours.

	19-07-2003 17:39									#52
	Inflate your Upload Space

Ouch, sorry Quinns . Didn't mean to underestimate you.

Mathe - what's wrong with the Quinns formulas ?

	19-07-2003 17:45									#53
	Full PM-box? Change here!

quote: Originally posted by Solver Mathe - what's wrong with the Quinns formulas ?

just that i believe the exponential attempt comes closer to the probability estimation than the quadratic attempt.

	19-07-2003 18:03									#54
	Suffering from ads?

Well, that's just your belief . Probability isn't an exact thing, so both methods are rather close to the real amount.

Now... I'm too lazy atm to do it, but some tests should be ran with the same game results, e.g, with both the Quinns-tennis formulas, and the ELO exponential ones... and see how much do the ratings change after a game in these systems.

	19-07-2003 18:16									#55
	Get a bigger avatar today!

quote: Originally posted by Solver Well, that's just your belief . Probability isn't an exact thing, so both methods are rather close to the real amount.

probability is, just not its estimation

	19-07-2003 18:28									#56
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

But seeing how we are humans we can only estimate .

	19-07-2003 18:33									#57
	Support Apolyton, buy Civilization III: Complete

quote: Originally posted by Solver But seeing how we are humans we can only estimate .

who is human ? you ?

sorry for you . didnt know that.

	19-07-2003 19:02									#58
	Support Apolyton, buy Civilization 2

Yeah, that hurts .

	20-07-2003 02:49									#59
	Support Apolyton, buy Civilization 2

quote: Originally posted by Solver But seeing how we are humans we can only estimate .

Estimate the probability of being expotentially human?

Two types:

Version One:


How about the winner gets this:

Each game gets 100 points assigned to it. PERIOD!

whether you have 2,3,4 or more...

First place 50 points

Second Place 35 points

Third place 15 points

Fourth ya just didnt make the cut

Fifth..hmm..you need much more practice!

no having to do a bunch of math..(not the Deutche Expert herein!!)..but arithametic (?? spelling?)

I know..Im just a simple minded Troll but hey..its a simple way to keep all understanding?

Version Two

take 100 points per player in a game
(i.e. 5 players=500 points, 7 players 700 points)

First place player gets 40%

2nd place 25%

3rd place 15%

split the remaining between the rest (20%)

If only 3 people keep the above formula and no one be rewarded the rest.

Just my unsolicited $0.02 worth!!

Ya dont need a spreadsheet, a program or a degree from Apolyton University!

Ill be good now and go back in my hole!!

Peace

Grandpa Troll

	20-07-2003 04:03									#60
	Put an end to popups!

quote: Originally posted by Solver Ouch, sorry Quinns . Didn't mean to underestimate you. Mathe - what's wrong with the Quinns formulas ?

No problem, Solver. I was going to ignore it, but I just couldn't continue to see my simple-minded formulas being called "tennis formulas"!

Troll, with your system you'd still need a big old fat spread sheet, along with about 2 hours a day arguing with people that say your system is "unfair" and "doesn't reflect the true ability of the player", etc, etc, etc.!! Ratings and rankings are a pain. Ladders are easy! Join the PBEM Challenge Ladder! (I'll crawl back into MY hole now... )