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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Elo Difference Calculator</title>
<style>
body {
font-family: Arial, sans-serif;
text-align: center;
margin-top: 50px;
background-color: pink;
}
.container {
display: flex;
flex-direction: column;
align-items: center;
}
.input-group, .button-group {
margin-top: 20px;
display: flex;
flex-direction: column;
align-items: center;
}
.input-group h3, .button-group button {
margin-bottom: 5px;
}
.input-group input {
margin: 5px;
padding: 5px;
width: 60px;
}
.button-group button {
padding: 8px 15px;
}
#sum, #product {
margin-top: 20px;
}
/* For mobile devices */
@media only screen and (max-width: 600px) {
.input-group input {
width: 10%; /* Set input width to 90% of container width */
max-width: 200px; /* Set max-width to prevent input from expanding too much */
}
footer {
position: relative;
bottom: 10px;
width: 100%;
}
}
</style>
</head>
<body>
<h1>Elo Difference Calculator</h1>
<div class="container">
<div class="input-group">
<h3>Win-Draw-Loss Model</h3>
<div>
<label for="losses">Losses:</label>
<input id="losses" type="number" min="0" oninput="validity.valid||(value='');">
<label for="draws">Draws:</label>
<input id="draws" type="number" min="0" oninput="validity.valid||(value='');">
<label for="wins">Wins:</label>
<input id="wins" type="number" min="0" oninput="validity.valid||(value='');">
<br>
<label for="elo0wdl">elo0:</label>
<input id="elo0wdl" type="number" value="0">
<label for="elo1wdl">elo1:</label>
<input id="elo1wdl" type="number" value="0">
<label for="eloTypeWDL">LLR:</label>
<select id="eloTypeWDL">
<option value="nElo">nElo</option>
<option value="Elo">Elo</option>
<option value="BayesElo">BayesElo</option>
</select>
<label for="errormarginWDL">Margin:</label>
<select id="errormarginWDL">
<option value="CI95">95% CI</option>
<option value="CI80">80% CI</option>
<option value="CI85">85% CI</option>
<option value="CI90">90% CI</option>
<option value="CI99">99% CI</option>
<option value="sigma1">1-sigma</option>
<option value="sigma2">2-sigma</option>
<option value="sigma3">3-sigma</option>
<option value="sigma4">4-sigma</option>
<option value="sigma5">5-sigma</option>
<option value="sigma6">6-sigma</option>
</select>
</div>
</div>
<div class="button-group">
<button onclick="calculateWDLElo()">Calculate Elo</button>
<div id="WDLElo"></div>
</div>
<div class="input-group">
<h3>Pentanomial Model</h3>
<div>
<label for="LL">LL:</label>
<input id="LL" type="number" min="0" oninput="validity.valid||(value='');">
<label for="LD">LD:</label>
<input id="LD" type="number" min="0" oninput="validity.valid||(value='');">
<label for="WLDD">DD/WL:</label>
<input id="WLDD" type="number" min="0" oninput="validity.valid||(value='');">
<label for="WD">WD:</label>
<input id="WD" type="number" min="0" oninput="validity.valid||(value='');">
<label for="WW">WW:</label>
<input id="WW" type="number" min="0" oninput="validity.valid||(value='');">
<br>
<label for="elo0penta">elo0:</label>
<input id="elo0penta" type="number" value="0">
<label for="elo1penta">elo1:</label>
<input id="elo1penta" type="number" value="0">
<label for="eloTypePenta">LLR:</label>
<select id="eloTypePenta">
<option value="nElo">nElo</option>
<option value="Elo">Elo</option>
</select>
<label for="errormarginPenta">Margin:</label>
<select id="errormarginPenta">
<option value="CI95">95% CI</option>
<option value="CI80">80% CI</option>
<option value="CI85">85% CI</option>
<option value="CI90">90% CI</option>
<option value="CI99">99% CI</option>
<option value="sigma1">1-sigma</option>
<option value="sigma2">2-sigma</option>
<option value="sigma3">3-sigma</option>
<option value="sigma4">4-sigma</option>
<option value="sigma5">5-sigma</option>
<option value="sigma6">6-sigma</option>
</select>
</div>
</div>
<div class="button-group">
<button onclick="calculatePentanomialElo()">Calculate Elo</button>
<div id="PentanomialElo"></div>
</div>
<div class="input-group">
<h3>SPRT</h3>
<div>
<label for="Elo">Elo:</label>
<input id="Elo" type="number">
<label for="Variance">Variance:</label>
<input id="Variance" type="number">
<label for="elo0">elo0:</label>
<input id="elo0" type="number" value="0">
<label for="elo1">elo1:</label>
<input id="elo1" type="number" value="0">
<label for="alpha">alpha:</label>
<input id="alpha" type="number" value="0.05">
<label for="beta">beta:</label>
<input id="beta" type="number" value="0.05">
<br>
<label for="eloType">Model:</label>
<select id="eloType">
<option value="nElo">normalized (nElo)</option>
<option value="Elo">logistic (Elo)</option>
</select>
<select id="model">
<option value="Pentanomial">Pentanomial</option>
<option value="WDL">WDL</option>
</select>
</div>
</div>
<div class="button-group">
<button onclick="calculateSPRT()">Calculate SPRT</button>
<div id="SPRT"></div>
</div>
</div>
<footer>
<p><br><br>This page is used to calculate the elo difference and other match stats between two chess engines/players based on match results.<br>Written by justanothertester from Stockfish Discord.</p>
</footer>
<script>
function score_to_elo(score) {
return -400 * Math.log(1 / score - 1) / Math.LN10;
}
function elo_to_score(elo) {
return (1 / (1 + Math.pow(10, (-elo / 400))));
}
function score_to_nelo_penta(score, std_deviation) {
return (score - 0.5) / (Math.sqrt(2) * std_deviation) * (800 / Math.LN10);
}
function score_to_nelo_wdl(score, std_deviation) {
return (score - 0.5) / (std_deviation) * (800 / Math.LN10);
}
function nelo_to_score_penta(nelo, std_deviation) {
return nelo * Math.sqrt(2) * std_deviation / (800 / Math.LN10) + 0.5;
}
function score_to_bayeselo(score, drawelo) {
x = Math.pow(10, -drawelo / 400)
return score_to_elo(score)/(4 * x / Math.pow(1 + x, 2))
}
function bayeselo_to_score(bayeselo, drawelo) {
var pwin = 1.0 / (1.0 + Math.pow(10.0, (-bayeselo + drawelo) / 400.0))
var ploss = 1.0 / (1.0 + Math.pow(10.0, (bayeselo + drawelo) / 400.0))
var pdraw = 1.0 - pwin - ploss
return pwin + 0.5 * pdraw + 0 * ploss;
}
function nelo_to_score_wdl(nelo, std_deviation) {
return nelo * std_deviation / (800 / Math.LN10) + 0.5;
}
function ncdf(x, mean, std) {
var x = (x - mean) / std;
var t = 1 / (1 + 0.2315419 * Math.abs(x));
var d = 0.3989423 * Math.exp( -x * x / 2);
var prob = d * t * (0.3193815 + t * ( -0.3565638 + t * (1.781478 + t * (-1.821256 + t * 1.330274))));
if( x > 0 ) {prob = 1 - prob};
return prob;
}
function calculateWDLElo() {
var losses = parseFloat(document.getElementById("losses").value);
var draws = parseFloat(document.getElementById("draws").value);
var wins = parseFloat(document.getElementById("wins").value);
var total_games = losses + draws + wins;
var points = losses * 0 + draws * 0.5 + wins * 1;
var score = points / total_games;
var score_in_percent = score * 100;
var losses_ratio = losses / total_games;
var draws_ratio = draws / total_games;
var wins_ratio = wins / total_games;
var losses_dev = losses_ratio * Math.pow(0 - score, 2);
var draws_dev = draws_ratio * Math.pow(0.5 - score, 2);
var wins_dev = wins_ratio * Math.pow(1 - score, 2);
var variance = losses_dev + draws_dev + wins_dev;
var std_deviation = Math.sqrt(variance);
var zscore;
var errormargin = document.getElementById("errormarginWDL").value;
if (errormargin == "CI95") {zscore = 1.959963984540054}
else if (errormargin == "CI80") {zscore = 1.2815515655446004}
else if (errormargin == "CI85") {zscore = 1.4395314709384557}
else if (errormargin == "CI90") {zscore = 1.6448536269514729}
else if (errormargin == "CI99") {zscore = 2.5758293035489004}
else if (errormargin == "sigma1") {zscore = 1}
else if (errormargin == "sigma2") {zscore = 2}
else if (errormargin == "sigma3") {zscore = 3}
else if (errormargin == "sigma4") {zscore = 4}
else if (errormargin == "sigma5") {zscore = 5}
else if (errormargin == "sigma6") {zscore = 6}
var score_lower_bound = score - zscore * std_deviation / Math.sqrt(total_games);
var score_upper_bound = score + zscore * std_deviation / Math.sqrt(total_games);
var score_error_margin = (score_upper_bound - score_lower_bound) / 2;
var elo = score_to_elo(score);
var elo_lower_bound = score_to_elo(score_lower_bound);
var elo_upper_bound = score_to_elo(score_upper_bound);
var elo_error_margin_lower = elo - elo_lower_bound;
var elo_error_margin_upper = elo_upper_bound - elo;
var nelo = score_to_nelo_wdl(score, std_deviation);
var nelo_lower_bound = score_to_nelo_wdl(score_lower_bound, std_deviation);
var nelo_upper_bound = score_to_nelo_wdl(score_upper_bound, std_deviation);
var nelo_error_margin_lower = nelo - nelo_lower_bound;
var nelo_error_margin_upper = nelo_upper_bound - nelo;
var LOS = (1 - ncdf(0, (score-0.5), (std_deviation / Math.sqrt(total_games))))*100;
var win_loss_ratio = wins / losses;
var drawelo = 200 * Math.log10((1-losses_ratio)/losses_ratio * (1-wins_ratio)/wins_ratio)
var bayeselo = score_to_bayeselo(score, drawelo)
var bayeselo_lower_bound = score_to_bayeselo(score_lower_bound, drawelo);
var bayeselo_upper_bound = score_to_bayeselo(score_upper_bound, drawelo);
var bayeselo_error_margin_lower = bayeselo - bayeselo_lower_bound;
var bayeselo_error_margin_upper = bayeselo_upper_bound - bayeselo;
var elo0 = parseFloat(document.getElementById("elo0wdl").value)
var elo1 = parseFloat(document.getElementById("elo1wdl").value)
var eloType = document.getElementById("eloTypeWDL").value;
var score0;
var score1;
if (eloType == "BayesElo") {
score0 = bayeselo_to_score(elo0, drawelo)
score1 = bayeselo_to_score(elo1, drawelo)
} else if (eloType == "Elo") {
score0 = elo_to_score(elo0)
score1 = elo_to_score(elo1)
} else {
score0 = nelo_to_score_wdl(elo0, std_deviation)
score1 = nelo_to_score_wdl(elo1, std_deviation)
}
var losses_dev0 = losses_ratio * Math.pow(0 - score0, 2);
var draws_dev0 = draws_ratio * Math.pow(0.5 - score0, 2);
var wins_dev0 = wins_ratio * Math.pow(1 - score0, 2);
var variance0 = losses_dev0 + draws_dev0 + wins_dev0;
var losses_dev1 = losses_ratio * Math.pow(0 - score1, 2);
var draws_dev1 = draws_ratio * Math.pow(0.5 - score1, 2);
var wins_dev1 = wins_ratio * Math.pow(1 - score1, 2);
var variance1 = losses_dev1 + draws_dev1 + wins_dev1;
var llr = 0.5 * total_games * Math.log(variance0 / variance1)
document.getElementById("WDLElo").innerHTML =
"Points: " + points + "/" + total_games + " (" + score_in_percent.toFixed(2) + "%)"
+ "<br>Elo: " + elo.toFixed(2) + " (-" + elo_error_margin_lower.toFixed(2) + " / +" + elo_error_margin_upper.toFixed(2) + ")"
+ " [" + elo_lower_bound.toFixed(2) + " to " + elo_upper_bound.toFixed(2) + "]"
+ "<br>nElo: " + nelo.toFixed(2) + " (-" + nelo_error_margin_lower.toFixed(2) + " / +" + nelo_error_margin_upper.toFixed(2) + ")"
+ " [" + nelo_lower_bound.toFixed(2) + " to " + nelo_upper_bound.toFixed(2) + "]"
+ "<br>BayesElo: " + bayeselo.toFixed(2) + " (-" + bayeselo_error_margin_lower.toFixed(2) + " / +" + bayeselo_error_margin_upper.toFixed(2) + ")"
+ " [" + bayeselo_lower_bound.toFixed(2) + " to " + bayeselo_upper_bound.toFixed(2) + "]"
+ "<br>DrawElo: " + drawelo.toFixed(2)
+ "<br>LOS: " + LOS.toFixed(2) + "%"
+ "<br>W/L Ratio: " + win_loss_ratio.toFixed(2)
+ "<br>Draw Ratio: " + draws_ratio.toFixed(2)
+ "<br>LLR: " + llr.toFixed(4)
+ "<br>Variance: " + variance.toFixed(4)
}
function calculatePentanomialElo() {
var LL = parseFloat(document.getElementById("LL").value);
var LD = parseFloat(document.getElementById("LD").value);
var WLDD = parseFloat(document.getElementById("WLDD").value);
var WD = parseFloat(document.getElementById("WD").value);
var WW = parseFloat(document.getElementById("WW").value);
var total_pairs = LL + LD + WLDD + WD + WW;
var points = LL * 0 + LD * 0.25 + WLDD * 0.5 + WD * 0.75 + WW * 1;
var score = points / total_pairs;
var score_in_percent = score * 100;
var LL_ratio = LL / total_pairs;
var LD_ratio = LD / total_pairs;
var WLDD_ratio = WLDD / total_pairs;
var WD_ratio = WD / total_pairs;
var WW_ratio = WW / total_pairs;
var LL_dev = LL_ratio * Math.pow(0 - score, 2);
var LD_dev = LD_ratio * Math.pow(0.25 - score, 2);
var WLDD_dev = WLDD_ratio * Math.pow(0.5 - score, 2);
var WD_dev = WD_ratio * Math.pow(0.75 - score, 2);
var WW_dev = WW_ratio * Math.pow(1 - score, 2);
var variance = LL_dev + LD_dev + WLDD_dev + WD_dev + WW_dev;
var std_deviation = Math.sqrt(variance);
var zscore;
var errormargin = document.getElementById("errormarginPenta").value;
if (errormargin == "CI95") {zscore = 1.959963984540054}
else if (errormargin == "CI80") {zscore = 1.2815515655446004}
else if (errormargin == "CI85") {zscore = 1.4395314709384557}
else if (errormargin == "CI90") {zscore = 1.6448536269514729}
else if (errormargin == "CI99") {zscore = 2.5758293035489004}
else if (errormargin == "sigma1") {zscore = 1}
else if (errormargin == "sigma2") {zscore = 2}
else if (errormargin == "sigma3") {zscore = 3}
else if (errormargin == "sigma4") {zscore = 4}
else if (errormargin == "sigma5") {zscore = 5}
else if (errormargin == "sigma6") {zscore = 6}
var score_lower_bound = score - zscore * std_deviation / Math.sqrt(total_pairs);
var score_upper_bound = score + zscore * std_deviation / Math.sqrt(total_pairs);
var score_error_margin = (score_upper_bound - score_lower_bound) / 2;
var elo = score_to_elo(score);
var elo_lower_bound = score_to_elo(score_lower_bound);
var elo_upper_bound = score_to_elo(score_upper_bound);
var elo_error_margin_lower = elo - elo_lower_bound;
var elo_error_margin_upper = elo_upper_bound - elo;
var nelo = score_to_nelo_penta(score, std_deviation);
var nelo_lower_bound = score_to_nelo_penta(score_lower_bound, std_deviation);
var nelo_upper_bound = score_to_nelo_penta(score_upper_bound, std_deviation);
var nelo_error_margin_lower = nelo - nelo_lower_bound;
var nelo_error_margin_upper = nelo_upper_bound - nelo;
var LOS = (1 - ncdf(0, (score-0.5), (std_deviation / Math.sqrt(total_pairs))))*100;
var pairs_ratio = (WW + WD) / (LL + LD);
var gamepairs_L_score = (LL + LD) / total_pairs;
var gamepairs_D_score = (WLDD) / total_pairs;
var gamepairs_W_score = (WW + WD) / total_pairs;
var gamepairs_score = ((LL + LD) * 0 + WLDD * 0.5 + (WD + WW) * 1) / total_pairs;
var gamepairs_L_dev = gamepairs_L_score * Math.pow(0 - gamepairs_score, 2);
var gamepairs_D_dev = gamepairs_D_score * Math.pow(0.5 - gamepairs_score, 2);
var gamepairs_W_dev = gamepairs_W_score * Math.pow(1 - gamepairs_score, 2);
var gamepairs_variance = gamepairs_L_dev + gamepairs_D_dev + gamepairs_W_dev;
var gamepairs_std_deviation = Math.sqrt(gamepairs_variance);
var gamepairs_score_lower_bound = gamepairs_score - zscore * gamepairs_std_deviation / Math.sqrt(total_pairs);
var gamepairs_score_upper_bound = gamepairs_score + zscore * gamepairs_std_deviation / Math.sqrt(total_pairs);
var gamepairs_score_error_margin = (gamepairs_score_upper_bound - gamepairs_score_lower_bound) / 2;
var gamepairs_elo = score_to_elo(gamepairs_score);
var gamepairs_elo_lower_bound = score_to_elo(gamepairs_score_lower_bound);
var gamepairs_elo_upper_bound = score_to_elo(gamepairs_score_upper_bound);
var gamepairs_elo_error_margin_lower = gamepairs_elo - gamepairs_elo_lower_bound;
var gamepairs_elo_error_margin_upper = gamepairs_elo_upper_bound - gamepairs_elo;
var normalized_pair_elo = -100 * Math.log10((2 * LL + LD) / (2 * WW + WD));
var elo0 = parseFloat(document.getElementById("elo0penta").value)
var elo1 = parseFloat(document.getElementById("elo1penta").value)
var eloType = document.getElementById("eloTypePenta").value;
var score0;
var score1;
if (eloType == "nElo") {
score0 = nelo_to_score_penta(elo0, std_deviation)
score1 = nelo_to_score_penta(elo1, std_deviation)
} else {
score0 = elo_to_score(elo0)
score1 = elo_to_score(elo1)
}
var LL_dev0 = LL_ratio * Math.pow(0 - score0, 2);
var LD_dev0 = LD_ratio * Math.pow(0.25 - score0, 2);
var WLDD_dev0 = WLDD_ratio * Math.pow(0.5 - score0, 2);
var WD_dev0 = WD_ratio * Math.pow(0.75 - score0, 2);
var WW_dev0 = WW_ratio * Math.pow(1 - score0, 2);
var variance0 = LL_dev0 + LD_dev0 + WLDD_dev0 + WD_dev0 + WW_dev0;
var LL_dev1 = LL_ratio * Math.pow(0 - score1, 2);
var LD_dev1 = LD_ratio * Math.pow(0.25 - score1, 2);
var WLDD_dev1 = WLDD_ratio * Math.pow(0.5 - score1, 2);
var WD_dev1 = WD_ratio * Math.pow(0.75 - score1, 2);
var WW_dev1 = WW_ratio * Math.pow(1 - score1, 2);
var variance1 = LL_dev1 + LD_dev1 + WLDD_dev1 + WD_dev1 + WW_dev1;
var llr = 0.5 * total_pairs * Math.log(variance0 / variance1)
document.getElementById("PentanomialElo").innerHTML =
"Points: " + (points * 2) + "/" + (total_pairs * 2) + " (" + score_in_percent.toFixed(2) + "%)"
+ "<br>Elo: " + elo.toFixed(2) + " (-" + elo_error_margin_lower.toFixed(2) + " / +" + elo_error_margin_upper.toFixed(2) + ")"
+ " [" + elo_lower_bound.toFixed(2) + " to " + elo_upper_bound.toFixed(2) + "]"
+ "<br>nElo: " + nelo.toFixed(2) + " (-" + nelo_error_margin_lower.toFixed(2) + " / +" + nelo_error_margin_upper.toFixed(2) + ")"
+ " [" + nelo_lower_bound.toFixed(2) + " to " + nelo_upper_bound.toFixed(2) + "]"
+ "<br>Gamepairs Elo: " + gamepairs_elo.toFixed(2) + " (-" + gamepairs_elo_error_margin_lower.toFixed(2) + " / +" + gamepairs_elo_error_margin_upper.toFixed(2) + ")"
+ " [" + gamepairs_elo_lower_bound.toFixed(2) + " to " + gamepairs_elo_upper_bound.toFixed(2) + "]"
+ "<br>Normalized Pair Elo: " + normalized_pair_elo.toFixed(2)
+ "<br>LOS: " + LOS.toFixed(2) + "%"
+ "<br>Pairs Ratio: " + pairs_ratio.toFixed(2)
+ "<br>Draw Ratio: " + WLDD_ratio.toFixed(2)
+ "<br>LLR: " + llr.toFixed(4)
+ "<br>Variance: " + variance.toFixed(4)
}
function calculateSPRT () {
var elo = parseFloat(document.getElementById("Elo").value);
var variance = parseFloat(document.getElementById("Variance").value);
var elo0 = parseFloat(document.getElementById("elo0").value);
var elo1 = parseFloat(document.getElementById("elo1").value);
var elotype = document.getElementById("eloType").value;
var model = document.getElementById("model").value;
var alpha = parseFloat(document.getElementById("alpha").value);
var beta = parseFloat(document.getElementById("beta").value);
var score = elo_to_score(elo);
var score0;
var score1;
if (model == "Pentanomial") {
score0 = nelo_to_score_penta(elo0, Math.sqrt(variance))
score1 = nelo_to_score_penta(elo1, Math.sqrt(variance))
} else {
score0 = nelo_to_score_wdl(elo0, Math.sqrt(variance))
score1 = nelo_to_score_wdl(elo1, Math.sqrt(variance))
}
if (elotype == "Elo") {
score0 = elo_to_score(elo0)
score1 = elo_to_score(elo1)
}
var w2 = Math.pow((score1 - score0), 2) / variance;
var LA = Math.log(beta / (1 - alpha));
var LB = Math.log((1 - beta) / alpha);
var h = (2.0 * score - (score0 + score1)) / (score1 - score0)
var pass_prob;
var expected_games;
if (Math.abs(h * (LA - LB)) < 0.000001) {
// avoid division by zero
pass_prob = -LA / (LB - LA);
expected_games = -LA * LB / w2;
} else {
var exp_a = Math.exp(-h * LA);
var exp_b = Math.exp(-h * LB);
pass_prob = (1-exp_a)/(exp_b-exp_a)
expected_games = (2/h)*(LB*pass_prob+LA*(1-pass_prob)) / w2
}
if (model == "Pentanomial") {
expected_games = expected_games * 2
}
document.getElementById("SPRT").innerHTML =
"Pass Probability: " + (pass_prob*100).toFixed(2) + "%"
+ "<br>Expected # of games: " + (expected_games).toFixed(0)
}
</script>
</body>
</html>