Champinoman wrote:

tw2000 wrote:I have an idea. Why don't we simulate an all v all and make the rating adjustments needed for each one. So in a 9 player game you're basically playing 8 1v1's in a row, and so if you came third you've effectively lost against 1st and 2nd but you've won against everyone else?

This is the current system being used in the game.

Currently your rating is changed based off how you did in 1v1 battles with everybody else in the game. In these individual games the Elo is calculated using a base kValue of 20 and the delta of all the 1v1 games is calculated to end with your final Elo change.

The kValue of 20 means that if you win/lose against somebody with the same rating as you then you will see a movement of +/-10 rating. Whilst if you win/lose against somebody with a massive ratings difference you will see a gain of either +/-19 or +/-1 (depending on which way the difference is).

The only difference between the system Subterfuge uses and the system most games use for a multiplayer Elo system is that all of these changes are added up instead of being averaged. Other games use a larger kValue and then average out your ratings before applying the change.

So if you are winning a 6 player game with people of the exact same rating then you will get: +10,+10,+10,+10,+10 = +50. However if everybody in the game is 100 rating better than you it will look something more like this: +13,+13,+13,+13,+13 = +65. (aprox numbers)

Oh so they don't actually average out the rating?
Does this mean that, if you play a game with another player who ahs the same rating as you and you win, you get +10 to your rating? Isn't that a bit unresonable?

Champ, if what you are saying is correct, why then is there a precise +\-20 points per spot on the leaderboard?

If there is a per person calculation, shouldn't the amount of rating gained fluctuate, depending on the rating of those you beat, and the rating of those who beat you, and not by precise increments of 20?

tw2000 wrote:Does this mean that, if you play a game with another player who ahs the same rating as you and you win, you get +10 to your rating? Isn't that a bit unresonable?

That is correct. Why is that unreasonable? If you beat a player of equal skill you gain a set amount of rating points, in this case 10. If you beat someone who is slightly better than you you would gain slightly more points. If you beat someone slightly lower than you then you would gain slightly less rating points.

kevlargolem wrote:Champ, if what you are saying is correct, why then is there a precise +\-20 points per spot on the leaderboard?

If there is a per person calculation, shouldn't the amount of rating gained fluctuate, depending on the rating of those you beat, and the rating of those who beat you, and not by precise increments of 20?

The ratings on the leaderboard should fluctuate.

I have attached an image of my last rated game. You can see the different rating changes as you move down the list. Notice that chinahasowls had a bigger ratings boost than me even though I finished 1st. This is because I had a higher rating than most in the game and received less of a gain from beating them, whereas chinahasowls was lower and received a larger ratings gain per person even after losing some rating from finishing below me.

Forgot the most important part;

The reason the 'live' ratings appear to be in increments of 20 is because of a little math quirk. Consider the following scenarios:

Leaderboard
...
4th: PlayerA
5th: PlayerB
6th: PlayerC
...

Scenario 1: Ratings: PlayerA (1200), PlayerB (1200), PlayerC (1200)

If PlayerB moves up 1 position their rating increase would be +20 because they are gaining +10 because they are now beating PlayerA and they are no longer getting the -10 from losing the 1v1 battle against PlayerA.
The same applies if they drop below PlayerC. It's a net loss of 20 when you consider they lose the +10 from beating them and gain a -10 because they are now below them.

Scenario 2: Ratings: PlayerA (1300), PlayerB (1250), PlayerC (1200)

Firstly, these rating changes are guesses. But the theory is still applicable.

If PlayerB was able to move above PlayerA they would gain a boost of +13 (guesswork) to their rating. And because they are no longer losing to PlayerA they would lose the rating penalty of -7 that was previously being applied (it's -7 because they are theoretically better than us and therefore we are penalised less). Therefore we see a net gain of +20 in the 'live rating' even though the person we passed on the leaderboard was ranked higher. Yes we got a better than average rating increase for passing them, it just appears like a standard increase of 20 because the penalty for being below them counter balances it.

The same applies the other way. If you fell below PlayerC you would suffer a ratings loss of -13 and would have the +7 you had from being in front of them struck out. Another net loss of 20.


So as you can see. The ratings are dynamic. However when viewing the live ratings it may appear that they are not because of the way the Elo system works.

Champinoman wrote:

tw2000 wrote:Does this mean that, if you play a game with another player who ahs the same rating as you and you win, you get +10 to your rating? Isn't that a bit unresonable?

That is correct. Why is that unreasonable? If you beat a player of equal skill you gain a set amount of rating points, in this case 10. If you beat someone who is slightly better than you you would gain slightly more points. If you beat someone slightly lower than you then you would gain slightly less rating points.

Its unreasonable because you should be able to get at least +30 or so, which is the average of a win in other games

tw2000 wrote:Its unreasonable because you should be able to get at least +30 or so, which is the average of a win in other games

See my image above. I got +62 for winning a game.

If you believe each 1v1 battle within a game should also be worth 30 rating points then you are suggesting that in a 10 player game the person who finishes first and last should see movement on average of +/-270 rating points. In an Elo system with a base starting point of 1200 that would be extremely unbalanced.

The current system has a faster movement model than the averaging Elo system. In an averages system a win against similar ranked opponents would give you a net gain of ~40. With this current system it is much higher.

Another advantage of the system being used as opposed to the averaging system is that this model gives larger gains for those that win in games involving more players. The averaging system would give the same gains to a 2 player gain as it would a 2 player game.

Champinoman wrote:Another advantage of the system being used as opposed to the averaging system is that this model gives larger gains for those that win in games involving more players. The averaging system would give the same gains to a 2 player gain as it would a 2 player game.

I think this is a disadvantage. Or at least there should be some scaling so that winning a 4 player game puts you at about 2nd place in a 10 player game.

This conversation is starting to go way over my head, but I refuse to give up!

Champ, where I am getting lost is on the live leaderboard you described in Scenario 2 (and I've thought a lot about what you said). When I look at my leaderboard while a game is active, it shows me how many points I will earn based on what position I finish in. It always progresses by factors of 20, however where I start to gain/lose points and the precise number from where it starts seems to vary based on the TOTAL rating of the players in the room pooled together as a starting point.

I tried to understand your kValue 20 explanation, and while I can't quite fathom it, there are basic fundemental things that I can't even make sense of. I think what you are saying is something like:
(the most a player can shift in a given 1v1 calculation is 20 points. Depending on their ratings, each stands to get a chunk from each others rating, always totaling 20. 10-10 if they are even, 19-1 if they are extremely uneven. And correct me if I'm wrong, but you seem to be saying that the reason it always looks like standard movements of 20, is only because the live rating board is showing how much both players moved. So one dropping 19 and the other gaining 1 will still look like 20 because the net shift is = 20.)

Am I on the right page? If not, stop me here because I'm now moving into why this doesn't make sense to me.

1. The live leaderboard only shows MY rating if I were to finish between 1st-10th, right? (unlike the final leaderboard which shows how much rating everyone ended up with). So if thats the case, it shouldnt matter how much the other guy is losing, because the live leaderboard pertains to only my rating. So if beating someone would only give me 1 point of rating, thats what the leaderboard would show: +1, because the movement is only relevant to me.

2. The more I think about it, unless all the ELOs are prepooled, the only thing the live leaderboard should be able to show is my ELO if the game were to end exactly as is now. Because the amount my rating fluctuates if decided by multiple 1v1s, would depend not only on which place I finish in, but also which players finish above/below me. A 1200 3rd place finish with player1800 above me, and player1200 below me, would have a very different result than a 1200 3rd place finish with those same players in opposite positions around me.

kevlargolem wrote:I tried to understand your kValue 20 explanation, and while I can't quite fathom it, there are basic fundemental things that I can't even make sense of. I think what you are saying is something like:
(the most a player can shift in a given 1v1 calculation is 20 points. Depending on their ratings, each stands to get a chunk from each others rating, always totaling 20. 10-10 if they are even, 19-1 if they are extremely uneven. And correct me if I'm wrong, but you seem to be saying that the reason it always looks like standard movements of 20, is only because the live rating board is showing how much both players moved. So one dropping 19 and the other gaining 1 will still look like 20 because the net shift is = 20.)

The winning player will always gain the same amount of Elo as the losing player loses. If a player beats someone they are 100 points lower than then they will gain +12.8 points, whilst the loser will lose 12.8 points. The total of both players new ratings will equal the total of their old ratings. Elo is basically reassigning the points based off the result.

Have a play on this calculator to mimic this: https://ratings.fide.com/calculator_rtd.phtml

So, using the above example put in rating=1200, Rc=1300 (opponents rating), W=1 (for winning) & kVal=20. This results in +12.8.
Now flip the ratings and change W=0 for a loss. This is the calculation from the perspective of the higher rated losing player. You'll see a result of -12.8.

So that shows how the rating total between the 2 players remains the same after new ratings are calculated.

So now, for the reason why it appears all increments are 20 on the live list.

Using the original values again: rating=1200, Rc=1300 & kVal=20.
With W=1 the change is +12.8. With W=0 the change is -7.2. The difference between these 2 numbers is exactly 20.
Repeat this with as many different combinations that you can imagine and you'll see this keeps on happening.

So, when you notice that increasing 1 position in game gains you exactly 20 rating points you will understand that this is because the difference between 'losing to that player ahead of you' and 'beating that player' is exactly 20 points.

kevlargolem wrote:1. The live leaderboard only shows MY rating if I were to finish between 1st-10th, right? (unlike the final leaderboard which shows how much rating everyone ended up with). So if thats the case, it shouldnt matter how much the other guy is losing, because the live leaderboard pertains to only my rating. So if beating someone would only give me 1 point of rating, thats what the leaderboard would show: +1, because the movement is only relevant to me.

You are correct in saying that it shouldn't matter about the other persons rating. The live leaderboard does in fact only refer to your rating and not theirs.

kevlargolem wrote:2. The more I think about it, unless all the ELOs are prepooled, the only thing the live leaderboard should be able to show is my ELO if the game were to end exactly as is now. Because the amount my rating fluctuates if decided by multiple 1v1s, would depend not only on which place I finish in, but also which players finish above/below me. A 1200 3rd place finish with player1800 above me, and player1200 below me, would have a very different result than a 1200 3rd place finish with those same players in opposite positions around me.

The game does show what would happen if the game ended instantly. And it is applied to all players current rating. If ratings change before the end of the game you will see these numbers change.

And I setup this scenario from what you said. Imagine a 5 player game where 4 players, including you, have a rating of 1200 and one player has a rating of 1800. Here is the rating change for you finishing 3rd with the 1800 rating above and below you.

1st: Player1200 (-10)
2nd: Player1800 (-1.6)
3rd: You
4th: Player1200 (+10)
5th: Player1200 (+10)
Final rating difference of +8.4.
You didn't lose many points for finishing below Player1800 because they were realistically expected to beat you anyway.

1st: Player1200 (-10)
2nd: Player1200 (-10)
3rd: You
4th: Player1800 (+18.4)
5th: Player1200 (+10)
Final rating difference of +8.4.
You got a massive points gain from beating someone that mathematically was meant to beat you. However out of the 3 players equal to you, you only managed to beat one of them so you lost rating points that way.

So you can see that no matter the order, you still got +8.4 for finishing 3rd.

Why do you gain rating for finishing middle? Because the game's average Elo of 1320 is higher than your Elo so your expected finish position before the game started was ~4th. You mathematically performed better than expected.

A potential way to make rating matter is to combine it with the previous Faction idea I had.
(Here's the link: viewtopic.php?f=5&t=1191)

Maybe only people with a certain rating could create/maintain a Faction?
Or maybe even make some sort of 'L3' clearance for people who have reached a certain rating point?

Expanding on the L3 idea, maybe once people reach a certain rating, let's say 2500 for sake of explanation, then any rating they achieve beyond 2500 will be saved and put on their profile as a trophy.
e.g Imagine I had reached rating 2511, then even if I suddenly drop down to 1200, my profile will read my current rating as 1200 and then read my 'Highest Achieved Rating' below as 2511.
Then we could even have a 'Record Holder Leaderboard' which could be a leaderboard that doesn't rank players by current rating, but by their highest achieved rating,

Just thought this could potentially achieve the goal of making rating matter a bit more.