Rating calculator

This should be an example calculator for a possible bbc rating. The aim of the rating is to estimate the current strength of a player as good as possible.
This page uses the rating 5.

small explanation

You do not need to know the full details on how the rating will be computed, because this is very complicated. Here are some basic principles:

you start with a number of rating points. after each game you will win or loose points, depending on how good you play.
the place you get in a game has a big influence on how many points you make.
If you play against players with a higher rating than yours and are successful, you get many rating points
If you play against players with a higher rating than yours and are not successful, you loose a few rating points
If you play against players with a lower rating than yours and are successful, you win a few rating points
If you play against players with a lower rating than yours and are not successful, you loose many rating points

The number of games each player has played so far can also have an influence on the rating points, therefor there is an extra column.
If you want to know, how things look like if you consider many games, here is an example computation: (click here). it uses all BBC games in 2013. you can even get a graph of players of their rating over time.

Example calculation

Input

System parameters:
Difference between Players:
Speed at Start: Normal Speed:
first games:
Bonus for Winner:

#	Rating	Games played
Winner
Place 2
Place 3
Place 4
Place 5
Place 6
Place 7
Place 8
Place 9
Place 10

Number of Players (2-10):

Results

Place	Old Rating	New Rating	Difference	played games
1	5000	5421	421	1
2	5000	5273	273	1
3	5000	5193	193	1
4	5000	5113	113	1
5	5000	5033	33	1
6	5000	4953	-47	1
7	5000	4873	-127	1
8	5000	4793	-207	1
9	5000	4713	-287	1
10	5000	4633	-367	1

Source code

function noobratingmain($ratings,$gamec,$probdiff=3000,$startspeed=80,$minspeed=40,$mingames=30,$winbonus=1.17) 
{
    /* 
    this is the core function of the bbc rating. 
    it was programmed by some supernoob :)
    
    $ratings and $gamec are arrays of the same size
    the size is the number of players
    player with index 0 is winner, 9 is place 10
    gamec is the number of games played before this game
    */
    if(count($ratings) !=count($gamec) or count($ratings)>=11) return 0; //error
    $NN=count($ratings); // $NN is the number of players in the game
    $newrating=$ratings; // newrating will be return array
    for($i1=0;$i1<$NN;$i1++)
    {    
        $expect=0.0; // $expect is the expected score for each player
        for($i2=0;$i2<$NN;$i2++)
        {
            if($i1==$i2) continue;
            $diff = (float)($ratings[$i2]-$ratings[$i1]); //compare rating difference with each player
            if($i2==0 or $i1==0) $expect += $winbonus/(1.0 + pow(2.0,$diff/$probdiff)); // add expected score for winners
            if($i2!=0 and $i1!=0) $expect += 1.0/(1.0 + pow(2.0,$diff/$probdiff)); // add expected score for non-winners
        }
        if($gamec[$i1]<$mingames) $speed2 = (float)$startspeed + (float)($minspeed-$startspeed)*($gamec[$i1])/($mingames); 
        if($gamec[$i1]>=$mingames)$speed2=$minspeed; // determine the "speed" according to parameters
        $wonpoints=$NN-$i1-1; //
        if($i1==0) $wonpoints=$winbonus*9.0; // winners get more points
        $newrating[$i1] =$ratings[$i1] + (int) ceil($speed2*($wonpoints - $expect) -0.5); //round the rating points to integer
    }
    return $newrating;
}

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