Change Arena points and rankin

[BarnardsStar]

So where is the balance ? this matchs are all Elite vs Elite. So beat a bronze is 5 to 15 points and beat one Elite is 10 to 35 ???????? My win rate points is more less than my loose rate.

Every player in Arena has an “Arena Elo Score” or AES. This is completely independent of actual Elo but it uses the same formula (but with a high “k-value” so your AES changes by more with each win and loss). Even bronze players have an AES but it is hidden until they reach Elite—but it’s still there. It starts at 1500 and goes from there. So a bronze player near the top of bronze, who has won 2-3 games, could theoretically have an AES of almost 1600, and a gold players who’s on a winning streak could be significantly higher than that, in theory. Unfortunately, you just don’t know.

So the formula for Elo/AES looks at your likelihood of winning, as estimated by your prior scores. If you are 400 points apart, the higher player is a 10:1 favorite. It’s logarithmic, so 200 points apart means they are a √10:1 favorite. And 800 points means 100:1 favorite.

Then, if you win, you will gain 40*(likelihood of NOT winning) points, and if you lose you will lose 40*(likelihood of winning) points.

Let’s look at your first two examples.

Against same opponent Elite both :
https://boardgamearena.com/table?table=834052946 -26 points
https://boardgamearena.com/table?table=833194025 +17 points

Prior to that first match, your AES was 1673 and theirs was 1570. Difference here is 103, so your odds of winning are 10^(103/400) to 1 or 1.809:1. Put in percentages, that’s 1.809/2.809=64.4% for you and 35.6% for them. So when you lost you lost 40*0.644=25.76 points and they gained the same amount.

Prior to the second games now your AES is 1649 and theirs is 1599. The difference now is 1649-1599=50, so your calculated odds of winning are 10^(50/400) to 1 or 1.334:1. In percentages, that’s 1.334/2.334=57.2% for you and 42.8% for them. When you won, you gained 40*0.428=17.12 points and they lost the same amount.

In summary, when you are higher than the other player you gain less for a win and lose more for a loss; if you have a lower AES the reverse is true. (The general formula here is: Δp = k*r/(1+r) where k is 40 for AES and r is 10^((L-W)/400), where L and W are the AES before the game for the Loser and Winner.)

Now, you say this “doesn’t reflect your arena strength”, and I’m curious as to why you would say that, what your argument here is. I think, if you lose to somebody weaker than you, that means maybe you’re overrated and should be lower, and that’s what the AES formula reflects.

[Ceaseless]

Against same opponent Elite both :
https://boardgamearena.com/table?table=834052946 -26 points
https://boardgamearena.com/table?table=833194025 +17 points

Here others more than -20 against Elite :
https://boardgamearena.com/table?table=828922988 -29 points
https://boardgamearena.com/table?table=828984514 -29 points

Here my wins against Elite, under 20 points :
https://boardgamearena.com/table?table=815289901 +17 points
https://boardgamearena.com/table?table=828673903 +13 points
https://boardgamearena.com/table?table=833603882 +10 points

So where is the balance ? this matchs are all Elite vs Elite. So beat a bronze is 5 to 15 points and beat one Elite is 10 to 35 ???????? My win rate points is more less than my loose rate.

You say they're Elite, and then leave out the scores? Add those in and things aren't so mysterious. Funny how the rating gains and losses seem to line up with the stat gaps. If you beat up players lower than you then you win less. Beat up players higher than you and you win more. Naturally this is reversed for losses. The gap size dictates the swing too.

A 1570 beat a 1673, a player 103 points above them, for a 26-point gain.
A 1649 beat a 1589, a player 60 points below them, for a 17-point gain.

A 1510 beat a 1696, a player 186 points above them, for a 29-point gain.
A 1526 beat a 1690, a player 174 points above them, for a 29-point gain.

A 1701 beat a 1646, a player 55 points below them, for a 17-point gain.
A 1677 beat a 1543, a player 134 points below them, for a 13-point gain.
A 1666 beat a 1475, a player 191 below them, for a 10-point gain.

If you're looking for where the numbers come from then you need to know the gap and k-factor. The rating gap is easy, if you are 100 points above someone the gap is 100, if you are 100 points below them the gap is -100. 1 / [1 + 10^(−D/400)] tells you your chances of victory in decimal form. Multiply that by the k factor and you have your changes in a 1 v 1. The k-factor can be found by totaling what a player would win for a victory with what they'd lose for a defeat. the easiest way to see that is an even game, where the win and loss stats are equal. Since the baseline in Arena seems to be 20, that means the k-factor is 20+20, which is 40.

So we can predict Elo gain and losses in 2-player Arena with 40/ [1 + 10^(−D/400)]. If D is 103, that's a gain of roughly 25.76, or 26 if we round to the nearest integer. If D is -60, that's a gain of roughly 16.58, or 17 if we round to the nearest integer. That matches up with the first two games listed. Where did 1 / [1 + 10^(−D/400)] come from? https://en.wikipedia.org/wiki/Elo_ratin ... ite_note-3

[tbhp]

You can't use win percentage because everyone is matched with a unique set of opponents of various levels, and the percentage doesn't tell you who they won and lost against.

The whole point of Elo is that it makes you gain or lose points based on the strength of the opponent you played against. The way it works is not perfect, but it's much better than your suggestion.

[Patrick_CAJE]

BarnardsStar, I understand but why in this game : 844761891 ?

You said :
"In summary, when you are higher than the other player you gain less for a win and lose more for a loss; if you have a lower AES the reverse is true. (The general formula here is: Δp = k*r/(1+r) where k is 40 for AES and r is 10^((L-W)/400), where L and W are the AES before the game for the Loser and Winner.)

Now, you say this “doesn’t reflect your arena strength”, and I’m curious as to why you would say that, what your argument here is. I think, if you lose to somebody weaker than you, that means maybe you’re overrated and should be lower, and that’s what the AES formula reflects."

So I'm lower (gold).... I win against 3 Elites.... and one Elite have +5 AES and me +4.... That's why I said that. The ELO is ok but the arena, for me, not.

[Jellby]

So I'm lower (gold).... I win against 3 Elites.... and one Elite have +5 AES and me +4.... That's why I said that. The ELO is ok but the arena, for me, not.

https://boardgamearena.com/table?table=844761891

You are confusing +4 shields/league points with AES. You most likely got +29 AES (because the total change should be 0), but that's not visible until you reach Elite. Also the AES change is computed based on your (hidden) AES, which could be much higher than those of the Elite players, we don't know (everyone starts at 1500, so the other players aren't really much better than default). Until you reach Elite, you only see shields based on your and your opponents' leagues.

[Patrick_CAJE]

You are confusing +4 shields/league points with AES. You most likely got +29 AES (because the total change should be 0), but that's not visible until you reach Elite. Also the AES change is computed based on your (hidden) AES, which could be much higher than those of the Elite players, we don't know (everyone starts at 1500, so the other players aren't really much better than default).

So, that's another things I don't love. Logically, if AES is based on your points, not your classements, that's not represent your season if a Gold or Sylver can have more points of an Elite for this season. He wins more games, against Elite and others. And for go on Elite he must have win minimum 15 games with no loose. So when you are on Elite, just no playing for stand your classement. It's a push your luck's system I don't like.

So that's my opinion : season its a classement of wins/looses, not a ELO disguise.

[BarnardsStar]

I would do the opposite, personally… get rid of the current stepladder system and lean into AES. Divide into Lead, Bronze, Silver, Gold, Platinum, Titanium, Elite (ok, maybe not quite so many tiers), based on solely on AES. Then you do in fact get “demoted” and “promoted” between the different leagues etc.

Biggest issue would be deciding the dividing lines between the tiers, and I think that would probably have to vary by game. Maybe it could be percentile-based?

[Patrick_CAJE]

The percentile is what I propose, defining the number of wins in X games, and the tiers would be based on a number of games depending on the percentile number.

[Ceaseless]

The percentile is what I propose, defining the number of wins in X games, and the tiers would be based on a number of games depending on the percentile number.

They're saying the percentile based on the rating system, since obviously doing it by numbers of wins would be ridiculous.

[Ceaseless]

I would do the opposite, personally… get rid of the current stepladder system and lean into AES. Divide into Lead, Bronze, Silver, Gold, Platinum, Titanium, Elite (ok, maybe not quite so many tiers), based on solely on AES. Then you do in fact get “demoted” and “promoted” between the different leagues etc.

Biggest issue would be deciding the dividing lines between the tiers, and I think that would probably have to vary by game. Maybe it could be percentile-based?

We could just get rid of the tiers/leagues, I guess they're cute decorations, but I don't see much of a functional point for them. Anything reading them for pairing purposes would be better off using a rating range instead, which would be far better grouping.