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Replace Glicko-2 with Glicko-1

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This commit is contained in:
Guangcong Luo
2014-01-16 00:23:37 -06:00
parent 726709c2fb
commit 3aa5c6825e
3 changed files with 54 additions and 106 deletions
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2
js/client-chat.js
View File

@@ -556,7 +556,7 @@
if (!data.length) {
buffer += '<tr><td colspan="7"><em>This user has not played any ladder games yet.</em></td></tr>';
} else {
buffer += '<tr><th>Format</th><th>Elo</th><th>GXE</th><th>Glicko2</th><th>W</th><th>L</th><th>T</th></tr>';
buffer += '<tr><th>Format</th><th>Elo</th><th>GXE</th><th>Glicko-1</th><th>W</th><th>L</th><th>T</th></tr>';
for (var i=0; i<data.length; i++) {
var row = data[i];
buffer += '<tr><td>'+row.formatid+'</td><td><strong>'+Math.round(row.acre)+'</strong></td><td>'+Math.round(row.gxe,1)+'</td><td>';

4
ladder.php
View File

@@ -20,7 +20,7 @@ $ladder = new NTBBLadder($serverid, $formatid);
?>
<table>
<tr>
<th></th><th>Name</th><th><abbr title="Elo rating">Elo</abbr></th><th><abbr title="user's percentage chance of winning a random battle (aka GLIXARE)">GXE</abbr></th><th><abbr title="Glicko2 rating system: rating&#177;deviation (provisional if deviation>50)">Glicko2</abbr></th>
<th></th><th>Name</th><th><abbr title="Elo rating">Elo</abbr></th><th><abbr title="user's percentage chance of winning a random battle (aka GLIXARE)">GXE</abbr></th><th><abbr title="Glicko-1 rating system: rating&#177;deviation (provisional if deviation>100)">Glicko-1</abbr></th>
</tr>
<?php
@@ -42,7 +42,7 @@ foreach ($toplist as $row)
?>
<tr<?php /* if (floatval($row['rprd']) > 100) echo ' style="color:#999"'; */ ?>>
<td><?php echo $i; ?></td><td><?php echo htmlspecialchars($row['username']); ?></td><td><strong><?php echo round($row['acre']); ?></strong></td><td><?php echo number_format($row['gxe'],1); ?></td>
<td><?php echo '<em>'.round($row['rpr']).'<small> &#177; '.round($row['rprd']).'</small></em>'; if (floatval($row['rprd']) > 100) echo ' <small>(provisional)</small>'; ?></td>
<td><?php echo '<em>'.round($row['rpr']).'<small> &#177; '.round($row['rprd']).'</small></em>'; /* if (floatval($row['rprd']) > 100) echo ' <small>(provisional)</small>'; */ ?></td>
</tr>
<?php
}

154
lib/ntbb-ladder.lib.php
View File

@@ -22,142 +22,92 @@ if (empty($ladderdb)) {
}
}
class Glicko2Player {
class GlickoPlayer {
public $rating;
public $rd;
public $sigma;
public $mu;
public $phi;
public $tau;
private $pi2 = 9.8696044;
private $RDmax = 130.0;
private $RDmin = 25.0;
private $c;
private $q = 0.00575646273 ;
var $M = array();
function __construct($rating = 1500, $rd = 350, $volatility = 0.06, $mu = null, $phi = null, $sigma = null, $systemconstant = 0.75) {
function __construct($rating = 1500, $rd = 130.0) {
// Step 1
$this->rating = $rating;
$this->rd = $rd;
// volatility
if (is_null($sigma)) {
$this->sigma = $volatility;
} else {
$this->sigma = $sigma;
}
// System Constant
$this->tau = $systemconstant;
// Step 2
// Rating
if (is_null($mu)) {
$this->mu = ( $this->rating - 1500 ) / 173.7178;
} else {
$this->mu = $mu;
}
// Rating Deviation
if (is_null($phi)) {
$this->phi = $this->rd / 173.7178;
} else {
$this->phi = $phi;
}
$this->c = sqrt(($this->RDmax * $this->RDmax - $this->RDmin * $this->RDmin) / 365.0);
}
function AddWin($OtherPlayer) {
function addWin($OtherPlayer) {
$this->M[] = $OtherPlayer->MatchElement(1);
}
function AddLoss($OtherPlayer) {
function addLoss($OtherPlayer) {
$this->M[] = $OtherPlayer->MatchElement(0);
}
function AddDraw($OtherPlayer) {
function addDraw($OtherPlayer) {
$this->M[] = $OtherPlayer->MatchElement(0.5);
}
function Update() {
$Results = $this->AddMatches($this->M);
$this->rating = $Results['r'];
$this->rd = $Results['RD'];
$this->mu = $Results['mu'];
$this->phi = $Results['phi'];
$this->sigma = $Results['sigma'];
function update() {
$results = $this->AddMatches($this->M);
$this->rating = $results['R'];
$this->rd = $results['RD'];
$this->M = array();
}
function MatchElement($score) {
return array( 'mu' => $this->mu, 'phi' => $this->phi, 'score' => $score );
function matchElement($score) {
return array('R' => $this->rating, 'RD' => $this->rd, 'score' => $score);
}
function AddMatches($M) {
// This is where the Glicko2 rating calculation actually happens
function addMatches($M) {
// This is where the Glicko rating calculation actually happens
// Follow along the steps using: http://www.glicko.net/glicko/glicko2.pdf
// Follow along the steps using: http://www.glicko.net/glicko/glicko.pdf
if (count($M) == 0) {
$phi_p = sqrt( ( $this->phi * $this->phi ) + ( $this->sigma * $this->sigma ) );
return array( 'r' => $this->rating, 'RD' => 173.7178 * $phi_p, 'mu' => $this->mu, 'phi' => $phi_p, 'sigma' => $this->sigma ) ;
$RD = sqrt(($this->rd * $this->rd) + ($this->c * $this->c));
return array('R' => $this->rating, 'RD' => $RD);
}
// summation parts of Step 3 & 4 & 7
$v_sum = 0;
$delta_sum = 0;
$mu_p_sum = 0;
$A = 0.0;
$d2 = 0.0;
for ($j = 0; $j < count($M); $j++) {
$E = $this->E( $this->mu, $M[$j]['mu'], $M[$j]['phi'] );
$g = $this->g( $M[$j]['phi'] );
$v_sum += ( $g * $g * $E * ( 1 - $E ) );
$E = $this->E($this->rating, $M[$j]['R'], $M[$j]['RD']);
$g = $this->g($M[$j]['RD']);
$delta_sum += $g * ( $M[$j]['score'] - $E );
$d2 += ($g * $g * $E * (1 - $E));
$mu_p_sum += $g * ( $M[$j]['score'] - $E );
$A += $g * ($M[$j]['score'] - $E);
}
// Step 3
// Estimated variance
$v = 1.0 / $v_sum;
$d2 = 1.0 / $this->q / $this->q / $d2;
// Step 4
// Estimated improvment in rating
$delta = $v * $delta_sum;
$RD = 1.0 / sqrt(1.0 / ($this->rd * $this->rd) + 1.0 / $d2);
$R = $this->rating + $this->q * ($RD * $RD) * $A;
// Step 5
$a = log( $this->sigma * $this->sigma );
$x_prev = $a;
$x = $x_prev;
$tausq = $this->tau * $this->tau;
$phisq = $this->phi * $this->phi;
$deltasq = $delta * $delta;
do {
$exp_xp = exp( $x_prev );
$d = $this->phi * $this->phi + $v + $exp_xp;
$deltadsq = $deltasq / ($d * $d);
$h1 = -( $x_prev - $a ) / ( $tausq ) - ( 0.5 * $exp_xp / $d ) + ( 0.5 * $exp_xp * $deltadsq );
$h2 = ( -1.0 / $tausq ) - ( ( 0.5 * $exp_xp ) * ( $phisq + $v ) / ( $d * $d ) ) + ( 0.5 * $deltasq * $exp_xp * ( $phisq + $v - $exp_xp ) / ( $d * $d * $d ) );
$tmp_x = $x;
$x = $x_prev - ( $h1 / $h2 );
$x_prev = $tmp_x;
} while (abs($x - $x_prev) > 0.1);
$sigma_p = exp( $x / 2 );
if ($RD > $this->RDmax) {
$RD = $this->RDmax;
}
// Step 6
$phi_star = sqrt( $phisq + ( $sigma_p * $sigma_p ) );
if ($RD < $this->RDmin) {
$RD = $this->RDmin;
}
// Step 7
$phi_p = 1.0 / ( sqrt( ( 1.0 / ( $phi_star * $phi_star ) ) + ( 1.0 / $v ) ) );
// New mu
$mu_p = $this->mu + $phi_p * $phi_p * $mu_p_sum;
return array( 'r' => ( 173.7178 * $mu_p ) + 1500, 'RD' => 173.7178 * $phi_p, 'mu' => $mu_p, 'phi' => $phi_p, 'sigma' => $sigma_p );
return array('R' => $R, 'RD' => $RD);
}
function g($phi) {
return 1.0 / ( sqrt( 1.0 + ( 3.0 * $phi * $phi) / ( $this->pi2 ) ) );
function g($RD) {
return 1.0 / sqrt(1.0 + 3.0 * $this->q * $this->q * $RD * $RD / $this->pi2) ;
}
function E($mu, $mu_j, $phi_j) {
return 1.0 / ( 1.0 + exp( -$this->g($phi_j) * ( $mu - $mu_j ) ) );
function E($R, $R_j, $RD_j) {
return 1.0 / (1.0 + pow(10.0, -$this->g($RD_j) * ($R - $R_j) / 400.0));
}
}
@@ -203,12 +153,11 @@ class NTBBLadder {
'userid' => $user['userid'],
'username' => $user['username'],
'r' => 1500,
'rd' => 350,
'sigma' => 0.06,
'rd' => 130,
'sigma' => 0,
'rpr' => 1500,
'rprd' => 350,
'rpsigma' => 0.06,
'gxe' => 0,
'rprd' => 130,
'rpsigma' => 0,
'rptime' => $rp,
'rpdata' => '',
'w' => 0,
@@ -306,7 +255,7 @@ class NTBBLadder {
return false;
}
$rating = new Glicko2Player($user['rating']['r'], $user['rating']['rd'], $user['rating']['sigma']);
$rating = new GlickoPlayer($user['rating']['r'], $user['rating']['rd']);
if ($user['rating']['rpdata']) {
$rpdata = explode('##',$user['rating']['rpdata']);
if (count($rpdata) > 1) $offset = floatval($rpdata[1]);
@@ -320,17 +269,15 @@ class NTBBLadder {
$i++;
if ($i > 1000) break;
$rating->Update();
$rating->update();
if ($offset) {
$rating->rating += $offset;
$rating->mu += $offset/173.7178;
$offset = 0;
}
$user['rating']['rptime'] = $this->nextrp($user['rating']['rptime']);
}
$user['rating']['r'] = $rating->rating;
$user['rating']['rd'] = $rating->rd;
$user['rating']['sigma'] = $rating->sigma;
$user['rating']['gxe'] = 0;
if ($user['rating']['rd'] < 100) {
$user['rating']['gxe'] = 1; //round(100 / (1 + pow(10,((1500 - $user['rating']['r']) * pi() / sqrt(3 * log(10)*log(10) * $user['rating']['rd']*$user['rating']['rd'] + 2500 * (64 * pi()*pi() + 147 * log(10)*log(10)))))));
@@ -360,7 +307,6 @@ class NTBBLadder {
$user['rating']['rpr'] = $rating->rating;
$user['rating']['rprd'] = $rating->rd;
$user['rating']['rpsigma'] = $rating->sigma;
$user['rating']['gxe'] = round(100 / (1 + pow(10,((1500 - $rating->rating) * pi() / sqrt(3 * log(10)*log(10) * $rating->rd*$rating->rd + 2500 * (64 * pi()*pi() + 147 * log(10)*log(10)))))), 1);
@@ -388,6 +334,8 @@ class NTBBLadder {
$E = 1 / (1 + pow(10, ($newMelo - $elo) / 400));
$elo += 50 * ($newM['score'] - $E);
if ($elo < 1000) $elo = 1000;
$user['rating']['lacre'] = $user['rating']['acre'] = $elo;
}
@@ -398,11 +346,11 @@ class NTBBLadder {
if (!@$p2['rating']) $this->getRating($p2, true);
if (!$p1M) {
$p2rating = new Glicko2Player($p2['rating']['r'], $p2['rating']['rd'], $p2['rating']['sigma']);
$p2rating = new GlickoPlayer($p2['rating']['r'], $p2['rating']['rd']);
$p1M = $p2rating->MatchElement($p1score);
}
if (!$p2M) {
$p1rating = new Glicko2Player($p1['rating']['r'], $p1['rating']['rd'], $p1['rating']['sigma']);
$p1rating = new GlickoPlayer($p1['rating']['r'], $p1['rating']['rd']);
$p2M = $p1rating->MatchElement(1 - $p1score);
}
$p1M['score'] = $p1score;