{
 "model_version": "mp_monte_carlo/0.2.2",
 "snapshot_hash": "9d03839c4a94271b211528cd3533cd97ab499905a794bfde56adc69b568793a1",
 "snapshot_time": "2026-09-20T17:18:58.161Z",
 "master_seed": 20260917,
 "trials": 50000,
 "run": {
  "model_version": "mp_monte_carlo/0.2.2",
  "snapshot_hash": "9d03839c4a94271b211528cd3533cd97ab499905a794bfde56adc69b568793a1",
  "snapshot_time": "2026-09-20T17:18:58.161Z",
  "snapshot_path": "chess_model_tournament/data/runs/timeline/snapshot_r4.json",
  "config": {
   "_comment": "Spec §4.1 defaults. Every run stamps the RESOLVED config (this + event + CLI overrides) into simulation_summary.json. Changing a calibration value here is a decision (ai/decisions.md) with evidence, never a silent edit.",
   "model_version": "mp_monte_carlo/0.2.2",
   "boards_per_match": 4,
   "match_points": {
    "win": 2,
    "draw": 1,
    "loss": 0
   },
   "ranking_mode": "MP_ONLY",
   "tie_policy": "SHARED_MAX_MP",
   "win_split_policy": "EQUAL_SPLIT",
   "_win_split_comment": "D4: p_win_equal_split = 1/k among k tied leaders, reported beside p_highest_mp. Future: TB_PROXY (spec v1.1).",
   "board_model": {
    "kind": "rating_davidson_softmax",
    "_kind_comment": "D5 (operator 2026-09-17): the board W/D/B comes from an Elo formula — chess_model's pre-game Davidson-softmax form, refit here on the whole human field (1400-2900) with a draw-vs-gap term; artifact below. 'spec_v1_closed_form' (the spec's d0/kappa/H construction) is kept as the alternative and is what the spec text describes.",
    "artifact": "config/board_model_olympiad_v0.2.json",
    "_artifact_comment": "D16 (2026-09-18): fitted on 17,331 Olympiad boards 2014-2024 (tools/fit_board_model_olympiad.py) with a level-by-gap term; beats the relay-corpus fit v0.1 (config/board_model_davidson_v0.1.json, kept) on every held-out Olympiad by 0.010-0.023 nats. v0.1 under-rated an elite favourite by up to 8 points of expected score.",
    "white_advantage_elo": 35,
    "equal_rating_draw_rate": 0.5,
    "draw_decay_elo": 400,
    "_spec_params_comment": "white_advantage_elo / equal_rating_draw_rate / draw_decay_elo are used ONLY by kind=spec_v1_closed_form. Under rating_davidson_softmax the White advantage is the artifact's fitted intercept (~45 Elo).",
    "probability_sum_tolerance": 1e-9,
    "unrated_rating_floor": 1400,
    "_unrated_comment": "D8: Chess-Results prints unrated as Rtg 0; 16 of 205 teams have <4 rated players. Simulated at FIDE's own floor (1400), flagged unrated:true; the snapshot keeps rating:null."
   },
   "team_elo_adjustments": {
    "USA": 6,
    "IND": 25.8,
    "UZB": 19.5,
    "CHN": 0,
    "GER": 11.9,
    "NED": 0,
    "AZE": 11.9,
    "HUN": 0,
    "FRA": 7.9,
    "ARM": 7.6
   },
   "team_elo_adjustments_max_starting_rank": 10,
   "_team_elo_comment": "D35 (operator, 2026-09-20), REPLACING D17's rating-change buckets. Elo added to every player of the team = the mean AGE SHIFT of its strongest four, where the shift is fitted on RESULTS (not on rating change): four age bins relative to 27+, <=20 +31.7, 21-23 +23.8, 24-26 +15.2, 27+ 0, measured with the board model held fixed on 5,939 elite relay games (both players 2600+, 2023-2026, 226 players, 51 federations, population-complete). D17's rating-change rates were selection-inflated (they vanish above 2650) and its 24-30 bucket understated the 24-26 group about fourfold; the one-year lag it assumed IS confirmed by the results fit (1.07 years, CI 0.54-1.64). Evidence and every caveat: docs/rating_lag_review_2026-09-20.md. Applied to seeds 1-10 ONLY, enforced by team_elo_adjustments_max_starting_rank (a federation key alone used to reach Uzbekistan 2 and 3); a team_id key overrides a federation key. Every other team is 0. UZB +30 stays NOT adopted (D15). What-ifs: config/scenarios.json. The backtest applies this only via tools/backtest.mjs --adjustments. Recompute: ages from tools/rating_trajectory.mjs; the bins from data/runs/review_20260920/scripts/.",
   "run_modes": {
    "interactive": 100000,
    "final": 1000000,
    "test": 10000
   },
   "thresholds_mp": [
    14,
    16,
    18,
    20
   ],
   "trajectory_quantiles": [
    0.1,
    0.5,
    0.9
   ],
   "pairing": {
    "bye_enabled": false,
    "bye_mp": 1,
    "bye_game_points": 2,
    "_bye_comment": "FIDE Olympiad Pairing Rules art. 4.3: a bye is 1 matchpoint and 2 gamepoints — NOT the spec's 2 MP (§8.4). Used when crediting a real bye in the snapshot (Kiribati, round 3); the simulator never awards one under D6. Verify against the round-4 'MP before' column.",
    "merge_adjacent_groups_only_when_no_legal_matching": true,
    "pairing_order": "top_down",
    "_order_comment": "Olympiad rules 6.4 pair top groups down to the middle, then bottom groups up, then the middle; the spec (§8.2) pairs top-down only. Implemented as the spec says; TASK-9 measures the divergence."
   }
  },
  "config_hash": "7ec2a044183a19765a91c828d3d2822087035f0542afcb533dad75542edd3d70",
  "artifact": "chess_model_tournament/config/board_model_olympiad_v0.2.json",
  "artifact_sha256": "1f24c5aa9d6e69497a66d333b9f72fbb7117776e0bc924e1633879d45c876074",
  "master_seed": 20260917,
  "trials": 50000,
  "workers": 4,
  "started_at": "2026-09-20T17:18:58.323Z",
  "elapsed_s": 44.804
 },
 "tournament": {
  "tournament_id": "olympiad_open_2026",
  "rounds_total": 11,
  "boards_per_match": 4,
  "team_count": 206,
  "active_teams": [
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  ],
  "excluded_teams": []
 },
 "excluded_teams": [],
 "sums": {
  "p_highest_mp": 1.4096399999999998,
  "p_win_equal_split": 1,
  "p_win": 1
 },
 "p_win_method": "TB_PROXY (Sonneborn-Berger on the trial, then game points, then shared)",
 "as_of": {
  "last_completed_round": 4,
  "current_round": null
 },
 "note_highest_mp": "p_highest_mp counts every team sharing the maximum MP; tied leaders are counted independently, so the column can sum to more than 1. p_win_equal_split splits a k-way tie 1/k (D4) and sums to 1.",
 "teams": [
  {
   "team_id": 1,
   "team_name": "United States of America",
   "federation": "USA",
   "starting_rank": 1,
   "active": true,
   "expected_final_mp": 17.996599999999997,
   "median_final_mp": 18,
   "final_mp_pmf": {
    "13": 0.00006,
    "14": 0.0019,
    "15": 0.03014,
    "16": 0.13434,
    "17": 0.2391,
    "18": 0.23864,
    "19": 0.18252,
    "20": 0.1132,
    "21": 0.04662,
    "22": 0.01348
   },
   "p_highest_mp": 0.3787,
   "p_unique_highest_mp": 0.22502,
   "p_win_equal_split": 0.2899564523809524,
   "p_win_tb_proxy": 0.30276,
   "p_win": 0.30276,
   "p_mp_at_least": {
    "14": 0.99994,
    "16": 0.9679,
    "18": 0.59446,
    "20": 0.1733
   }
  },
  {
   "team_id": 2,
   "team_name": "India",
   "federation": "IND",
   "starting_rank": 2,
   "active": true,
   "expected_final_mp": 18.10002,
   "median_final_mp": 18,
   "final_mp_pmf": {
    "13": 0.00006,
    "14": 0.00156,
    "15": 0.02592,
    "16": 0.12376,
    "17": 0.22682,
    "18": 0.23986,
    "19": 0.19092,
    "20": 0.12118,
    "21": 0.0543,
    "22": 0.01562
   },
   "p_highest_mp": 0.40558,
   "p_unique_highest_mp": 0.2462,
   "p_win_equal_split": 0.3135739285714286,
   "p_win_tb_proxy": 0.32205,
   "p_win": 0.32205,
   "p_mp_at_least": {
    "14": 0.99994,
    "16": 0.97246,
    "18": 0.62188,
    "20": 0.1911
   }
  },
  {
   "team_id": 3,
   "team_name": "Uzbekistan",
   "federation": "UZB",
   "starting_rank": 3,
   "active": true,
   "expected_final_mp": 17.51366,
   "median_final_mp": 17,
   "final_mp_pmf": {
    "13": 0.00022,
    "14": 0.00524,
    "15": 0.05612,
    "16": 0.19408,
    "17": 0.27852,
    "18": 0.2279,
    "19": 0.13866,
    "20": 0.07068,
    "21": 0.02358,
    "22": 0.005
   },
   "p_highest_mp": 0.25814,
   "p_unique_highest_mp": 0.13544,
   "p_win_equal_split": 0.18623581746031745,
   "p_win_tb_proxy": 0.1963,
   "p_win": 0.1963,
   "p_mp_at_least": {
    "14": 0.99978,
    "16": 0.93842,
    "18": 0.46582,
    "20": 0.09926
   }
  },
  {
   "team_id": 4,
   "team_name": "China",
   "federation": "CHN",
   "starting_rank": 4,
   "active": true,
   "expected_final_mp": 16.77086,
   "median_final_mp": 17,
   "final_mp_pmf": {
    "12": 0.00002,
    "13": 0.00074,
    "14": 0.01628,
    "15": 0.12318,
    "16": 0.31078,
    "17": 0.29702,
    "18": 0.15968,
    "19": 0.06318,
    "20": 0.0234,
    "21": 0.00494,
    "22": 0.00078
   },
   "p_highest_mp": 0.11794,
   "p_unique_highest_mp": 0.04856,
   "p_win_equal_split": 0.07590510317460318,
   "p_win_tb_proxy": 0.08522,
   "p_win": 0.08522,
   "p_mp_at_least": {
    "14": 0.99924,
    "16": 0.85978,
    "18": 0.25198,
    "20": 0.02912
   }
  },
  {
   "team_id": 5,
   "team_name": "Germany",
   "federation": "GER",
   "starting_rank": 5,
   "active": true,
   "expected_final_mp": 16.447200000000002,
   "median_final_mp": 16,
   "final_mp_pmf": {
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    "14": 0.02922,
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   "p_highest_mp": 0.0717,
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   "p_win_equal_split": 0.04252087301587301,
   "p_win_tb_proxy": 0.03324,
   "p_win": 0.03324,
   "p_mp_at_least": {
    "14": 0.99804,
    "16": 0.80094,
    "18": 0.16908,
    "20": 0.01216
   }
  },
  {
   "team_id": 6,
   "team_name": "Netherlands",
   "federation": "NED",
   "starting_rank": 6,
   "active": true,
   "expected_final_mp": 16.260980000000004,
   "median_final_mp": 16,
   "final_mp_pmf": {
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    "14": 0.0393,
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    "22": 0.00012
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   "p_highest_mp": 0.04954,
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   "p_win_equal_split": 0.02774781746031746,
   "p_win_tb_proxy": 0.01813,
   "p_win": 0.01813,
   "p_mp_at_least": {
    "14": 0.99678,
    "16": 0.75746,
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    "20": 0.00666
   }
  },
  {
   "team_id": 7,
   "team_name": "Azerbaijan",
   "federation": "AZE",
   "starting_rank": 7,
   "active": true,
   "expected_final_mp": 16.206780000000002,
   "median_final_mp": 16,
   "final_mp_pmf": {
    "12": 0.00004,
    "13": 0.00326,
    "14": 0.03402,
    "15": 0.20834,
    "16": 0.38558,
    "17": 0.27006,
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   "p_highest_mp": 0.04274,
   "p_unique_highest_mp": 0.012,
   "p_win_equal_split": 0.02333804761904762,
   "p_win_tb_proxy": 0.01834,
   "p_win": 0.01834,
   "p_mp_at_least": {
    "14": 0.9967,
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   }
  },
  {
   "team_id": 8,
   "team_name": "Hungary",
   "federation": "HUN",
   "starting_rank": 8,
   "active": true,
   "expected_final_mp": 15.955160000000001,
   "median_final_mp": 16,
   "final_mp_pmf": {
    "12": 0.0002,
    "13": 0.00664,
    "14": 0.06468,
    "15": 0.2511,
    "16": 0.39692,
    "17": 0.21764,
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    "21": 0.00018,
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   "p_highest_mp": 0.02286,
   "p_unique_highest_mp": 0.00564,
   "p_win_equal_split": 0.011818968253968254,
   "p_win_tb_proxy": 0.00628,
   "p_win": 0.00628,
   "p_mp_at_least": {
    "14": 0.99316,
    "16": 0.67738,
    "18": 0.06282,
    "20": 0.00176
   }
  },
  {
   "team_id": 9,
   "team_name": "France",
   "federation": "FRA",
   "starting_rank": 9,
   "active": true,
   "expected_final_mp": 15.815719999999999,
   "median_final_mp": 16,
   "final_mp_pmf": {
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    "13": 0.00894,
    "14": 0.07402,
    "15": 0.29188,
    "16": 0.38574,
    "17": 0.20066,
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   "p_highest_mp": 0.01496,
   "p_unique_highest_mp": 0.0034,
   "p_win_equal_split": 0.00742852380952381,
   "p_win_tb_proxy": 0.00664,
   "p_win": 0.00664,
   "p_mp_at_least": {
    "14": 0.9908,
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  },
  {
   "team_id": 10,
   "team_name": "Armenia",
   "federation": "ARM",
   "starting_rank": 10,
   "active": true,
   "expected_final_mp": 15.865379999999998,
   "median_final_mp": 16,
   "final_mp_pmf": {
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    "14": 0.07366,
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   "p_win": 0.00544,
   "p_mp_at_least": {
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  {
   "team_id": 11,
   "team_name": "England",
   "federation": "ENG",
   "starting_rank": 11,
   "active": true,
   "expected_final_mp": 15.54224,
   "median_final_mp": 16,
   "final_mp_pmf": {
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   "p_win_equal_split": 0.0025303015873015876,
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   "p_win": 0.00114,
   "p_mp_at_least": {
    "14": 0.98078,
    "16": 0.51962,
    "18": 0.01842,
    "20": 0.0002
   }
  },
  {
   "team_id": 12,
   "team_name": "Ukraine",
   "federation": "UKR",
   "starting_rank": 12,
   "active": true,
   "expected_final_mp": 15.51694,
   "median_final_mp": 16,
   "final_mp_pmf": {
    "12": 0.00112,
    "13": 0.0198,
    "14": 0.12472,
    "15": 0.33696,
    "16": 0.37164,
    "17": 0.12622,
    "18": 0.01776,
    "19": 0.00164,
    "20": 0.00014
   },
   "p_highest_mp": 0.00546,
   "p_unique_highest_mp": 0.0007,
   "p_win_equal_split": 0.0023753015873015874,
   "p_win_tb_proxy": 0.00078,
   "p_win": 0.00078,
   "p_mp_at_least": {
    "14": 0.97908,
    "16": 0.5174,
    "18": 0.01954,
    "20": 0.00014
   }
  },
  {
   "team_id": 13,
   "team_name": "Spain",
   "federation": "ESP",
   "starting_rank": 13,
   "active": true,
   "expected_final_mp": 15.48668,
   "median_final_mp": 16,
   "final_mp_pmf": {
    "12": 0.001,
    "13": 0.02124,
    "14": 0.12864,
    "15": 0.34136,
    "16": 0.3735,
    "17": 0.1168,
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    "19": 0.00104,
    "20": 0.00014
   },
   "p_highest_mp": 0.0046,
   "p_unique_highest_mp": 0.0006,
   "p_win_equal_split": 0.0019333015873015873,
   "p_win_tb_proxy": 0.00104,
   "p_win": 0.00104,
   "p_mp_at_least": {
    "14": 0.97776,
    "16": 0.50776,
    "18": 0.01746,
    "20": 0.00014
   }
  },
  {
   "team_id": 14,
   "team_name": "Turkiye",
   "federation": "TUR",
   "starting_rank": 14,
   "active": true,
   "expected_final_mp": 15.43534,
   "median_final_mp": 15,
   "final_mp_pmf": {
    "11": 0.00004,
    "12": 0.0012,
    "13": 0.0241,
    "14": 0.13484,
    "15": 0.34986,
    "16": 0.37274,
    "17": 0.103,
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   "p_win_tb_proxy": 0,
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    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 199,
   "team_name": "Niger",
   "federation": "NIG",
   "starting_rank": 199,
   "active": true,
   "expected_final_mp": 5.751879999999999,
   "median_final_mp": 6,
   "final_mp_pmf": {
    "0": 0.00022,
    "1": 0.0016,
    "2": 0.00844,
    "3": 0.02986,
    "4": 0.09812,
    "5": 0.26282,
    "6": 0.33414,
    "7": 0.1952,
    "8": 0.06076,
    "9": 0.00848,
    "10": 0.00036
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   "p_win_tb_proxy": 0,
   "p_win": 0,
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    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 200,
   "team_name": "Greenland",
   "federation": "GRL",
   "starting_rank": 200,
   "active": true,
   "expected_final_mp": 6.155760000000001,
   "median_final_mp": 6,
   "final_mp_pmf": {
    "2": 0.00128,
    "3": 0.00888,
    "4": 0.05624,
    "5": 0.21144,
    "6": 0.3472,
    "7": 0.25778,
    "8": 0.09914,
    "9": 0.01678,
    "10": 0.00126
   },
   "p_highest_mp": 0,
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   "p_win_tb_proxy": 0,
   "p_win": 0,
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    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 201,
   "team_name": "Guinea",
   "federation": "GUI",
   "starting_rank": 201,
   "active": true,
   "expected_final_mp": 5.697500000000001,
   "median_final_mp": 6,
   "final_mp_pmf": {
    "2": 0.00458,
    "3": 0.0249,
    "4": 0.1124,
    "5": 0.27738,
    "6": 0.3459,
    "7": 0.1823,
    "8": 0.0474,
    "9": 0.00496,
    "10": 0.00018
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   "p_highest_mp": 0,
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   "p_win_tb_proxy": 0,
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    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
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  },
  {
   "team_id": 202,
   "team_name": "Laos",
   "federation": "LAO",
   "starting_rank": 202,
   "active": true,
   "expected_final_mp": 5.64574,
   "median_final_mp": 6,
   "final_mp_pmf": {
    "2": 0.0057,
    "3": 0.0289,
    "4": 0.1225,
    "5": 0.27458,
    "6": 0.34348,
    "7": 0.17908,
    "8": 0.04168,
    "9": 0.00394,
    "10": 0.00014
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   "p_highest_mp": 0,
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    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 203,
   "team_name": "Saint Kitts and Nevis",
   "federation": "SKN",
   "starting_rank": 203,
   "active": true,
   "expected_final_mp": 4.372240000000001,
   "median_final_mp": 4,
   "final_mp_pmf": {
    "0": 0.00854,
    "1": 0.0304,
    "2": 0.08292,
    "3": 0.1507,
    "4": 0.22892,
    "5": 0.25792,
    "6": 0.17554,
    "7": 0.05574,
    "8": 0.0087,
    "9": 0.0006,
    "10": 0.00002
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   "p_highest_mp": 0,
   "p_unique_highest_mp": 0,
   "p_win_equal_split": 0,
   "p_win_tb_proxy": 0,
   "p_win": 0,
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    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 204,
   "team_name": "Tonga",
   "federation": "TGA",
   "starting_rank": 204,
   "active": true,
   "expected_final_mp": 5.1209999999999996,
   "median_final_mp": 5,
   "final_mp_pmf": {
    "2": 0.02222,
    "3": 0.07616,
    "4": 0.19916,
    "5": 0.30762,
    "6": 0.27152,
    "7": 0.10406,
    "8": 0.01758,
    "9": 0.00164,
    "10": 0.00004
   },
   "p_highest_mp": 0,
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   "p_win_tb_proxy": 0,
   "p_win": 0,
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    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 205,
   "team_name": "Kiribati",
   "federation": "KIR",
   "starting_rank": 205,
   "active": true,
   "expected_final_mp": 4.87446,
   "median_final_mp": 5,
   "final_mp_pmf": {
    "1": 0.01162,
    "2": 0.04012,
    "3": 0.10678,
    "4": 0.20208,
    "5": 0.3002,
    "6": 0.23598,
    "7": 0.08964,
    "8": 0.01266,
    "9": 0.0009,
    "10": 0.00002
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   "p_highest_mp": 0,
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   "p_win_equal_split": 0,
   "p_win_tb_proxy": 0,
   "p_win": 0,
   "p_mp_at_least": {
    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  },
  {
   "team_id": 206,
   "team_name": "Marshall Islands",
   "federation": "MHL",
   "starting_rank": 206,
   "active": true,
   "expected_final_mp": 4.16442,
   "median_final_mp": 4,
   "final_mp_pmf": {
    "0": 0.01314,
    "1": 0.04448,
    "2": 0.10324,
    "3": 0.16554,
    "4": 0.22814,
    "5": 0.23384,
    "6": 0.15464,
    "7": 0.04914,
    "8": 0.00734,
    "9": 0.00046,
    "10": 0.00004
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   "p_highest_mp": 0,
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   "p_win_tb_proxy": 0,
   "p_win": 0,
   "p_mp_at_least": {
    "14": 0,
    "16": 0,
    "18": 0,
    "20": 0
   }
  }
 ]
}