Elo system with a reliability purpose

v1.0 2014-11-26 09:56 UTC

This package is not auto-updated.

Last update: 2020-10-16 20:13:25 UTC


README

Another Elo implementation in PHP ! But this one introduce a reliability purpose.

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Reliability purpose

A history: You have a good player A which played many games and have a score of 2100 Elo. A new player B subscribe to the game website, so his Elo score is initialized to 1500. But in fact, he is a very good player, better than A, and beat him like crushing an ant.

The problem: New player B will win many Elo because he won against a 2100 Elo player. That's ok. But player A (2100 Elo) will lose many Elo because he lost against a 1500 Elo player, but in fact strongest.

The fact is that the new player Elo score is not reliable, so it should not impact others players Elo scores.

The solution: This library. It introduces a reliability coefficient (decimal between 0.0 and 1.0) for Elo A and Elo B.

Composer

Install via composer

{
    "require": {
        "alcalyn/elo": "1.x"
    }
}

Or download the library manually if you don't use composer.

Usage

  • Instantiate a standard Elo system
use Alcalyn/Elo/EloSystem;

$eloSystem = new EloSystem();
  • Calculate updated Elo scores from old Elo
/**
 * A player with 1650 Elo beat another with 1920
 */
$updatedElos = $eloSystem->calculate(1650, 1920, 1);

print_r($updatedElos);
/* Output:
    Array
    (
        [0] => 1663.2084157978
        [1] => 1906.7915842022
    )
*/
  • Set reliability coefficient to Elo scores
/**
 * A player with 1907 Elo (1.0 reliability)
 * lose against a new player with 1500 (and reliability to 0.0)
 */
$updatedElos = $eloSystem->calculate(1907, 1500, 0, 1.0, 0.0);

print_r($updatedElos);
/* Output:
Array
(
    [0] => 1907
    [1] => 1514.5978664353
)
*/
  • Using method aliases for win, lose or draw
/**
 * Method Aliases
 */
$elo->win(2100, 1500, 1.0, 0.0);
$elo->lose(2100, 1500, 1.0, 0.0);
$elo->draw(2100, 1500, 1.0, 0.0);
  • Instanciate a system with a different K factor (default is 16)
/**
 * Use a different K factor in your Elo system
 */
$eloSystemK32 = new EloSystem(32);

Detailled examples

A new player:

Player A has 2100 Elo, reliability 1.0
Player B has 1500 Elo, reliability 0.0

A wins: Expected result, so B loses a small amount of Elo, and A win nothing.
B wins: NOT expected result, so B wins a BIG amount of Elo, and A lose nothing.

A Elo score will not be updated when he plays versus a new player with an unreliable Elo score.

(And new player B should have its Elo reliability increased by something like 1/10 after every games until his reliability reaches 1)

$elo = new EloSystem();

/**
 * Result without reliability
 */
print_r($elo->lose(2100, 1500));

/* Output:
    Array
    (
        [0] => 2084.4904548805 // lose -16 Elo
        [1] => 1515.5095451195 // win  +16 Elo
    )
*/

/**
 * Result with reliability
 */
print_r($elo->lose(2100, 1500, 1.0, 0.0));

/* Output:
    Array
    (
        [0] => 2100 // don't lose Elo against new player
        [1] => 1515.5095451195 // win +16 Elo vs reliable Elo score
    )
*/

Another example: two newbies players:

Player A has 1500 Elo, reliability 0.0
Player B has 1500 Elo, reliability 0.0

There is two new players, so their reliabilities are both 0.0: the algorithm takes them like if they were both 1.0.

And if player A had an Elo reliability equal to 0.4, and player B equal to 0.0, the algorithm adds them +0.6 so one of reliabilities reaches 1.0.

License

This project is under MIT Lisense