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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>BehaviorBench Leaderboards</title>
<style>
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.sc-rank { left: 0; text-align: center; width: 3rem; }
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#main-table .sc-distrib { left: 33rem; }
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#cat-table .sc-distrib { left: 33rem; }
th.sc-rank, th.sc-model, th.sc-score, th.sc-indiv, th.sc-distrib {
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background: var(--header-bg);
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th.sc-rank:hover, th.sc-model:hover, th.sc-score:hover, th.sc-indiv:hover, th.sc-distrib:hover {
background: #eef0f4;
}
/* Hover / BeFM backgrounds for sticky body cells */
tr:hover .sc-rank, tr:hover .sc-model, tr:hover .sc-score,
tr:hover .sc-indiv, tr:hover .sc-distrib { background: var(--row-hover); }
tr.befm .sc-rank, tr.befm .sc-model, tr.befm .sc-score,
tr.befm .sc-indiv, tr.befm .sc-distrib { background: var(--befm-bg); }
tr.befm:hover .sc-rank, tr.befm:hover .sc-model, tr.befm:hover .sc-score,
tr.befm:hover .sc-indiv, tr.befm:hover .sc-distrib { background: #e0e8ff; }
tr:hover td { background: var(--row-hover); }
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border-radius: 4px;
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transition: all 0.15s;
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.ranking-toggle {
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border-radius: 20px;
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margin-bottom: 1rem;
}
.ranking-toggle .toggle-btn {
padding: 0.3rem 0.85rem;
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}
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transition: all 0.15s;
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.action-btn:hover {
border-color: var(--accent);
background: var(--accent-light);
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background: #f1f5f9;
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border-radius: 3px;
margin-left: 0.2rem;
}
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display: flex;
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flex-wrap: wrap;
gap: 0.9rem;
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}
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display: inline-flex;
align-items: center;
justify-content: center;
min-height: 2.75rem;
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}
.partner-logo img {
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object-fit: contain;
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}
.partner-logo.stanford {
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font-size: 1.35rem;
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.partner-logo.moblab img {
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}
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.partner-logo.umich img { width: 170px; }
.partner-logo.stanford { font-size: 1.15rem; }
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.partner-logo.moblab img { width: 96px; }
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#ranking-select {
font-size: 0.82rem;
padding: 0.35rem 0.6rem;
border: 1px solid var(--border);
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cursor: pointer;
outline: none;
transition: border-color 0.15s;
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#ranking-select:hover { border-color: var(--accent); }
#ranking-select:focus { border-color: var(--accent); box-shadow: 0 0 0 2px rgba(67,97,238,0.15); }
.hero {
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position: relative;
}
.hero h1 {
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.hero .nav-internal a:hover { text-decoration: underline; }
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position: absolute;
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right: 0;
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.hero-figure {
margin: 1.4rem auto 1.6rem auto;
max-width: 640px;
text-align: center;
}
.hero-figure img {
max-width: 100%;
height: auto;
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.hero-figure figcaption {
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font-size: 0.8rem;
margin-top: 0.5rem;
line-height: 1.5;
}
.ranking-chip {
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align-items: center;
gap: 0.35rem;
padding: 0.18rem 0.7rem;
background: var(--accent-light);
color: var(--accent);
border-radius: 999px;
font-weight: 600;
font-size: 0.8rem;
margin-left: 0.35rem;
}
.ranking-chip::before {
content: "";
width: 6px;
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border-radius: 50%;
background: var(--accent);
display: inline-block;
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@media (max-width: 700px) {
.hero-version-toggle { position: static; margin-top: 0.5rem; justify-content: center; }
}
.header-row {
display: flex;
align-items: flex-start;
justify-content: space-between;
flex-wrap: wrap;
gap: 0.5rem;
}
@media (max-width: 768px) {
body { padding: 1rem; }
h1 { font-size: 1.4rem; }
.tab { padding: 0.4rem 0.7rem; font-size: 0.8rem; }
}
</style>
</head>
<body>
<div class="hero">
<h1>BehaviorBench Leaderboards</h1>
<p class="subtitle">A benchmark for foundation models on behavioral-science tasks, evaluated at the individual and distributional levels.</p>
<div class="action-bar" aria-label="External resources">
<a class="action-btn" href="https://arxiv.org/abs/2606.24162" target="_blank" rel="noopener noreferrer" title="BehaviorBench paper on arXiv">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M14 2H6a2 2 0 0 0-2 2v16a2 2 0 0 0 2 2h12a2 2 0 0 0 2-2V8z"/><path d="M14 2v6h6"/><path d="M16 13H8"/><path d="M16 17H8"/><path d="M10 9H8"/></svg>
Paper
</a>
<a class="action-btn" href="https://huggingface.co/befm/BeFM1.5-4B" target="_blank" rel="noopener noreferrer" title="BeFM1.5-4B on Hugging Face">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M21 16V8a2 2 0 0 0-1-1.73l-7-4a2 2 0 0 0-2 0l-7 4A2 2 0 0 0 3 8v8a2 2 0 0 0 1 1.73l7 4a2 2 0 0 0 2 0l7-4A2 2 0 0 0 21 16z"/><path d="M3.27 6.96 12 12.01l8.73-5.05"/><path d="M12 22.08V12"/></svg>
BeFM1.5-4B
</a>
<a class="action-btn" href="https://huggingface.co/befm/BeFM1.5-70B" target="_blank" rel="noopener noreferrer" title="BeFM1.5-70B on Hugging Face">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M21 16V8a2 2 0 0 0-1-1.73l-7-4a2 2 0 0 0-2 0l-7 4A2 2 0 0 0 3 8v8a2 2 0 0 0 1 1.73l7 4a2 2 0 0 0 2 0l7-4A2 2 0 0 0 21 16z"/><path d="M3.27 6.96 12 12.01l8.73-5.05"/><path d="M12 22.08V12"/></svg>
BeFM1.5-70B
</a>
<a class="action-btn" href="https://huggingface.co/datasets/befm/BehaviorBench" target="_blank" rel="noopener noreferrer" title="BehaviorBench dataset on Hugging Face">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><ellipse cx="12" cy="5" rx="9" ry="3"/><path d="M3 5v14c0 1.66 4.03 3 9 3s9-1.34 9-3V5"/><path d="M3 12c0 1.66 4.03 3 9 3s9-1.34 9-3"/></svg>
Dataset
</a>
<a class="action-btn" href="https://github.com/umich-foreseer/behaviorbench_eval" target="_blank" rel="noopener noreferrer" title="BehaviorBench evaluation code on GitHub">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="m16 18 6-6-6-6"/><path d="m8 6-6 6 6 6"/></svg>
Code
</a>
<a class="action-btn" href="https://huggingface.co/spaces/befm/BeFM" target="_blank" rel="noopener noreferrer" title="Chat with BeFM on Hugging Face">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M21 15a4 4 0 0 1-4 4H8l-5 3V7a4 4 0 0 1 4-4h10a4 4 0 0 1 4 4z"/><path d="M8 10h8"/><path d="M8 14h5"/></svg>
Chat with BeFM
</a>
</div>
<div class="partner-logos" aria-label="Partner institutions">
<div class="partner-logo umich" aria-label="University of Michigan">
<img src="assets/logos/umich-logo.png" alt="University of Michigan">
</div>
<div class="partner-logo stanford" aria-label="Stanford University">
<img src="assets/logos/stanford-logo.svg" alt="">
<span>Stanford</span>
</div>
<div class="partner-logo moblab" aria-label="MobLab">
<img src="assets/logos/moblab-logo.svg" alt="MobLab">
</div>
</div>
</div>
<div class="tabs" id="tabs">
<button class="tab active" data-tab="overall">Overall</button>
<button class="tab" data-tab="individual">Individual Level</button>
<button class="tab" data-tab="distributional">Distributional Level</button>
</div>
<div id="ranking-method-wrap" style="margin-bottom:1rem;display:flex;align-items:center;gap:0.6rem;flex-wrap:wrap;">
<span style="font-size:0.82rem;font-weight:500;color:#6b7280;">Ranking method:</span>
<div class="ranking-toggle" id="ranking-toggle">
<button class="toggle-btn active" data-ranking="winrate">Mean Win Rate</button>
<button class="toggle-btn" data-ranking="elo">ELO Rating</button>
</div>
</div>
<div id="content"></div>
<div class="legend" id="legend">
<strong>Ranking:</strong> <span id="legend-method">Mean Win Rate (HELM-style).</span> <a href="methodology.html" style="color:var(--accent);">See full methodology →</a><br>
<strong>Tags:</strong> the <span class="family-tag effort" style="margin-left:0;">reasoning: high</span> chip next to a model name shows the <code>reasoning_effort</code> used for evaluation. It applies only to reasoning models.
</div>
<section class="citation-block" aria-labelledby="citation-heading">
<div class="citation-header">
<h2 id="citation-heading">Citation</h2>
<button type="button" class="copy-btn" id="copy-bibtex" aria-label="Copy BibTeX">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg>
<span class="copy-btn-text">Copy BibTeX</span>
</button>
</div>
<p class="citation-note">If you use BehaviorBench or BeFM in your work, please consider citing:</p>
<pre id="bibtex-block">@misc{huang2026behaviorbenchbenchmarkingfoundationmodels,
title={BehaviorBench: Benchmarking Foundation Models for Behavioral Science Tasks},
author={Jin Huang and Yutong Xie and Wanli Song and Xingjian Zhang and Walter Yuan and Matthew O. Jackson and Qiaozhu Mei},
year={2026},
eprint={2606.24162},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2606.24162},
}</pre>
</section>
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document.getElementById("copy-bibtex").addEventListener("click", e => {
const btn = e.currentTarget;
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navigator.clipboard.writeText(text).then(() => {
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}).catch(() => {
label.textContent = "Press Ctrl+C";
});
});
</script>
<script src="data.js?v=3"></script>
<script>
// Public version: single dataset, Be.FM is always the 5-run mean.
const DATASETS = {
public: { label: "BehaviorBench", data: LEADERBOARD_DATA },
};
const DEFAULT_DATASET = "public";
// Default reasoning-effort labels per model id (from slide 04162026).
// Non-reasoning models (gpt4_1, claude_haiku, deepseek_v3_2, local) are absent.
const REASONING_EFFORT_DEFAULTS = {
gpt5_4: "none",
gpt5_4_mini: "none",
claude_opus: "high",
claude_sonnet: "high",
gemini_flash_lite: "minimal",
gemini_pro: "high",
};
// Strip temperature & "(5 runs, mean)" suffixes; split the reasoning-effort
// level into its own field so the table renderer can show it as a compact
// chip rather than letting it bloat the model-name column; canonicalize
// Be.FM* names to match the paper. Returns { name, effort }.
function normalizeModelName(id, name) {
let out = name.replace(/\s*\(T=[^)]*\)/g, "").trim();
// Drop the "(5 runs, mean)" / "(5 run mean)" suffix — 5-run mean is the default in public mode.
out = out.replace(/\s*\(\s*5\s*runs?[^)]*\)\s*$/i, "").trim();
// Rewrite a bare effort-level suffix like "(high)" to "(reasoning_effort=high)".
out = out.replace(
/\(\s*(none|minimal|low|medium|high|max|xhigh)\s*\)\s*$/i,
(_, lvl) => `(reasoning_effort=${lvl.toLowerCase()})`
);
const hasEffortSuffix = /\(reasoning_effort=/.test(out);
if (REASONING_EFFORT_DEFAULTS[id] && !hasEffortSuffix) {
out = `${out} (reasoning_effort=${REASONING_EFFORT_DEFAULTS[id]})`;
}
// Canonicalize Be.FM family naming to match the paper:
// "BeFM1.5-4B" → "Be.FM-1.5-4B", "BeFM1-8B" → "Be.FM-1-8B".
out = out.replace(/\bBeFM(\d+(?:\.\d+)?)(-\d+B)/g, "Be.FM-$1$2");
// Detach the reasoning-effort suffix so it can render as a chip beside the name.
let effort = null;
const effortMatch = out.match(/^(.*?)\s*\(reasoning_effort=([^)]+)\)\s*$/);
if (effortMatch) {
out = effortMatch[1].trim();
effort = effortMatch[2].trim();
}
return { name: out, effort };
}
// Collapse the "<id>_5runs" sibling into its base BeFM entry based on mode.
// mode: "single" keeps the base run; "mean" swaps in the 5-run mean values.
// In both cases the "_5runs" entries themselves are hidden from the view.
function applyBefmRunMode(raw, mode) {
const fiveRunMeta = {};
raw.models.forEach(m => {
if (m.id.endsWith("_5runs")) {
fiveRunMeta[m.id.replace(/_5runs$/, "")] = m;
}
});
const models = raw.models
.filter(m => !m.id.endsWith("_5runs"))
.map(m => {
const srcName = (mode === "mean" && fiveRunMeta[m.id])
? fiveRunMeta[m.id].name
: m.name;
const norm = normalizeModelName(m.id, srcName);
return { ...m, name: norm.name, effort: norm.effort };
});
const results = {};
Object.keys(raw.results).forEach(k => {
if (k.endsWith("_5runs")) return;
const fiveKey = k + "_5runs";
results[k] = (mode === "mean" && raw.results[fiveKey]) ? raw.results[fiveKey] : raw.results[k];
});
const flags = {};
Object.keys(raw.flags || {}).forEach(k => {
if (!k.endsWith("_5runs")) flags[k] = raw.flags[k];
});
return { ...raw, models, results, flags };
}
let befmRunMode = "mean";
// Default scenario filters: Merge Push/Pull is ON by default so the 5
// MobLab econ aggregates always include push/pull as a 9th game. Declared
// in this script block (before the initial buildLeaderboardData call) so
// the first render already reflects the merged numbers.
var scenarioFilters = new Set(["merge_pushpull"]);
// MobLab aggregate scenario -> push/pull field + n-count field used when merging.
// Merged value = (old_avg * n + pp_value) / (n + 1). When push/pull is flagged
// unreliable (parse failure > threshold), the merge still happens and the
// merged cell is annotated with a dagger via mergedUnreliable (matches the
// paper econ summary table's dagger policy). Declared in block 1 so the
// initial buildLeaderboardData() call below can invoke applyMergePushpull.
const MERGE_TARGETS = {
ml_multiround_mae: { pp: "ho_pp_multiround_mae", nKey: "ml_multiround_mae_n" },
ml_acrossgame_mae: { pp: "ho_pp_acrossgame_mae", nKey: "ml_acrossgame_mae_n" },
ml_multiround: { pp: "ho_pp_multiround_wd", nKey: "ml_multiround_n" },
ml_acrossgame: { pp: "ho_pp_acrossgame_wd", nKey: "ml_acrossgame_n" },
ml_game: { pp: "ho_pushpull", nKey: "ml_game_n" },
};
// Return a data object with the 5 MobLab aggregates replaced by (n+1)-game
// means that include push/pull. Also emits a mergedUnreliable sidecar so the
// renderer can mark cells whose push/pull contribution came from a run with
// parse-failure rate above the threshold (data.flags[mid][cfg.pp] != null).
function applyMergePushpull(data) {
const newResults = {};
const mergedUnreliable = {};
for (const mid of Object.keys(data.results)) {
const row = data.results[mid];
const modelFlags = (data.flags && data.flags[mid]) || {};
const newRow = { ...row };
for (const [sid, cfg] of Object.entries(MERGE_TARGETS)) {
const oldAvg = row[sid];
const n = row[cfg.nKey];
const ppVal = row[cfg.pp];
if (oldAvg == null || n == null || ppVal == null) continue;
newRow[sid] = (oldAvg * n + ppVal) / (n + 1);
if (modelFlags[cfg.pp] != null) {
if (!mergedUnreliable[mid]) mergedUnreliable[mid] = {};
mergedUnreliable[mid][sid] = modelFlags[cfg.pp];
}
}
newResults[mid] = newRow;
}
return { ...data, results: newResults, mergedUnreliable };
}
// Compose BeFM run-mode collapse and (optional) push/pull merge into a single
// data object. Called wherever LEADERBOARD_DATA is rebuilt; reads
// scenarioFilters to decide whether to fold in push/pull.
function buildLeaderboardData(datasetKey, runMode) {
let out = applyBefmRunMode(DATASETS[datasetKey].data, runMode);
if (scenarioFilters.has("merge_pushpull")) {
out = applyMergePushpull(out);
}
return out;
}
LEADERBOARD_DATA = buildLeaderboardData(DEFAULT_DATASET, befmRunMode);
</script>
<script>
"use strict";
// ── State ──
let currentDataset = DEFAULT_DATASET;
let rankingMethod = "winrate";
let showCatDetails = false;
// scenarioFilters (subset of "no_acrossgame", "merge_pushpull") is declared
// in the first <script> block as a var so it is visible before the initial
// buildLeaderboardData call that happens in that block.
const ACROSSGAME_IDS = new Set([
"ml_acrossgame_mae", "ml_acrossgame",
"ho_pp_acrossgame_f1", "ho_pp_acrossgame_wd",
]);
// Standalone push/pull scenarios hidden when "Merge Push/Pull" is on; they
// get folded into the 5 MobLab aggregates as a 9th game instead.
const PUSHPULL_IDS = new Set([
"ho_pp_multiround_f1", "ho_pp_acrossgame_f1",
"ho_pushpull", "ho_pp_multiround_wd", "ho_pp_acrossgame_wd",
]);
// MERGE_TARGETS and applyMergePushpull are declared in the first <script>
// block (so the initial buildLeaderboardData call can use them).
function filterScenarios(scenarios) {
let result = scenarios;
if (scenarioFilters.has("no_acrossgame")) {
result = result.filter(s => !ACROSSGAME_IDS.has(s.id));
}
if (scenarioFilters.has("merge_pushpull")) {
result = result.filter(s => !PUSHPULL_IDS.has(s.id));
}
return result;
}
// ── Levels ──
const levels = ["individual", "distributional"];
const levelNames = {
individual: "Individual Level",
distributional: "Distributional Level"
};
function getLevelScenarios(level) {
return filterScenarios(LEADERBOARD_DATA.scenarios.filter(s => s.level === level));
}
// ── Categories (capability-based, from Table 1) ──
const categories = ["predict_behavior", "infer_characteristics", "strategic_reasoning", "knowledge_reasoning"];
const categoryNames = {
predict_behavior: "Behavior Prediction and Simulation",
infer_characteristics: "Subject-Trait Inference",
strategic_reasoning: "Strategic Decision-Making",
knowledge_reasoning: "Knowledge Application"
};
const categoryShortNames = {
predict_behavior: "Behavior Prediction and Simulation",
infer_characteristics: "Subject-Trait Inference",
strategic_reasoning: "Strategic Decision-Making",
knowledge_reasoning: "Knowledge Application"
};
function getCategoryScenarios(cat) {
return filterScenarios(LEADERBOARD_DATA.scenarios.filter(s => s.category === cat));
}
function getCategoryLevelScenarios(cat, level) {
return filterScenarios(LEADERBOARD_DATA.scenarios.filter(s => s.category === cat && s.level === level));
}
// ── Compute win rates ──
// Return result value for ranking; null if missing or flagged (unreliable).
function rankVal(data, modelId, scenarioId) {
const v = data.results[modelId]?.[scenarioId];
if (v == null) return null;
if (data.flags?.[modelId]?.[scenarioId] != null) return null;
return v;
}
function computeWinRates(data) {
const { models, scenarios, results } = data;
const winRates = {};
models.forEach(m => { winRates[m.id] = {}; });
scenarios.forEach(s => {
const entries = [];
models.forEach(m => {
const val = rankVal(data, m.id, s.id);
if (val != null) entries.push({ id: m.id, val });
});
if (entries.length < 2) {
entries.forEach(e => { winRates[e.id][s.id] = null; });
return;
}
entries.sort((a, b) => s.direction === "lower" ? a.val - b.val : b.val - a.val);
const n = entries.length;
let i = 0;
while (i < n) {
let j = i;
while (j < n && entries[j].val === entries[i].val) j++;
const beaten = n - j;
const tiedWith = j - i - 1;
const wr = (beaten + 0.5 * tiedWith) / (n - 1);
for (let k = i; k < j; k++) {
winRates[entries[k].id][s.id] = wr;
}
i = j;
}
});
return winRates;
}
// ── Compute average ranks ──
function computeAvgRanks(data) {
const { models, scenarios, results } = data;
const ranks = {};
models.forEach(m => { ranks[m.id] = {}; });
scenarios.forEach(s => {
const entries = [];
models.forEach(m => {
const val = rankVal(data, m.id, s.id);
if (val != null) entries.push({ id: m.id, val });
});
if (entries.length < 1) return;
entries.sort((a, b) => s.direction === "lower" ? a.val - b.val : b.val - a.val);
const n = entries.length;
let i = 0;
while (i < n) {
let j = i;
while (j < n && entries[j].val === entries[i].val) j++;
const avgRank = (i + 1 + j) / 2;
for (let k = i; k < j; k++) {
ranks[entries[k].id][s.id] = avgRank;
}
i = j;
}
});
return ranks;
}
function avgScore(scoreMap, modelId, scenarioList) {
const vals = scenarioList
.map(s => scoreMap[modelId][s.id])
.filter(v => v != null);
if (vals.length === 0) return null;
return vals.reduce((a, b) => a + b, 0) / vals.length;
}
// ── Build pairwise win matrix ──
function buildWinMatrix(data, scenarioList) {
const { models, results } = data;
const ids = models.map(m => m.id);
const idx = {}; ids.forEach((id, i) => { idx[id] = i; });
const M = ids.length;
const wins = Array.from({ length: M }, () => new Array(M).fill(0));
scenarioList.forEach(s => {
for (let i = 0; i < M; i++) {
const vi = rankVal(data, ids[i], s.id);
if (vi == null) continue;
for (let j = i + 1; j < M; j++) {
const vj = rankVal(data, ids[j], s.id);
if (vj == null) continue;
const better = s.direction === "lower" ? vi < vj : vi > vj;
const tie = vi === vj;
if (tie) { wins[i][j] += 0.5; wins[j][i] += 0.5; }
else if (better) { wins[i][j] += 1; }
else { wins[j][i] += 1; }
}
}
});
return { ids, idx, wins };
}
// ── ELO Rating ──
function buildEloMatchups(data, scenarioList) {
const { models } = data;
const ids = models.map(m => m.id);
const M = ids.length;
const matchups = [];
scenarioList.forEach(s => {
for (let i = 0; i < M; i++) {
const vi = rankVal(data, ids[i], s.id);
if (vi == null) continue;
for (let j = i + 1; j < M; j++) {
const vj = rankVal(data, ids[j], s.id);
if (vj == null) continue;
if (vi === vj) {
matchups.push({ a: i, b: j, sa: 0.5, sb: 0.5 });
} else {
const better = s.direction === "lower" ? vi < vj : vi > vj;
matchups.push({ a: i, b: j, sa: better ? 1 : 0, sb: better ? 0 : 1 });
}
}
}
});
return { ids, matchups };
}
function seededRandom(seed) {
let state = seed >>> 0;
return function() {
state = (Math.imul(1664525, state) + 1013904223) >>> 0;
return state / 4294967296;
};
}
function computeEloRatings(data, scenarioList, numShuffles, seed) {
if (numShuffles == null) numShuffles = 200;
if (seed == null) seed = 42;
const { ids, matchups } = buildEloMatchups(data, scenarioList);
const M = ids.length;
if (matchups.length === 0) {
const result = {};
ids.forEach(id => { result[id] = null; });
return result;
}
const rand = seededRandom(seed);
function shuffle(arr) {
for (let i = arr.length - 1; i > 0; i--) {
const j = Math.floor(rand() * (i + 1));
[arr[i], arr[j]] = [arr[j], arr[i]];
}
}
const ratingSums = new Array(M).fill(0);
const order = matchups.map((_, i) => i);
for (let s = 0; s < numShuffles; s++) {
const R = new Array(M).fill(1500);
shuffle(order);
for (let k = 0; k < order.length; k++) {
const m = matchups[order[k]];
const ea = 1 / (1 + Math.pow(10, (R[m.b] - R[m.a]) / 400));
const eb = 1 - ea;