Dice Analogy to ELO Hell

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ONLY MID THX

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Junior Member

06-03-2011

I'm pasting this from a post that my buddy "Decency" made at the HoN forums more than a year ago, in response to the many complaints I see about the rating system.

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Say we have two "teams" of 5 dice that we roll at the same time. Whichever team has the highest sum after we add all the dice on each team is the winner. You as a new player are given a rating of 1200 and gain or lose points after each game.

The other 9 dice (players) are 100% random, and you only account for 20% of your team's potential, but this doesn't matter, the system still works. We're measuring the one value that isn't random (but that the system doesn't yet know): your skill. Say your true skill is a "6" because you're a great player: you always roll a 6. Because you're a 6, your team will win more frequently than the other team and your rating will go up. Likewise, if you're a 1, your team will lose more than the other team, and your rating will go down.

Now, say you're a 4. You're not great, but you are still above average, and your team will win more frequently because of that. However, you won't help your team win as much as a 6 would, because you aren't as dominant. That doesn't matter: you are above average, so your rating will increase over time. You will seem to have more fluctuation than a 6 because your true skill is so close to the average one, but on average you will still rise.

Now, say you're a 3.5. You're the exact average that a player can be. Obviously though, you aren't going to tie every game. You're going to have winning streaks and losing streaks, and your rating will fluctuate accordingly, maybe you'll even get up to 1400 or down to 1000. But in the end, your rating will settle back to around 1200, because you're an average player.

This doesn't mean that you as a 6 can't get stuck with a bunch of 1's and 2's, dropping in rating because of them. However, when your rating drops from the average you get matched against worse players, maybe on average they only roll a 2 instead of a 3.5, so you have even more of an influence on your team due to your rating being lower than it should be. This leads to you winning, on average, far more frequently until you rise to your true rating level. The inverse is true if you're a 1: you might rise to a higher rating than you should because you played with 6's on your team for a few games in a row, but then you're facing people who can roll 7's and 8's and because you are over-rated, you are even more likely to cause your team to lose. So, your rating will be more likely to drop, and eventually it will settle to its true value.

QED: Matchmaking works


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DuffTime

Senior Member

06-03-2011

Truth.

And the people who complain about ELO hell could be better psending their time playing and improving their skills so that their ELO would rise steadily =p


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Zguz

Junior Member

06-03-2011

First good post about ELO i see in days...

+1


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CyraLoL

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Senior Member

06-03-2011

This is sorta true, but makes assumptions about probability that are just not necessarily true.

The common example of why this does not actually work the way you think it does is that say for example you flip a coin one hundred times. The chance of getting 99 tails and 1 heads is actually the exact same as getting exactly 50 heads and 50 tails. While the system you mention is a weighted average, thus more likely to trend, it still far far far from statistically impossible for someone to move vastly the wrong direction in a hundred games.

While averages will come out, yes, only in large numbers of players. To argue that a player will "average out" while rolling a 4 is rather unfair in that not only is it going to take a statistically improbably number of games to do so, it only holds true for the average - which means that countless players could, in fact, roll a 6 every time and still easily get to 1000 ELO.

Further - your contribution can bother matter more or less the lower or higher your ELO is. Yes, a staggering a good player can probably carry an 800 team completely since he's likely to get massively fed. However, around 1100-1300, he'll run into trouble - not because his still not better, but he will no longer likely be able to single handedly carry a team, even if he's a 1600 player. His team has a higher chance to win, but as noted, that average may not play out for hundreds of games, or, quite literally, ever.

Lastly, there is less difference in ELO than many people seem to think. If you take the average 1200 player and put them in 1400 ELO, more often than not they stay roughly at 1400 ELO. Due to how the system works of matching a team that is likely to win (favored) vs team that is unlikely to win (disadvantaged) there is an unnatural weight towards having a static ELO, since the major weight to winning or losing rests of on the MMR weighting - which is, as far as I know, completely random as to wether your on the favored team or disadvantaged team.

So while your point is interesting, it is not entirely valid. Personally, I don't claim that my ELO is incorrect. I do however know from personally experience that 300 points in either direction makes a very small impact on my win/loss or KDA ratios. The vast majority of my games are obviously determined by the weighted system, as one can observe by checking the average team ratings in the score screen after the game.


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DuffTime

Senior Member

06-03-2011

Quote:
Originally Posted by CyraLoL View Post
This is sorta true, but makes assumptions about probability that are just not necessarily true.

The common example of why this does not actually work the way you think it does is that say for example you flip a coin one hundred times. The chance of getting 99 tails and 1 heads is actually the exact same as getting exactly 50 heads and 50 tails. While the system you mention is a weighted average, thus more likely to trend, it still far far far from statistically impossible for someone to move vastly the wrong direction in a hundred games.

While averages will come out, yes, only in large numbers of players. To argue that a player will "average out" while rolling a 4 is rather unfair in that not only is it going to take a statistically improbably number of games to do so, it only holds true for the average - which means that countless players could, in fact, roll a 6 every time and still easily get to 1000 ELO.

Further - your contribution can bother matter more or less the lower or higher your ELO is. Yes, a staggering a good player can probably carry an 800 team completely since he's likely to get massively fed. However, around 1100-1300, he'll run into trouble - not because his still not better, but he will no longer likely be able to single handedly carry a team, even if he's a 1600 player. His team has a higher chance to win, but as noted, that average may not play out for hundreds of games, or, quite literally, ever.

Lastly, there is less difference in ELO than many people seem to think. If you take the average 1200 player and put them in 1400 ELO, more often than not they stay roughly at 1400 ELO. Due to how the system works of matching a team that is likely to win (favored) vs team that is unlikely to win (disadvantaged) there is an unnatural weight towards having a static ELO, since the major weight to winning or losing rests of on the MMR weighting - which is, as far as I know, completely random as to wether your on the favored team or disadvantaged team.

So while your point is interesting, it is not entirely valid. Personally, I don't claim that my ELO is incorrect. I do however know from personally experience that 300 points in either direction makes a very small impact on my win/loss or KDA ratios. The vast majority of my games are obviously determined by the weighted system, as one can observe by checking the average team ratings in the score screen after the game.
Insightful, and cannot be refuted =P


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sn3aks

Senior Member

06-04-2011

Quote:
Originally Posted by DuffTime View Post
Insightful, and cannot be refuted =P
yup the trolls who insits match making works are just trolls


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LoLasagna

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Member

06-04-2011

Quote:
Originally Posted by CyraLoL View Post
The common example of why this does not actually work the way you think it does is that say for example you flip a coin one hundred times. The chance of getting 99 tails and 1 heads is actually the exact same as getting exactly 50 heads and 50 tails
ಠ_ಠ

http://en.wikipedia.org/wiki/Binomial_coefficient

Chance to get 50/50 is like 10^27 times more likely than 99/1.


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Loptyr

Senior Member

06-04-2011

Quote:
Originally Posted by CyraLoL View Post
This is sorta true, but makes assumptions about probability that are just not necessarily true.

The common example of why this does not actually work the way you think it does is that say for example you flip a coin one hundred times. The chance of getting 99 tails and 1 heads is actually the exact same as getting exactly 50 heads and 50 tails. While the system you mention is a weighted average, thus more likely to trend, it still far far far from statistically impossible for someone to move vastly the wrong direction in a hundred games.
Quote:
Originally Posted by CyraLoL View Post
The common example of why this does not actually work the way you think it does is that say for example you flip a coin one hundred times. The chance of getting 99 tails and 1 heads is actually the exact same as getting exactly 50 heads and 50 tails.
Quote:
Originally Posted by CyraLoL View Post
The chance of getting 99 tails and 1 heads is actually the exact same as getting exactly 50 heads and 50 tails.
Where the hell did you learn probability from?


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MTaur

Senior Member

06-04-2011

But oh noez, I want the president of Riot to come over to my house and watch me play a few games and make a patch that keeps my Elo above 1400 at all times!!!


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MTaur

Senior Member

06-04-2011

Just kidding. I haven't started ranked games yet. May hold off a little if they're planning a reset soon, idk. But yes, I know a little background theory in stats, and laws of large numbers ain't be lyin'.


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