[Attempt at] New PBEM rating system - continued

[Mathemagician]

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

[Mathemagician]

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.

[Solver]

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.

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.

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

[Solver]

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 .

[Mathemagician]

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.

[Mathemagician]

Originally posted by Solver

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.

[ricketyclik]

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.

[Mathemagician]

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 !

[Mathemagician]

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.

[Solver]

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

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 .

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.

[Solver]

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 .

[ricketyclik]

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

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:

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.

[Solver]

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

[Mathemagician]

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

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.

[ricketyclik]

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.