The new ELO-based ranking system

MrRoboto

It’s impossible to put a number on it like you ask for.

Maybe I’ll try to explain the general function of the ELO system and this could help you understand how it works.

The ELO system tries to measure your skill. For example on a 0 - 10 scale, you could be a 5.84 and the system would try to find out that number.
Now we all start at 1500, which on a 0-10 scale would be a 5. Everyone starts at 5.
Why do I not use a 0-10 scale? Because we don’t have a fixed limit on how good or how bad someone can be, so we need an open-ended scale. And in many many other cases where ELO is used, 1500 has been established as some kind of standard starting point.

Now let’s say your skill is around 1650. The system doesn’t know it yet, of course. But that would mean you should win most games against players below 1650 and lose most games against players above 1650. That’s why your ELO will gravitate towards that number.

Every unexpected result (wins against players above 1650 or losses against players below 1650) will deflect you from that path. You might be above that 1650 because you had some lucky unexpected wins, so you might be at 1700 now. But now the system expects you to win against 1680 players most of the time so whenever you do lose against a 1680, it will bring you down a bit more than if you were at your “ACTUAL” skill level of 1650. Of course the opposite is true as well.

You might have had a loss streak and now stand at 1500. The system would expect you to lose against 1600 players. But since you are ACTUALLY better than 1600, you DO win against them (which the system didn’t expect) so you will gain more points than usual.

In the end you will gravitate towards the your skill level and your ELO will oscillate around that number.
The only way to inrease that center of that gravitation is to actually improve your skill.

There is one caveat though, a small weakness in the system.

If you only choose opponents better than you are thus lose most of those games, the system can’t find your actual skill level. Let’s say you only play the top 1-5 players - each loss will only cost 1-2 ELO rating and thus the rating will only fall EXTREMELY slowly, but there are not enough wins to tell the system where you belong. In the end, if you lose to a 2000 player that could mean everything: You could be 600, 1500 or 1900.

Same goes for the opposite.

If you only choose weaker players and play the bottom 1-5 all the time, these wins are almost worthless (giving you 1-2 points). It’s not practical to climb the rankings that way, because you can’t play the bottom player 500 times in a row. But again, if there are no losses the system cannot know how good you really are. Defeating a 700 ELO player can mean everything as well…

MrRoboto

And to give some perspective, here is your personal BM4 graph, @oysteilo with all your 74 completed BM4-results.

As you can see, there is not that much movement, so let’s zoom in a little bit:

The orange line is the trend line.
From looking at this, I’d say your skill level is between 1550 and 1600.
Between Dec 2019 and May 2020 you had a couple of wins in a row which lead to your all-time high of 1684, but that was followed by a 9-game loss streak.
On 8 Nov 2021 it seemed like you mass forfeited 6 games, which of course brought you down a lot.
However, with 4 wins our of your last 5 you almost got back to where you were before those forfeits. (1573 on 8 Nov 2021, 1538 now).

As you can see, a single result 30 games ago has basically no impact on your current rating.
A blunder against a much better opponent with an expected loss? No impact. A blunder against a weaker opponent that cost you the expected win? That hurts and you need at least a game, maybe 2 to offset that unexpected ELO drop.

MrRoboto

My own BM4-Graph looks like this btw:

When I first played in 2016, it looks like I was a 1480 player. These were some of my very first A&A games.
However, 6 wins out of the last 7 games rewarded me with my then highest rating of 1563.

I came back playing 2 years later and it seems like I improved to be something like a 1530 player.
2 forfeited games (because I went AWOL) brought me down from 1536 to 1466 though (70 points in 2 games!)

In my current stretch of games, it looks like I have improved once more to be around 1570. My current rating is 1591 but I have some losses incoming, so that sounds about right.

oysteilo

All right, thanks for the explanation. I guess you just have to focus on winning games and dont accept more than you can handle. It will be fun to see how this turns out!

MrRoboto

And because it’s so much fun, some more data :-)

Who has played the most BM4 games? That would be our beloved @simon33 who unfortunately went AWOL a couple of weeks ago.

You can see clearly how he improved a lot, from his lowest point in March 2017 (1077 ELO) to his highest Rating in May 2019 (1693 ELO). Which is to be expected!

Now from then on his rating gradually declined - slowly but steady. Did he become worse? Maybe.

But remember, we are not measuring an absolute value. Your ELO rating is actually only a number that gives you a relation to the other players. So it’s not absolute, it’s relative to every other player.
I’d interpret this graph differently: I think over the past ~4 years his skill level plateaued or stagnated but A) more and more other people did improve while he did not and B) more and more new people joined the league who are on average better than him.

And now a completely different graph. The player with the 3rd most completed BM4-games, after @simon33 and @Giallo ?
Our very own @axis-dominion

Here is your graph, Mister:

A steady climb at the beginning where he chose mostly average players and won consistently almost all of those games.
The opponents were weaker than him, but still reasonably close so the games were still worth something. The climb could have been a lot faster had he won against the top players from the get go - but he didn’t! The matches against already strong Adam514 back then were almost all losses.

An unbelievable streak of 30 wins in 31 games between July 18 and March 19 (the only loss was against, of course, Adam514) rewarded him his all-time high of 2101.

3 losses on 16 Apr 2019 (probably mass forfeit?) saw him drop a whopping 158 points before his break.
A steady climb after his return brought him back to the top, although his rating seems to have plateaued around 2030

gamerman01

@MrRoboto said in Proposal for a new, ELO-based, ranking system:

A steady climb after his return brought him back to the top, although his rating seems to have plateaued around 2030

@axis-dominion is so transcendent, he’s not just 1-2 moves ahead of you, he’s 6-7 years ahead of all of us.
During 2024-2030, he wholly devoted his life to increasing his A&A skills, playing 500 more games.
Word is, he just stepped out of his time machine and is about to share his extra knowledge with us poor slobs who plod on 1 day at a time. He’s only going to take the Axis, so it will finally, truly be…

a time of the Axis Dominion

gamerman01

Most under-rated A&A league skill:
Starting a game with a good player who’s going to drop all his games before yours is done

oysteilo

For the OOB ranking most top players are not active. It should be a tool to filter away the non active players to achieve a current/up to date ranking of active players. How do ido that? If you were great in 2014, 16 and 17 and havent played a game since, then, I dont care what your ranking is

AndrewAAGamer

Yeah, originally we were going to have a historic ELO for posterity and curious interest only and a second ELO for yearly playoffs then @MrRoboto explained we really don’t play enough games to have a yearly ELO.

oysteilo

definately it should be possible to filter for active players. The current format is close to useless for browsing relative strength of active players

oysteilo

I think there could be an historic rating like @AndrewAAGamer says and one showing active players. If you havent finished a game in 18?? months (or whatever) you should be moved to the historic sheet. If you re-appear you are moved back to active

oysteilo

@oysteilo said in The new ELO-based ranking system:

definately it should be possible to filter for active players. The current format is close to useless for browsing relative strength of active players

yeah, just make a filter where you can chose if you like all players or only active players

gamerman01

@oysteilo There already is one, but maybe you guys can’t use it right now.
But maybe you can. Go to the filter views icon - is at top right next to the Sigma/summation symbol.

If you can’t do that, you maybe don’t have the capability yet (I’m not sure if it’s married to edit game results capability)

Have no fear, it’s a simple toggle.

And as soon as I win or lose against you I will be active even though the other 56 games are all from many years ago

Can you not see the tier color bands? It seems pretty easy to me to see the ranking of actives, but maybe you don’t have the same view.

gamerman01

And those top 11 inactives are pretty awesome players

oysteilo

My bad, it works. I just did not understand/know. I am happy with this

gamerman01

It’s good to know everyone has that capability so thanks.
Yeah I had to ask MrRoboto about it too - didn’t know what that box was

oysteilo

maybe it is explained somewhere, but there are so many pages…Now I have a question about this formula

What is RB? Is it RBold? If it is RBold then what happens if two players with the same rating meet? Well then EA =1

And putting EA = 1 here makes no sense for the winning person:

So I am doing something incorrect. Maybe the skilled people here can show their work (just like we did in school) with a couple of examples

gamerman01

I don’t know the formula yet, but 2 new players have exactly 1500 each.
With the current sensitivities, one goes up 55, the other goes down 55, if that helps.
MrRoboto is the formula guy

Stucifer

@oysteilo said in The new ELO-based ranking system:

maybe it is explained somewhere, but there are so many pages…Now I have a question about this formula

What is RB? Is it RBold? If it is RBold then what happens if two players with the same rating meet? Well then EA =1

R(B) is only used in context with R(A) to find the Expected Outcome (should A or B win). So yes it is R(B(old)) if you want to think of it that way.

And putting EA = 1 here makes no sense for the winning person:

EA = Expected outcome for Player A

If you have two players of equal rating, EA formula looks like this:

EA = 1 / { 1 + 10^[(RB - RAold)/F] }

RB - RAold = 0 since they are equal; formula then simplifies to:
EA = 1 / { 1 + 10^(0/F) }
10 ^ 0 = 1, so formula simplifies to:
EA = 1 / { 1 + 1 }
EA = 1/2

EA is always 1/2 for equal ratings, this conceptually is that they both have a 50% chance of winning.

EA will never equal 1, but it can get close to 1 if Player A is significantly higher rated than player B.

As an example, if A is rated 2250 and B is rated 750, and F is 500; we have:

EA = 1 / {1 + 10^[(750 - 2250)/F] }
EA = 1 / {1 + 10^[-1500/500] }
EA = 1 / {1 + 10^( -3) } = 1 / {1.001}
EA = .999 or 99.9% expected chance of Player A winning

Stucifer

@oysteilo For another example, our comparative overall ELO is:

Oysteilo - 1621 Player A
Stucifer - 1549 Player B

The expected outcome EA is:
1/ {1+10^[ (RB - RAold = 1549 - 1621 = -72) / 500] }

this piece 10^[ (RB - RAold = 1549 - 1621 = -72) / 500]
is 10^(-72/500) = 10^(-0.144) = 0.71779

EA = 1 / { 1 + 0.71779}

EA = .58214 or 58% expected chance Oysteilo wins, 42% Stucifer wins

The new ELO-based ranking system

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