The expected win rate VS ELO curve is quite impressive

[L Kama Smurf]

So I plotted the expected winrate VS ELO difference between 2 players and found the result to be quite interesting.

If you have 100 ELO more than your opponent, you're expected to win almost 2 games out of 3.
At +200 ELO, it's 3 games out of 4.
At +300 ELO, it's around 5 games out of 6.
At +400 ELO, it's 9 games out of 10.

For me, it's really impressive that some players manage to reach 1000 ELO in some games. It means that they win 5 out of 6 times vs Master players ! It's insane.

[Grimwold]

That's the problem with numbers.
7 times out of 10 you can make them say what you want.


For me it seems that this work for 'reasonnable' elo value (with one player at 300ish at the very most)

But yeah if you have a demi god at 1200 and a two-third god at 1500, I don't think the 1500 player will win 5 out of 6 games.

[L Kama Smurf]

I'm not sure I understand your comment, the plot just shows how the system works. Do you think it's more "ELO profitable" to play against lower rank players ?

I think there is something interesting to understand about the impact of luck and ranking systems. ELO is great for chess were there is 0 luck. But if a game has some randomness in it, then I believe the formula should be adjusted:
Let's say 1 game in 20 is automatically lost because of draft. Then even if you're a perfect player, you'd lose to any player with that draft. Therefore there is an ELO difference (in this made upo example around 500) where playing will always make you lose on average. An easy fix would be to "flatten" the ELO curve more if the game has mor luck in it.

[Jellby]

But yeah if you have a demi god at 1200 and a two-third god at 1500, I don't think the 1500 player will win 5 out of 6 games.

If these two players play many times against each other, that's exactly what will happen. Otherwise both their elos will change the the appropriate difference, e.g. 1300 & 1400 if the win rate is "only" 2 in 3.

[ahyangyi]

Well, Elo flattens itself when there's a large amount of randomness, no need to change the formula.

[silentProtest]

hey, very nice to have it plotted!!

If one wants a quick approximation (and maybe understanding) for the elo differences, and "by elo presumed skill differences", here some copy paste from another post:
the charm in elo is that you can very easily asses your winning chances, just by the point difference.

70 elo difference, youre x1,5 more likely to win than your opponent (1,5/(1,5+1)=1,5/2,5=0,6=60% vs 40%)
120 -> x2 more likely
190 [120+70] -> x3
240 [120+120] -> x4
etc....

HF

[silentProtest]

For me, it's really impressive that some players manage to reach 1000 ELO in some games. It means that they win 5 out of 6 times vs Master players ! It's insane.

its almost 6 out of 7 (since they are 6 times more likely to win) vs 700 elo players

[Ceaseless]

I'm not sure I understand your comment, the plot just shows how the system works. Do you think it's more "ELO profitable" to play against lower rank players ?

Yes, it often can be, depending on the game. Some players I can beat all day, if I only win 1 point each time those are just free points to my score. Even if I only win .5 points each time, free is free. The skill gap has to top the any variation by enough to pull it off, but it's a rating fill-up tactic by some players in the games it works in. Once the gap variation gets large enough weird things happen that go beyond what the elo was meant to account for. In high enough variation games it can be to the detriment of the higher rated player, but as the variation goes down the trend often reverses.

I think there is something interesting to understand about the impact of luck and ranking systems. ELO is great for chess were there is 0 luck. But if a game has some randomness in it, then I believe the formula should be adjusted:
Let's say 1 game in 20 is automatically lost because of draft. Then even if you're a perfect player, you'd lose to any player with that draft. Therefore there is an ELO difference (in this made upo example around 500) where playing will always make you lose on average. An easy fix would be to "flatten" the ELO curve more if the game has mor luck in it.

I fail to see why this is a bad thing. There's going to be a peak rating where you stop moving up. The lower that number is (all other things being equal), the less skill is a factor in that game. This is a rather handy factor in BGA, where the same site and elo system can help give a decent correlation between a game's peak ratings and skill, though factors such as activity, etc. still have to be taken into account Not really sure where you're going with the "flatten the elo curve".

[maveleo]

I'm not sure I understand your comment, the plot just shows how the system works. Do you think it's more "ELO profitable" to play against lower rank players ?

I think there is something interesting to understand about the impact of luck and ranking systems. ELO is great for chess were there is 0 luck. But if a game has some randomness in it, then I believe the formula should be adjusted:
Let's say 1 game in 20 is automatically lost because of draft. Then even if you're a perfect player, you'd lose to any player with that draft. Therefore there is an ELO difference (in this made upo example around 500) where playing will always make you lose on average. An easy fix would be to "flatten" the ELO curve more if the game has mor luck in it.

I totally agree, this is the reason why you get winning and loosing sequences with some games. I wish one day they will differentiate the system based on the luck factoras this is one of the things that they totally missed on here.

[Ceaseless]

I'm not sure I understand your comment, the plot just shows how the system works. Do you think it's more "ELO profitable" to play against lower rank players ?

I think there is something interesting to understand about the impact of luck and ranking systems. ELO is great for chess were there is 0 luck. But if a game has some randomness in it, then I believe the formula should be adjusted:
Let's say 1 game in 20 is automatically lost because of draft. Then even if you're a perfect player, you'd lose to any player with that draft. Therefore there is an ELO difference (in this made upo example around 500) where playing will always make you lose on average. An easy fix would be to "flatten" the ELO curve more if the game has mor luck in it.

I totally agree, this is the reason why you get winning and loosing sequences with some games. I wish one day they will differentiate the system based on the luck factoras this is one of the things that they totally missed on here.

You mean like Chess? Winning and losing streaks are a rather known phenomenon there.