Elo calculation in detail

[souly4]

Hi, one question just sprang to my mind. I wonder how the actual elo gain/loss after each game is calculated. For instance I won against a lower player today and got +1 supposedly, but my rating stayed the same. As there are no decimals, could it be that in fact it was something like 0,7 and it increases when I get the next 0,3 points?
Of even more importance to me are the thresholds in elo difference of two players and the resulting calculation associated with it. So one might win +1 when being 450-500 elo points better, +2 when 450-420 and so on (these are just arbitrary numbers to give an example). Is there a chart for it somewhere? Thanks.

[lap63]

I remember there are hidden decimals (?)

Yes for the second one I think they should display the possible elo change during / before the game, including in 3+ players games to let players know whether they should put someone in last or stop competing for the first rank to maximize the elo they gain.

[Liallan]

There's lots of posts around with ELO discussions if you will try the search feature. Just be careful to stick with whatever is most recently since some of the really old stuff doesn't count anymore.

As to how much you move, that's more dependent on how many games you have played. I'm not sure that yours or your opponents current levels come into play, or at least I think that's what I've heard. (I've read those threads but don't really remember tons about it.)

[souly4]

Okay thanks to both of you. Liallan (btw I'm impressed how active you are in the forum despite your moderate amount of games), I used the search function but nothing helpful appeared on the first site. I'm aware there's lots of stuff about the purpose and pros and cons of elo in general, but my question was more specific. Still, after your advice, i tried it again with different wording and indeed one informative thread came up.

https://de.boardgamearena.com/#!forum/v ... difference

In particular that part:

I think the numbers boil down to that if the difference in ELO is 100, the stronger player is expected to win 2 out of every 3 matches, and if the difference is 200, they are expected to win 3 out of every 4 matches.

That doesn't answer my question exactly but it's a good approximation as now I can check the history of various games and calculate the missing value on my own. For an elo difference of 200, the lower player must get thrice the points for a win to be fair, so I just need to multiply/divide by three depending on who has won. Well, when I think about it again I'm not sure if that's correct. If we continue the pattern above, a player 600 elo points higher should win 7 of 8 matches. That contradicts that masters/experts usually get +0 or +1 points for a victory against someone with elo 100, while the other way it's more than 30 points if I'm not mistaken.

I know that the amount of games is taken into consideration for the elo calculation, but I always thought it would only apply to the first 20 games and then stop forever, so that it's not gradual. Here is a quote from another thread that supports this claim:

If you have less than 10 games played, K=60 (you win 30 points against a player with the same ELO).
If you have between 10 and 20 games played, K=40 (you win 20 points against a player with the same ELO).
Above 20 games played, K=20 (you win 10 points against a player with the same ELO).

I'm not sure that yours or your opponents current levels come into play, or at least I think that's what I've heard.

How shall I understand this? What else should come into play?^^ Maybe you confused level with rank...

[lap63]

After first 20 games winning against a same elo player gives you 10 elo, you can get a most of 20 elo per game, the same elo become negative if you lose. A little elo difference may give you 15 elo after winning, but if you want to get 20 elo, you need a much bigger elo difference in comparison.

elo change : K/(1+10^((Ra-Rb)/400))

both players' elo are taken into account in elo calculation

viewtopic.php?t=11132

[Liallan]

Okay thanks to both of you. Liallan (btw I'm impressed how active you are in the forum despite your moderate amount of games),

LOL. There are people who are not impressed by that. Right now I'm not playing much and sticking to quicker games cause I'm supposedly going to have an interruption... which keeps not happening. Though I still don't play more than 10 or so games at a time, and all turn-based so they are slow. But forums are kind of a way to make what is otherwise not terribly social a little more social.

In the end, I'm not really the one to be posting about this, because I'm not that concerned about ELO and therefore not that well versed in it, though I've read the threads. Which is why I was pointing you to the threads, cause no one much was responding.

[ydk2000]

I noticed something with regard to ELO today that made me wonder about how ELO is calculated.

Generally, if a game ends in a tie, or if the first place ends in a tie, I noticed the player with the lower ELO gets more points and the other player lesser. But today I saw the higher ranking player get almost double the points than the lower ranking player.

This made me wonder what other factors would affect the ELO points being calculated