{
  "abstract": "Before every neutral objective in professional League of Legends, each team decides which of its five players walk to the pit, which hold a lane, and when to commit. The leading analysis of such setups, TAGNet for Counter-Strike 2, clusters graph-network embeddings of player positions and reads cluster win rates as tactical quality. We treat a setup as an allocation on a walled map: formations are set partitions on the lattice $Π_5$, control is a geodesic Voronoi split of a navigation graph, and commitment is an allocation game solved as a quantal response equilibrium priced in win probability. On all 164 games of MSI and Worlds 2025 (2,994 team-setups, minimap tracks validated against Riot positions), trailing teams leave the pit empty far more often than leading teams, by +34.8 percentage points at the first baron and +30.4 percentage points at Atakhan. Our model, HASSE-QRE, finds six setup patterns that whole-model series-bootstrap refits reproduce (ARI 0.819, comparable to 0.813 for TAGNet's $K$-Means step alone) and indicates that teams price fights, travel and committed players, not the objective itself (weight 0.018; fixing it to one costs 59.9 log-likelihood points). The equilibrium reproduces a quarter of the commitment gap, almost all of it through state variables rather than its strategic channels. Weighting a team-level contrast by exposure moves it across $p=0.05$ (0.046 against 0.052). We release the tracks, setups and code.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33626",
  "author_total": 4,
  "authors": [
    {
      "name": "Zheng Gao"
    },
    {
      "name": "Zhenyu Liu"
    },
    {
      "name": "Yifan Yang"
    },
    {
      "name": "Xiaoyu Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dd8v3yrf1a9z2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33626",
  "fulltext_url": null,
  "id": "dd8v3yrf1a9z2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33626",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "openalex",
      "2002|Sports Analytics and Performance"
    ]
  ],
  "openalex": "W7223854826",
  "pdf_url": "https://arxiv.org/pdf/2610.33626",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dd8v3yrf1a9z2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:49Z",
      "native_id": "2610.33626",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33626"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Allocation Before the Clock: Graph, Set and Game Theory of Professional League of Legends Objective Setups",
  "title_text": "Allocation Before the Clock: Graph, Set and Game Theory of Professional League of Legends Objective Setups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/dd8v3yrf1a9z2",
  "venue": "arXiv",
  "versions": []
}