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The Mathematics and Psychology behind "Elo Hell"

In this post I will explain the mathematical reasoning behind why elo hell does not exist, then I will explore the  psychological reasons behind why people think it does, and finally I will conjecture as to the effect that the concept of elo hell has on the game and explain my reasoning as to why I belive the concept needs to be ejected from the public concisness.

Yes I just put an abstract onto my blogpost about League of Legends, I am a true nerd.

The concept of elo hell is that there is a range of elo, normally centered around the 1200 elo mark, where due to the abundance of trolls and bad players it is almost impossible to raise ones elo past without luck.  This elo range is viewed as a virtual mine field of bad players, afks, and trolls.  So the fist question we must ask ourselves is what makes this elo range so special.  In elo 1200 is the starting point for all new players so the area around it and is the average point representing the largest portion of players.  Now in elo it is assumed that if both sides have the same elo they are equally likely to win and while this is more or less true at most elo's the 1200 hundred range is a special case as there is going to be high skill players and low skill who have yet to reach their proper elo playing with and against one another.  This means that it is much more likely for games in this elo range to be decided by one player, either by having that player feed horribly or carry tremendously.  At higher and lower elo ranges the individual skill levels between the players is not as wide ranging so the results are more focused on the team as a whole rather than the effects of one player on said teams.  Now this does make it seem like there is an elo hell and that players there are just at the stuck, completely subject to whims of the matchmaker, but this is not the case. 

Note for this next section I am going to be refering to two types of elo, a players real elo and a players skill elo.  Real elo is the player actual elo, skill elo is the representation of the players elo assuming he has played an infinite number of games at is current skill level (meaning it represent his acutal skill) and will be shortened to s-elo.  We are also assuming that the players s-elo is static and never fluctuates.

First let us look at 10 players, 9 of these have s-elo of 1200 and the remaining one has an s-elo of 100.  These 10 players play 100 games against eachother and are randomly assigned teams each time.  Whichever team has the 100 s-elo player always loses.  After 100 games the 1200 elo players should have averaged around 56 wins a piece.  This is because for each 1200 player there is only a 4/9 chance he ends up on your team.  This means that the existence of low s-elo players in elo hell has actually raised the elo of everyone else.  This math holds true for all the elo hell excuses for every 4 games you have lossed because of bad players, disconects, or trolls you have won 5 due to the same thing happening to the other team. 

Next we are going to look at a modle that represents the mindset of those who say they are in elo hell.  Lets look at 10 new players 8 have an s-elo of 1200, 1 has an s-elo of 100, and 1 has an s-elo of 2300.  For simplicities sake we are going to assume that the 2300 and 100 elo player cancle eachohter out, so that if they are on the same team there is a 50/50 for either team to win.  Again we put them through 100 games with randomly assigned teams each time and this time we look at the higher elo player.  First of all he again has the 56 free wins from having the low s-elo player on the other team, in addition he has 22 more wins from the times when the did have the low elo player on his team.  Now if we again ajust this modle so that there isn't alway a troll in the game the high s-elo player wins even more often.  Any more adjustments you make to the model continue this trend high s-elo players rise out of elo hell low s-elo players fall out of it.  The only effect of elo hell is actually a quickening effect making players move their real elo toward their s-elo slightly faster.

If this is the case then why does the myth around elo hell persist so strongly.  The answer to this question has to do with psychology.  The primary reasons behind the myth are memory space, ego, and pattern recognition.  Memory space deals with how your brain store information, you don't really remember all the times where the game plays like it was expected and you win or lose without any remarkable circumstances because these games don't carry any significant emotional impact, they just give you a small feeling of satisfaction or disapointment depending on whether you won or lost and you move on.  Games where you lossed because of a particuarly unskilled player, disconect, or troll on the other hand take up a lot of memory space so when you think about your last few games you are more likely to remember these ones.  Also since people go into most games assuming that they will win, wins in general take up less memory space.

Which takes us to our next point ego.  Ego is what it sounds like, LoL players as a group think they are more skilled then they are and are unwilling to except that their elo might be low because of themselves rather than their teamates.  Saying that they're stuck in elo hell allows them to shift the blame for their lower than desired elo to an unidentified group of people,  which is much easier and often feels better (note there isn't anything really wrong with that assuming they don't abuse other players because of it, it just hurts how likely they are to improve).

Finally humans as a species have evolved to look for patterns, this pattern recognition is an extremely powerful tool that allows us to make preditctions of actions before they happen, and have enabled math, science, and technology and allowed us to become the dominant speices on the planet, all in all it is pretty awesome, but it gives us issues with comprehending randomness.  We are fantastic when their is a pattern to be seen but when looking at actual random data, especially random data we don't like we attempt to find a pattern in it and make connections (this is actually the same phenomenon that causes conspiracy theories).  Thusly when looking back at your losses you will see a group that are decided by the actions of other players you connect them and decide that these are the primary cause of your dificulties raising your elo, not bothering to check on how they effected your wins.  It can get especially bad when you lose multiple times in a row for the same reason.

So that is the reasoning behind why elo hell is believed to exist and why it doesn't mathematically, lastly lets look at the effects of the concept of elo hell existing.  The only real effect is that the people who are stuck in elo hell are less likely to attempt to improve their play instead deciding that their elo is out of their control.  The secondary effect can be feelings of frustration which can cause players to lash out at other players,  which according to the data given by Riot lowers win percentages, and as a result elo, significantly.  This also can result in these players being more likely to be banned.

TL;DR/Conclusion:

The concept of elo hell is based entirely off of psychological reasons with no mathematical bearing and it only serves to hurt the game experience of the player base as a whole.  This myth should be layed to rest and forgotten as it isn't true and it has no positve effects upon the game.

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