40% Trolls vs 50% Trolls: Is it Really True?

When the cries of Elo Hell over ran the Reddit / Forums, a group of Scholar summoners brought forward the 40v50 idea that calmed the storm...

Alright, enough big openings lets get straight to what this blog is about: the validity of that 40v50 claim. To begin with, the name "40v50" is how I usually refer to the theory where "Assuming you, as a player, are not a troll/feeder/rager/disconnecter then your team has a 44% chance of getting a troll compared to the 56% chance the opponent has. Hence, you will always get to your 'true elo' eventually". This is often stated to invalidate the idea of Elo-hell. 

But is this claim 100% true? 

So What is Wrong?

Something can be right in most cases, but still be wrong in that one specific case...

The largest problem with this claim is the part "Eventually". To anyone who knows a fair amount of statistics, the Large number theory should be fairly familiar. For anyone who doesn't refer to the wikipedia site on it - Law of large numbers. According to the Large Number theory it is possible for a 'small' sample size of data to be skewed. 

It should be very clear by now then what is wrong with the claim. A person who has only played 10, 50, 100, 300 or even 1000 games could experience a skewed percentage. This is because there is no definition for what is a 'small' or 'large' sample size. 

So according to the large number theory, it is possible for the percentage of troll/feeder/rager/disconnecter (s) in your game to be as high as 80-100% when you don't have that many games yet. The curve will slowly be smoothed out with every few games you play. Since there is no set rate for 'smoothing out' it is possible for this % to stay high for a few hundred games. This is, where "Luck" kicks in. 


"Win more games with the Kage's Lucky Pick item Kage's Lucky Pick!" - Item promotion video on the Rift

So this is the true point I've been hinting at all this time, the factor of "Luck". This is what I believe to be one of the very important factors of games on the Rift. 

1. You are "Unlucky" for having troll/rager/feeder/disconnector (s) in 90 out of the 120 games you have played. 
2. You are "Lucky" for having only 1 troll/rager/feeder/disconnector out of the 20 games you have played. 

Luck is the ultimate factor aside from your skills that can influence your chances of winning. 

But Wait... [Warning!]

"But wait...what about taking Baron?" - Random Teammate

But what about "skill"? Skills are still the only factor in which you can influence your chances of Victory in your games.  While "Luck" is a huge factor, "Skill" is still the only factor you have control over that influences your chances of victory!