Elo system
Another Elo implementation in PHP ! But this one introduce a reliability purpose., (*1)
, (*2)
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., (*3)
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., (*4)
The fact is that the new player Elo score is not reliable, so it should not impact others players Elo scores., (*5)
The solution: This library. It introduces a reliability coefficient (decimal between 0.0 and 1.0) for Elo A and Elo B., (*6)
Composer
Install via composer, (*7)
``` js
{
"require": {
"alcalyn/elo": "1.x"
}
}, (*8)
*Or download the library manually if you don't use composer.*
## Usage
- Instantiate a standard Elo system
``` php
use Alcalyn/Elo/EloSystem;
$eloSystem = new EloSystem();
- Calculate updated Elo scores from old Elo
``` php
/**
* A player with 1650 Elo beat another with 1920
*/
$updatedElos = $eloSystem->calculate(1650, 1920, 1);, (*9)
print_r($updatedElos);
/* Output:
Array
(
[0] => 1663.2084157978
[1] => 1906.7915842022
)
*/, (*10)
- Set **reliability** coefficient to Elo scores
``` php
/**
* 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
``` php
/**
* 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);, (*11)
- Instanciate a system with a different K factor (default is 16)
``` php
/**
* Use a different K factor in your Elo system
*/
$eloSystemK32 = new EloSystem(32);
Detailled examples
A new player:, (*12)
Player A has 2100 Elo, reliability 1.0
Player B has 1500 Elo, reliability 0.0
, (*13)
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.
, (*14)
A Elo score will not be updated when he plays versus a new player with an unreliable Elo score., (*15)
(And new player B should have its Elo reliability increased by something like 1/10
after every games until his reliability reaches 1), (*16)
``` php
$elo = new EloSystem();, (*17)
/**
* Result without reliability
*/
print_r($elo->lose(2100, 1500));, (*18)
/* Output:
Array
(
[0] => 2084.4904548805 // lose -16 Elo
[1] => 1515.5095451195 // win +16 Elo
)
*/, (*19)
/**
* Result with reliability
*/
print_r($elo->lose(2100, 1500, 1.0, 0.0));, (*20)
/* Output:
Array
(
[0] => 2100 // don't lose Elo against new player
[1] => 1515.5095451195 // win +16 Elo vs reliable Elo score
)
*/
```, (*21)
Another example: two newbies players:, (*22)
Player A has 1500 Elo, reliability 0.0
Player B has 1500 Elo, reliability 0.0
, (*23)
There is two new players, so their reliabilities are both 0.0:
the algorithm takes them like if they were both 1.0., (*24)
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., (*25)
License
This project is under MIT Lisense, (*26)
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