Change in ELO system: Why ELO should only be for 1v1

Introduction
With the update to the ELO system that came out a while back, it seemed as though the system was fixed. No one had any absurdly ratings anymore; it was stabilizing towards a normal distribution. However, recently some of the ratings have begun to escalate, clearly because some players are finding others to let them win in large games. Thus, we get some ELO ratings that are an inaccurate representation of skill.

Math and Chess
It is important to understand the math behind this system. Obviously, when a person wins they gain points and vice versa. Typically, like in SSL, the average player will have a rating of 1200. In chess, players with an organization such as FIDE are given a rating that is close to an average of 1200. In reality it is a bit higher, but more important than the mean is the distribution of scores. In chess, the typical standard deviation is around 400. A z-score of 1 equals 1 standard deviation from the mean. Here is a table to help understand:
(z-score/rating/percent of players above)

• -3/0/100%
• -2/400/97.725%
• -1/800/84.135%
• 0/1200/50%
• 1/1600/15.866%
• 2/2000/2.275%
• 3/2400/0.135%
• 4/2800/0.003%

Currently, there are 12 or so Grandmasters (rating >2800) in chess in around 500,000 ranked players. This corresponds to .00248% (close to the ELO model)
You may notice that the ratings in SSL don't match up too well to this. This is because all players start at 1200 (average score). It would take a lot of games to lose to get to the lower ranks, however the average rating remains around 1200 (a ton of 1000s and 1100s cancel out all the scores above 1200).

So what is the problem with SSL's system?

Gaining rating through games with more than 2 players
Well you can probably guess it by the title. Gaining rating through larger ffa games is way easier than 1v1s. Players are able to gain points way easier than the ELO system intends. This is especially true if players can convince a few of their friends to constantly let them win. I won't say any names, but it is obvious this is happening. Through this method, after a relatively short amount of time, a player can get their rating in the high 2000s. To show you why this is wrong, let me provide an example:

A player gained a rating of 2800. He then decides to play a player with a rating of 1800. According the rating, which is supposed to model the player's skill, how often should the better player win? 75%? 90%?
Nope, 99.7%. Alternatively, in a 300 game series, the better player would win 299-1 on average.

Think about a player ranked 1800 and one ranked 2800 in SSL. Do you think the player rated 2800 would win 299 out of 300 games against a player with a rating of 1800? (The answer is not even close)

Back to chess, why ELO only changing after 1v1s would be ideal
There are two main reasons why this is a good idea.

1. Prevent quick skill rating increase by playing weaker players

Think about a chess player just starting out with a rating of 1200. If he wanted to play his buddy who was just starting also until he got to 2500, how many games would he have to play? Hint: its much greater than a million. This is obviously ridiculous, so how does he get to his goal of 2500? He plays players with higher rating. This is how it should be. Therefore, the only way to actually get to 2500 is if he was actually a top .1% player.

2. Prevent players "giving" rating to their friends

Like I said before, this is obviously going on. Get a few friends who don't care about their rating in an 8 person game, and have them let you win every time. If ELO was just changed to 1v1s, this would be much harder to do. His friends rating would drop at a much quicker rate, so much so that it would be incredibly inefficient. Unless he has 100s of willing friends to sacrifice their rating, this would not work. To realistically get past around 1800, he would actually have to beat other good players which was intended.
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Summary
Because ELO is affected by ffa games with more than 2 players, players can very easily increase their rating to a point where the ratings have lost their meaning, as it is no longer an accurate representation of true skill. By changing the system to only 1v1, players would only be able to rise higher up by beating good players, not by their friends giving them rating or winning games where they are a much higher level than everyone else.

*Note, I didn't show a lot of the math because of space but I can put it into the comments if need be

 

Great summary and glad you posted this. It needed to be brought up considering kChamp once again didn't fix the problem fully.

If the system is purely 1 vs 1 like you suggested it would more fairly and more accurately represent the term "skill" in this context related to SSL then it is currently.

Also it more fairly couldn't be abused as the current system can be.

As always amazed by your take on things and mathematical way of reasoning on matters.

 

Was wierd i actualy payed attention to rating for once yesterday i played 1v1 with my friend for about an hour, we both started at 1721 after about an hour i lookd at our rating and it was 1711 each. So eventually everyone will have 0 skill rating.