Issues of MMR/ Elo and LP (League Point)

You love League! No doubt.

That is why you have decided immediately to read this post once your eyes catch the title: a kind of the most fundamental, basic, exciting, secret, ambiguous, and... complicated – but also a kind of by far  the most familiar, regular, boring, popular, unclear, and... simplest issues on playing League. On one hand, we have to deal with them every day of playing League; on the other hand, we almost have no certain understanding of them: nothing about them is ever published or confirmed by the Publisher – Riot Game(s)[1].

How should we deal with the paradoxes? How can we know what we want to know, master what we want to master, improve what we want to improve,... if we have no certain understanding of them? Anyways, “every problem always has more than one solution”[2], at least in my opinion. And in this post, I want to try to cast some light on these issues – my way, my own solution. So, let's start our journey!

Introduction

Like other competitive games (chess, tennis, basketball,...), one of the most important interest for us is to have an exact table of standings, to be able to see how good or bad we – or other players or teams we love or “hate” – are in comparison with others. While the problem of establishing such standings for single competitor versus single competitor (two-player) games (like chess) is not so easy to do (and the situation for establishing such standings for teams in team games is somewhat similar to that of two-player games, when we consider a team just as a single player of the game), the problem of establishing such standings for individuals of team games like basketball and football would be by far the most complicated issue of the field.

For the nature of the issue, say, you can kinda easily agree that at a certain time, Roger Federer or Novak Djokovic is the number one in tennis, and quite the same for Barcelona or Manchester United in football; however, to say "Messi or Ronaldo is the number one in football" is a completely different issue. Unfortunately, the situation is applied for us (the summoners): we can say a certain team is the number one in a certain region at a certain period of time, but to say "some body is the number one (in a certain region at a certain period of time)" is a different problem.

So, the question is how we are rated on playing League? How we gain and lose LP (League Point) and how we are put in Divisions and Tiers? How the standings for individual summoners can be established? Prior to the second season, League of Legends used an Elo system for rating players[3], and we will start with the famous rating system: Elo rating system, to answer the questions.

1. Elo rating system

Elo is a rating system named after the author Arpad Elo[4], a chess master and a Hungarian-born American professor of physics. Elo was originally created for rating chess players, but then gradually adopted to use for many games. The term “Elo” is now very popular in many games to indicate the rating of players in comparison. The most fundamental principles of Elo rating system are[5]:

(1) Each player who is rated is represented by a number (the Elo); the Elo number then will change based on the outcomes of games with other rated players.

(2) For each game, the winner takes points from the loser.

(3) The difference between the ratings of the two players determines how many points will be exchanged:

+) For a particular game, the higher-rated player is expected to win. So, if the higher-rated player does win, he only takes less points from the lower-rated player. If the lower-rated player makes an upset win, however, the player takes many points from the higher-rated player – much more than those he would be taken by the higher-rated player if he lost.

+) Particular in chess, the lower-rated player also takes few points from the higher-rated player for a draw (a tie).

At this point, I think those are enough for us to have an idea of what is a rating system and what is the Elo rating system in particular. More details and deeper analyses on this matter may be not necessary and may have to invoke much more complicated issues which may be uncertain for me myself.

2. MMR (MatchMaking rating system)

Obviously, using an Elo rating system designed for two-player games like chess for a team game like League of Legends is not that much effective, for many reasons (which we may discuss at an other time). That would be why Riot Games must design their own rating system for League of Legends, and the rating system is named “Matchmaking rating” system (MMR).

So, first of all, MMR stands for MatchMaking System – the rating system Riot designs and use for League. Consequently, in League we must use the term MMR for more exactly, but due to the popularity of the term “Elo”, the two words are always used in the same meaning in League: to talk about the particular numbers representing the skill levels of players in playing League, measured by the MMR system.

Now, we should probe the main characteristics of this MMR system for our main purpose: to have an idea of how our skill on playing League is measured. According to Riot Games[6]:

+) The goal of the MMR system is to create games which is as fair as possible, so that the chance of winning for the both teams would be equal (50%).

+) The process is described in three steps: (1) determine strength of players, (2) determine eligible opponents, and finally (3) build a match. With adjustments for whether the players are solo or pre-made and some protection for new players.

+) Players have a separate MMR for each queue, developing independently from each other.

+) Initially, the system only matches players of similar MMR. The MMR difference then will be slowly increased to some degree.

3. League Point (LP), Division, and Tier: the table of standings

With all the basic knowledge of the rating systems, it now should be easy for us to have a clear idea on the issues we interest most: Division and Tier, LP.

+) Based on MMR, a player will gain or lose a certain amount of points for a winning or losing game; these points are called League Points (LP). When a player reaches a little bit more than 100 LP, they will reach the higher level and their LP will be reset. These levels which are equivalent to a little bit more than 100 LP are called Divisions.

+) When a player overcomes the fifth division, they will be put in the next higher stage (and their division and LP will be reset). These stages which are equivalent to 5 divisions (about 500 LP) are called Tiers. There are 7 Tiers at the moment: Bronze, Silver, Gold, Platium, Diamon, Master, and Challenger.

We can say that, Riot Games uses these concepts (LP and Division and Tier) to organize the table of standings of League players rated by the MMR system. This is “the table of standings” of League players on the bottom line.

Some important conclusions

The Elo, or more exactly, MMR index of League players (which is rated by the MMR system) is hidden by Riot's policy; until now, it is not officially publicized. Consequentially, all other sources which provide what is so-called Elo or MMR of League players are not official, and definitely cannot use the rating system Riot Games designs – the MatchMaking Rating system (MMR system) due to copyright issues. They can, however, use an other and somewhat similar to the MMR system developed outside of Riot Games. In other words, the "Elo" index other sources provide cannot be called "MMR".

+) The MMR for each queue develops independently, but this doesn't mean that the initial MMR for each queue is treated in the same way, especially for fresh accounts which have never played a certain queue yet. This is unclear.

+) Gradually, the MMR difference would be increased; this means more many games we play, more different players we may meet: may be very higher-skill players as well as very lower-skill players in comparison with ourselves.

The LP gained and lost should be calculated in somewhat the same way with Elo and MMR. This would be the reason why we may gain or lose very different amount of LP for different games. In addition, if we win many consecutive games, the system should match us with very higher skill players; consequentially, the LP gained for each winning game would be very large, while the LP lost for each losing game would be very small: since the opponents are supposed to be rated much higher than us, on the Elo perspective. The opposite dimension would be, in case we lose many consecutive games.

+) It would be a big problem for smurf accounts: it should be very hard to determine a new account is a smurf or not on the internet world of anonymity. The same issue if very high skill players play accounts of low skill players for certain purposes.

Finally, although LP and Divisions and Tiers reflect the standings of us on playing League, the most fundamental index – which would exactly describe how good or bad we are on playing League – is not LP or Division or Tier. That is MMR index, which is hidden by Riot Games' policy. Consequentially, it should be best for us to deal with the MMR index rather than focus on LP or Divisions or Tiers: on the perspective of rating systems, these concepts (LP and Division and Tier) don't convey any meaning. But this is a different problem, I guess!

This post was completed

There would be just minor adjustments if any on this post

The Silencekeeper

References

[1] “Riot Games” (plural form) but they have published only one game so far, right?! xD
[2] For more morals from League: Morals from League
[3][5] According to wikipedia.org: https://en.wikipedia.org/wiki/Elo_rating_system
[4] For more details: https://en.wikipedia.org/wiki/Arpad_Elo
[6] From the official guide at: https://support.riotgames.com/hc/en-us/articles/201752954