Initial Elo and ‘fresh account’, provisional matches and ‘soft reset’

DISCLAIMER: Due to the hidden policy of Riot Games on these issues (MMR related issues[1]), it is impossible for a third party to claim any fact regarding the issues. This post, on the same spirit, is not to claim: “this is what Riot has been doing or used to do”. The purpose of this post is to provide a probe on how the system works, by providing the strict reasoning – which in my opinion is the optimizational method for the system to work properly.

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In the post regarding the issues of MMR/ Elo and LP, we discussed the principle of the methods used to rate League players (to establish the table of standings). To understand the principles is one problem, to interpret the table of standings obtained is an other problem. The later (how to interpret the table of standings) provides very important interests of us, the summoners, like:

+) The initial Elo and fresh account (who never play a certain queue, ranked queue for example): How is this initial value assigned?

+) Soft reset: How is Elo reset for a new season?

+) Provisional matches, and the like.

As the final record of players' skill levels on playing League (all players as a whole community), the table of standings would provide us critical insights of ourselves in relation to other players as a whole, if we can interpret it the right way. This work (interpreting the table of standings), however, may invoke many complicated concepts, and in this post I will try to provide some view on these issues – in the clearest and easiest way as I can do, and use fewest statistical concepts possible.

These concepts (soft reset, provisional matches, fresh account, initial Elo,...), on one hand, are the "League concepts"; on the other hand, they are also the concepts of statistics; on yet an other hand[2], they also are the concepts of daily life (how to rate people on their work of doing something). In other words, there are three different angles of view to look at these concepts; each way of view gives us different information about the issues. To be able to look at the concepts from the different points of view would give us a complete and full understanding of them.

1. Elo spectrum (the distribution of Elo indexes): the bell curve

First off and very importantly: the Elo spectrum has the bell shape.

In a perfect case, the bell curve describes a distribution in which almost of the values (like 70%) are somewhat at the center of the bell: the average value or the median value (M). The remaining portion (like 25%) distributes equally on the both sides, decreases when the tails advance towards the vanishing point(s) of zero. This kind of distributions plays a vital role in the natural as well as social world, including Elo spectrum of League players.

This claim can be seen as the origin of all my discussion on this post, and can be seen as the origin of all the issues relating to the concepts of initial Elo, fresh account, provisional matches,...

To claim this is easy, to prove it is very difficult (without using complicated concepts of statistics, which is unnecessary for us, the summoners). So, I will illustrate this via two exemplary models which have the same nature with the Elo spectrum; it would be easy to accept that due to the similarity of these models, the Elo spectrum must fall into the same category of distributions: the bell curve.

The acceptance of the truth is very important. However, no one can accept what is so-called the truth if it is not proved strictly without even one single flaw. So at the end of this section, I will provide some reasoning which can be used to prove it, for people who want to go until the final limits of the truth. All of these, although is necessary for people to accept the truth, is not necessary for us (the summoners); so if you don't want to check the reasoning, simply accept it and ignore the spoiler part and go to the next sections.

Exemplary model 1: distribution of grades of students

This is one kind of distributions which falls into the category of bell curve. More exact the teaching and training as well as the rating processes are, more bell-like curve will be obtained for the spectrum of grades when the number of students increases. This proven theory is used very popularly, in education and pedagogy for rating learners for example.

In the ideal scene, if the grades are rated on the 5 scales (A, B, C, D, and E) for example, a large number of students would fall into the range from D to B, while a very small groups would get A and E.

Exemplary model 2: distribution of IQ indexes (Intelligent Quotient[2])

Although many people may argue or doubt or disagree with many aspects of this index for rating intelligence, almost agree that the spectrum of IQ distribution must have the bell curve shape to exactly describe the phenomenon.

In many standardized IQ tests, the average value or median value (M) is normalized to be 100 IQ.

Elo spectrum of League players

Reasonably, we don't have to say much more to see the Elo index, just like the two examples of grades and IQ, must fall into this category of distributions: if it exactly describes the phenomenon and really reflects the skill levels of players on playing League.

Some bell curve distributions. (1) When we organize the values into smaller ranges, the curve will be come the bars, like in the two upper images. (2) Many distributions, due to different reasons, don't have the exact shape of a bell, but somewhat similar, like the two bottom images.

Both of these cases (regarding the bar-style organization and the ugly bell shapes) may be applied for League: Divisions and Tiers may be organized into the bars, and the bell shape may be changed accordingly, when the bars are changed by changing some parameters in the algorithms for example.

The scientific theory

Scientifically, we can use theories of probability and statistics to prove the truth: Elo index obeys the distribution of bell curve. I will point out the major characteristics of the Elo index which will scientifically prove the fact. To do that, we will consider the Elo values of League players as discrete random variables, and the set of all the players' Elo(s) as the set of discrete random variables.

+) These variables are independent. Although each game consists of ten different players, each player must in fact determine the result themself, especially when the number of games they play is large enough. For more clarity, after hundreds or thousands games, for example, a player's skill level is what defines the player's Elo, independent from all the other players they played with in the games. Elo value represents a player's skill level; consequentially, it is independent as well.

+) Each of the value of the variables is in fact a sum (or average) of the independent variables. Since the Elo of a player is obtained through many games, it is subtracted and added many times to have the final value. The final Elo of a player, so, is in fact a sum of many Elo values.

+) The variables are identically distributed, since they have the same probability distribution (or the same probability mass function): their values are always found within the range from the minimum Elo to the maximum Elo with the same corresponding probability for every Elo within the range.

+) The variance is finite: the average value of the squared deviations of the Elo values and the arithmetic mean of the Elo values. All of these numbers can be calculated, so the final value or the variance is able to calculate: it is finite.

These four characteristics, according to the central limit theorem[3], ensure that the distribution approaches the normal distribution when the number of variables grows, or the Elo spectrum has the bell shape when the number of players is large enough (the number of few thousands would be considered to be "large enough" in this case, let alone the number of millions).

2. Initial Elo and fresh account, provisional matches

Initial Elo

No matter which methods and algorithms are used to calculate the Elo indexes, the calculations must have a number to begin: we cannot begin from nowhere. When we start playing a certain queue (ranked queue for example), we must be assigned an initial Elo number. How is this initial Elo assigned?

One of the best initial values is the median value or the average value obtained from the bell curve of the Elo spectrum[4]. Why? Since this is the average Elo of all players, it would be fair for all players to have the same value as the initial one for the process of being rated.

However, since this initial Elo is the same for every player to begin; on one hand it would be fair; on the other hand it may least exactly reflect players' skill differences: different players must have different skill levels, more or less. Those whose real skill levels are higher than the median will gradually climb towards the top, while those whose real skill is lower will finally drop down.

The initial Elo, consequentially, is not the most suitable value for every player to begin: it doesn't reflect the differences in skill levels of different players, as well as the direction a player would go for the coming games.

Provisional matches

One of the best ways to have a more exact Elo value for each player is to adjust the initial Elo via a certain set of "initial games"; the number of these initial games must be enough to see more information about the player: the difference in skill level in comparison with the initial Elo and other players, the trend the player would go for the coming games: advance or fall down. These games are called "provisional matches" in League and include ten games in total.

Initial Elo value and provisional matches together will provide the beginning Elo of a player to be rated in playing League. This "beginning Elo" is the adjusted value of the initial Elo by the ten provisional matches: it is different for different players, so more exact reflects the differences in skill levels of different players, and somewhat reflects the trend each player will go for the coming games: up to the top or downwards.

For the best of the purpose (to see the most difference possible of each player's skill level as well as the trend for the coming games), each provisional match should weight much more than a regular match. In the meaning that a winning or losing game should give a huge amount of Elo exchanged (added to or subtracted from the player's Elo). No one but Riot Games knows how much weight these provisional games are, but it must be like five times greater than a regular game (and the ten provisional games might be equivalent to like fifty regular games, for example).

Fresh accounts and soft reset

The players who (or more exactly, the accounts which) have never played a certain queue (ranked queue for example) are called "fresh accounts". The process of assigning the initial Elo and obtain the beginning Elo is applied for all fresh accounts who have just started to play a certain queue (ranked queue for example).

For the accounts which are played many games (more than the ten provisional games), obviously, their Elo much more exactly reflects their skill levels. So, it should be best to use their Elo of the previous season (instead of the initial Elo as fresh accounts) to obtain their beginning Elo for the upcoming season.

The process of obtaining the beginning Elo for the upcoming season based on the Elo of the previous season are called "soft-reset" in League. If the process uses the initial Elo of fresh accounts for all players (including players who did play many games in the previous season), the process is called "hard-reset" in League: in hard-reset, all players' initial Elo will be reset to be equal and to be that of fresh accounts.

Just like all other competitive games (tennis, football, etc.), League's Elo indexes and table of standings must be reset for a new season. This process (soft reset) is to compress the Elo spectrum towards the center point of the spectrum (the average value or the median value of the bell curve). So that all the players will start the new season in a reasonable basis.

3. Some special conclusions

The average Elo value or the median Elo value may change slightly for different seasons, and the trend of changing would be increasing since all the players may get better over time. This means, if the median Elo for the first season is 1200 (for example, which may be equivalent to silver V of the first season), the median Elo for the sixth season may increase to 1300 (silver IV of the sixth season, for example).

The soft reset should more exactly reflect players' skill levels in comparison with hard reset, since it is based on the Elo the players got the whole previous season. The hard reset, which puts all players at the same initial Elo, would bring topmost players into the games with lowest players; this is obviously not a good idea. That should be why Riot Games always prefers a soft reset for a new season.

Due to the compressing nature of the process, basically after the soft reset, very low-rated players at the bottom of the spectrum would receive a higher Elo, while very high-rated players at the top of the table of standings would receive a lower Elo (in comparison with their Elo of the previous season). And the players somewhat at the center of the spectrum would see least or even no change in their positions.

Finally, by changing parameters of MMR rating algorithms, Riot Games can vastly change the shape of the curve of the distribution. No matter how enthusiastically and curiously people want to know about the true shape, they have their own reasons for the hidden policy:

+) If the shape (of the computational MMR values) is really the bell curve (as that of the theoretical Elo indexes), that means their methods and especially their MMR system's theories and algorithms are very exact in scientific meanings.

+) If the shape is not like the bell curve, that means their methods and theories and algorithms have critical flaws.

In both ends, on business perspective, they are definitely right to hide the MMR index: no matter whether it is to hide their business secrets and achievements or their flaws. They design the system, so they possess the rights on how to use the system.

This post was completed; there would be just minor adjustments if any on this post
Last update: February 08, 2016

The Silencekeeper

References

[1] For the purpose of this post, the term "Elo" will be used in almost of the discussion (instead of the term "MMR"), in the meaning that it is the theoretical value of Elo: which, in theory, truly represents players' skill levels. MatchMaking Rating system is designed to be expected to be able to calculate this theoretical Elo, and "MMR" is the computational value the system actually obtains.
[2] Of course, we only have two hands, ikr! xD

[3] For more details: https://en.wikipedia.org/wiki/Intelligence_quotient (section Current Tests)
[4] For more details:
     https://en.wikipedia.org/wiki/Central_limit_theorem
     https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables

[5] This value is estimated to be around 1200 in League (which is equivalent to the Divisions of Silver V or IV or III); however, this cannot be verified due to the publisher's policy.