ELO & Ranking - problems and suggesting solutions

[lachimi red]

so when the N is greater, there is less elo gain/loss after the game?
And in the post, some players suggest about suggested number of players. as tokaido have 4 as suggested number of players, so when 5players play this game the N is still 4, right?
About the example, it looks great but I still dont understand how do you calculate 'the expected score of certain rank with others'. do you mind further explain ? thx

Exactly, with Tokaido, calculating a 5p game still use the coefficient N = 4.
However, when the N is greater, there seems to be more elo gain/loss after the game, as the actual score will increase as well when you win. However, we don't have an exact formula for this increasing/decreasing; depends on the elo of players in the table

About the example, in the first case, the expected score of the 1st player (520 elo) with 2nd player (489 elo) is: 1/(1+10^((489-520)/400)), using the formula for calculating elo; therefore the results is approx. 0.54 and vice versa, the expected score of the 2nd player with 1st player is 0.46 (the sum of 2 expected scores here must equal to 1). And so on, the expected score of the 1st with 3rd (520-433) is 1/(1+10^((433-520)/400)) = 0.62 (here is bigger, since the elo of 3rd player is lower than 2nd player),...

Calculating all the expected score and take 20*2/3*(3- three expected scores), you will have the plus/minus elo of the 1st player. 3 here is because the 1st player is considered to have 3 victories with 3 other players. And so on...

Hope that's clear enough

[Jessicannot Sp eak]

but why each player has the 3 same sets of numbers in each cases? for example, in case 2, should the player with 489 elo has 0.544 expected score against the 520 elo player instead of 0.455, because he wins? otherwise he will have the same elo change in the two games..

[lachimi red]

but why each player has the 3 same sets of numbers in each cases? for example, in case 2, should the player with 489 elo has 0.544 expected score against the 520 elo player instead of 0.455, because he wins? otherwise he will have the same elo change in the two games..

Each player has a set of 3 numbers which displays the expected score against 3 other players

In case 2, the player with 489 elo only has 0.455 expected score against 520 elo ... that's obvious, the player which has higher elo will have bigger expected score; so when the player with 489 elo wins against 520, he will gain more elo than when 520 elo player wins against him.

Maybe I used an example which has the difference elo of 489 and 433 = 433 and 377 so you'll see some stats are the same....

[Jessicannot Sp eak]

is that elo is calculated as 20*2/3*(3-sum of 3set of scores)? if so, then 489 elo player will have gain 17 elo in the first case.. ?

[lachimi red]

is that elo is calculated as 20*2/3*(3-sum of 3set of scores)? if so, then 489 elo player will have gain 17 elo in the first case.. ?

In the first case, 489 elo player will be 20*2/3*(2-sum expected scores), as he finishes 2nd, means that he wins against 2 others.

[Jessicannot Sp eak]

oh i thought 3 is fixed number, now I understand.. thanks very much

[RobertBr]

At least part of the problem the OP raised might be solved by adding a new indicator I have suggested - best ever rank.

Your best ever ranks is the lowest value of p/n, where p is your position at any one time and n was the number of ranked players at that moment.

You could then move a lot of trophies to that p/n ranking. Yep, you once achieved the top 1% in a game, so have a trophy for X. No, you do not need to keep re-activate your ranking to maintain that, and no you are not risking that achievement of having once been no.1 when there were 1000 players by continuing to play (and not being no.1) much less frequently now there are 4000 players.

It would also just be cool to know what your best ever position was.

[Espina]

At least part of the problem the OP raised might be solved by adding a new indicator I have suggested - best ever rank.

Your best ever ranks is the lowest value of p/n, where p is your position at any one time and n was the number of ranked players at that moment.

You could then move a lot of trophies to that p/n ranking. Yep, you once achieved the top 1% in a game, so have a trophy for X. No, you do not need to keep re-activate your ranking to maintain that, and no you are not risking that achievement of having once been no.1 when there were 1000 players by continuing to play (and not being no.1) much less frequently now there are 4000 players.

It would also just be cool to know what your best ever position was.

I really like the idea of "best ever rank". But...
Unless the prestige associated with having once been the best player, do you think the best player will be content to just give that up?

[senatorhung]

At least part of the problem the OP raised might be solved by adding a new indicator I have suggested - best ever rank.

Your best ever ranks is the lowest value of p/n, where p is your position at any one time and n was the number of ranked players at that moment.

You could then move a lot of trophies to that p/n ranking. Yep, you once achieved the top 1% in a game, so have a trophy for X. No, you do not need to keep re-activate your ranking to maintain that, and no you are not risking that achievement of having once been no.1 when there were 1000 players by continuing to play (and not being no.1) much less frequently now there are 4000 players.

It would also just be cool to know what your best ever position was.

I really like the idea of "best ever rank". But...
Unless the prestige associated with having once been the best player, do you think the best player will be content to just give that up?

i also like the idea of "best ever rank"

however, i think the best ever rank could just be a separate trophy ... with the prestige value of (best rank prestige - current rank prestige at that game, with negative = 0 additional prestige). so you would never lose the prestige points for rank, but you don't get double for being the current #1.

so if you make it to #3, then drop down to #19, you would still have the total prestige value for #3, just split between the prestige value for the top #20, and your (best rank #3 trophy) prestige would cover the difference in values.

but perhaps this might be more appropriate to match this with ELO - so best ever ELO value instead of game rank ?

[Incentive]

I definitly agree with all of this (except the 3, there are some arguments against too, but this is not the most important subject).

It has been already discussed in the forum, we did some research and identify that for a large number of games this is true.

This is quite difficult to find a solution that satisfy everyone : those who wants to play few games, and those who want to play a lot, but we will make the system more favorable to those who play a lot. I can give you a date for this but definitly this year.

I agree with the OP that this is a problem in most games. I think that if you can't/don't play with elo-on regularly then you shouldn't be ranked. I look forward to your solution later this year. Good luck!