Rating systems description

There are two rating systems in use in Block. The Level system and the Elo rating system.

Only games played by different users count for rating purposes (this means, games where the same player controls both the light and dark pieces do not count for rating).

Level System

The Level system is a way to incentivize players to challenge (and win) stringer palyers, by gaining level faster. It works in the following way:

• All players start with Level 1 and 0 point of Experience, these being the lowest possible values.
• By winning a game, the winner gains Experience equal to the level of the loser (this means, if you defeat a level 5 player, you win 5 points of Experience). Nothing happens to the loser.
• You can go up more then one level per game if you have gained enough Experience to do so.
• The relationship between Experience and Level is that of an arithmetic series. In order to go from one level to the next, you have to gain Experience that is double the current level's value. For instance, if you are at Level 2, with 2 Experience, to go up to Level 3, you need 4 more points of Experience.

The following table shows how much total Experience you need to go up to the next level, for the first 15 levels. The Experience values needed are given by the formula shown below, where \(n\) is the current level, \(d\) and \(a_1\) are constants, both equal to 2.

\[S_n = \frac {1} {2} n (2 a_1 + d (n-1) ) \xrightarrow[d = 2]{a_1 = 2} S_n = n^2 + n\]

Elo rating System

The Elo system (usually employed in games such as Chess and League of Legends) used in the site works in the following way:

• All players, at sign in, start with a rating of 1400.
• After the end of a game, the following values are calculated

\(E_a = \frac {Q_a} {Q_a + Q_b}\), \(E_b = \frac {Q_b} {Q_a + Q_b}\)

Where

\(Q_a = 10^{R_a/400}\), \(Q_b = 10^{R_b/400}\)

And where \(R_a\) and \(R_b\) are the ratings of both players after the game ends, but before final ratings are calculated.

The final ratings are calculated through the following formulas:

\(R^{'}_{a} = R_a + K(S_a - E_a)\), \(R^{'}_{b} = R_b + K(S_b - E_b)\)

Where \(K\) corresponds to the biggest adjustment possible per game, and is considered dqual to 40, \(S_a\) e \(S_b\) correspond to the final value given to the game (which is 1 for a win and 0 for a loss). The final vaules are rounded to the unit.

Some examples. Picture two players, A and B, both with a rating of 1400, play and player A wins. A's rating goes up by 20, to 1420, while B's rating goes down the 20 points "given" to A. In the next game, player B wins. As his rating is lower than A's, he is (according to the mathematical model) less likely to win against player A. Therefore, by winning, player B gets his rating up to 1402, a gain of 22 points, while player A goes down in rating to 1398, losing 22 points in his rating.