Since elo systems work on a same basis, I have this post from another game that could explain how elo works, it explains why sometimes you gain more elo and sometimes you gain less. I do not believe there is a way to find out your actual elo, as most games hide them away.
First, let's begin with an explanation of the Elo system. I think it
would be good to cover what your Elo rating tells you, and what it
doesn't tell you.
An Elo rating IS NOT a measure of your skill level. Every single
complaint or suggestion about how it is unfair because you might be
more skilled but still lose points means you do not even understand
what the system is trying to measure.
The Elo system, and therefore your Elo rating, is a measure of "odds".
The Elo system was designed to give a metric that can be used to
determine a player's chances of winning. For example, two players with
exactly the same Elo rating have a 50/50 chance of winning the match.
This spread was originally designed logistically, such that a
difference of 200 points, regardless of values, would give the higher
player a 75% chance of winning (ignoring the possibility of a tie).
It is important to note that there is no point on the scale where you
are guaranteed to win. This is especially true of people who are in
the middle section (a.k.a. roughly average). Your chances to win do
not fluctuate very much, and therefore it is expected that you will
lose about as many games as you win.
WARNING! Scary Maths Incoming:
To calculate my chances of winning, based on known information, let's
look at an example. Since I like to play AD Carry, I will calculate my
chances of winning against my favorite AD Carry player aphromoo.
My Elo after the season 2 reset: 1270ish. aphromoo's current Elo:
2290ish
The formula to determine expected score is given as 1/[1+10^((Rb -
Ra)/400)] Where Ra is my rating and Rb is their rating.
Based on the above Elo ratings, I would have a 0.28% chance of
winning.
Alternatively, aphromoo would have a 99.72% chance of winning.
I can already tell that I'm setting myself up for massive whines by
using an example of 1 player against 1 player to explain Elo, so I
suppose now is the time to explain why the Elo rating works for League
of Legends, even though it is a 5v5 game.
It is impossible to measure your individual skill exactly. Your skill
can only be inferred based on your ability to beat other players. The
matchmaking system in League of Legends takes 10 players of similar
Elo ratings and splits them into two groups with team averages as
similar as possible. This is, indeed, a fair way of splitting people
up into teams. Two teams with similar average Elo ratings will have
approximately a 50% chance of winning.
Here's another example to demonstrate:
If I were to average the Elo of the 5 people I play with most often,
we would have an average Elo of 1176.
If I were to take the average Elo of the 5 members of team FeaR, they
have an average Elo of 2159.
Therefore, the expected chance of team FeaR winning would be 99.65%.
As everyone expects, we would probably get completely crushed in every
lane and it turns out that averaging the five Elo ratings of the
players gives a good estimate of who would win a 5v5 matchup.
================================================== =========================
Now, it's time to address some complaints about the Elo system.
Why does the thread title say "almost perfect" if everything works
fine?
Well, there is a slight problem with the Elo system as it is
implemented in League of Legends. The problem, though, is not the one
that you all think it is, nor is it a problem that has that big of an
overall effect on your individual rating. Really, I shouldn't even
call it a problem, but more like a potential slight improvement which
is likely hard to code and probably exploitable by some of the more
"clever" summoners.
The League of Legends Elo system uses k-values (a.k.a. how the system
determines how many points you gain or lose) that are mostly fixed
values based on how many games you play. The only real way to improve
on this would be to have a larger k-value for games which are
completely one-sided stomps.
To illustrate, a game where every lane gets beat, one team gets all
the dragons and barons, and completely crushes the enemy team, even
taking the nexus before the 20 minute surrender mark, the winning team
is clearly significantly better than the losing team and should move
up more than in a close game which drags on for 60-70 minutes.
There are a number of things that the variable k-value could be based
on, however I believe that a scale based on the difference in global
gold and game length would be the most fair.
What about leavers and trolls?
Every player at every Elo has to put up with leavers and trolls. I
genuinely believe that leavers should get an increased Elo loss while
the rest of the team should get a slightly reduced Elo loss, but again
it would have little overall effect on your personal score, but would
rather move chronic leavers to a lower Elo at a faster rate.
Also, over time, the enemy team will have as many leavers and trolls
as your team, so it really balances itself out.
I don't believe my Elo rating is accurate. (I think I'm better than it
says I am).
Play more games. Even with the above mentioned "flaw" with the k-value
system, over time you WILL get to your true Elo. More than likely
though, you will have to accept the fact that you are not as good as
you think you are. Most people are, in fact, average.
Finally, I will address what is perhaps the only legitimate complaint
about the League of Legends Elo system.
Many people around the starting Elo (1200) have not reached their true
Elo yet because they have not played very many games. This problem
would not be solved by measuring individual skill, nor can it be
completely solved with k-values based on the rate that new players
join the game.
It is a problem that cannot ever be completely solved, but could be
slightly alleviated by increasing the number of placement matches by
at least double.
It could be further alleviated by adjusting the placement matches to
measure more statistics than a simple win/loss measure.
Also, and this would absolutely help the situation, people doing their
placement matches should not be allowed to duo queue, and should be
completely segregated from the rest of the ranked population. I
personally remember teaming with and against players who had ~100+
wins while I was doing my placement matches, and remember dominating
at least three players who were currently doing their placement
matches. I can only speculate, but I believe the match ups were
directly related to duo-queueing.
These changes would, again, have a minor effect on your true Elo
rating after several hundred games, but would make it slightly more
enjoyable to play ranked matches if your true Elo was actually around
the 1200 mark.
A quote from later on in the thread
"More experience than the hundreds of games it takes to even get to
level 30 to play ranked? I'd contend that if anything, players should
be required to play a minimum number of Draft Normals before queuing
up for ranked. A change like what you're suggesting does nothing for
the integrity of the system and can actually work to worsen it's
effectiveness."
To summarize, the Elo rating system works very very well for League of
Legends with a few minor flaws. The Elo rating does indeed give a
fairly accurate measure of your chances to win against other rated
opponents, and this accuracy extends very well to 5v5 matches.
There are ways to make slight improvements to the actual matchmaking
(i.e. the process of selecting and placing 5 players on each team) but
these changes would have very small effects on individual Elo ratings.
Certain system changes would make ranked slightly more enjoyable, but
overall people are upset over the system because they believe they are
better than they actually are.
I hope I was able to help you all understand the Elo system a little
bit better, and hopefully you all will direct those who need some
clarification to this thread so that they may learn a little bit about
math.
Best Answer
It's a custom Valve's variation of the Elo Ranking System and no official documentation has been released.