A proposal for modifying the elo system

So I'm making this post because of the problems the community has been having with low ranks elo farming. I think that a slight adjustment could be made to the elo formula in order to fix this problem, without preventing low ranks from duelling and keeping their duels in the same league as high ranks. Sorry about my handwriting; I chose to handwrite sections of this thread because it's easier to get maths concepts across with handwriting than it is trying to write it using forum text.




That result is very important, because I think this is what we want for low ranks, so that when a low rank alt gains lots of elo from duelling other low ranks, he can't keep increasing his elo easily. This is because he would quickly run into a limit where he couldn't gain any more elo from the low ranks with elo's of around 100.

However, it is not what we want for high ranks because this would equally disadvantage them making it hard for them to earn elo from players with a lower elo. We want to allow higher ranks to keep earning elo as they can now, while making it basically impossible for low rank alts to earn large amounts of elo from other low ranks with lower elo.

The proposal



So QA = RA with limits on either end. I'll explain the reasons for having to have these later.

Now, we replace the divisor of 400 with a divisor that depends on the ranks of the players: 4QAQB





Here, the x axis represents QAQB and the y axis represents the elo gained by player A if player A has 200 more elo than player B (EA - EB = 200).

So, for high ranks dueling, A gains 6 elo, like he would at the moment QAQB = 100. However for 2 rank 5's dueling A gains only 0.25 elo (QAQB = 25).

Also, using a spreadsheet I created an iterative formula to show that, for a rank 5 to increace his elo from 1000 to 1250 by dueling other rank 5's with 1000 elo he would have to play 556 duels. As nobody can do that in a month they could never reach the season elo boards, and would probably give up trying after the elo gained per duel becomes very low.

The limit of QA = 10 for 10 ≤ RQA makes the playing field even for all high ranks as rank doesn't really matter at that point. The limit of QA = 4 for 0 ≤ RA ≤ 4 means that rank 3's can still gain some elo (because a divisor of 36 is way too small), and this prevents the computer having to evaluate too large powers of 10 which is potentially a problem.

There are also some other advantages, like that high ranks will gain less elo playing low ranks with lower elo, and that the same low ranks will stand to gain more by playing the higher rank higher elo player than they would by playing someone of a similar rank.

Low ranked players can still exchange large amounts of elo with each other (for two players with 1000 elo each, one player will always gain 12.5 elo by winning under this system), and this does not tail off much until the players have a difference of about 100 elo between them. This is ok because normal low ranks will not accumulate large amounts of elo while they remain low ranks.

The system also includes for the rare players like Prometheus who started duelling seriously when only a low rank, as they will be able to win large amounts of elo from beating higher ranked players with better elo scores, compared to what they would win from duelling similar ranked players, so the system encourages improvement and challenging yourself.

Honestly I think it really works on all accounts. Please post below with potential problems I haven't thought of. Also if any of the maths doesn't make sense say so and I'll try and explain it in a way you understand.

Ok, now I've actually included the graph

Damn it i though clovis life was atwar but its yours too.

Well, I guess nobody understood it. Still worth a try though.

Editied and cleaned up bits of the thread to present the steps in a different order. Maybe this will help.

Upvoted just because of the work put in it

I admit it, maths is not as fun as I once thought back when I was a kid. Taking a quick look at this, I guess that the most relevant and explanatory of all the post is the graphic. I must say I won't doubt your mathematical procedures since I barely understood or even had the energies to read through all of it. But the graphic does seem nice, right? Seems logic, pls install!