{
  "season": "2026-27",
  "model": "soccer_factor_model",
  "metric": "sar",
  "metric_label": "Skill Above Replacement (winsorized goals per 90)",
  "interval_mass": 0.9,
  "current_squads_only": true,
  "generated_from": {
    "n_players": 754,
    "n_observations": 31272,
    "min_minutes": 600,
    "seasons": [
      "2023-24",
      "2024-25",
      "2025-26",
      "2026-27"
    ],
    "time_variation": "season_re",
    "include_own_att": false,
    "ratings_source": "joint_sot",
    "max_rhat": 1.03,
    "divergences": 0
  },
  "appearances_through": "2026-10-25",
  "skill_change_note": "Season-to-season deltas are within posterior noise (sigma_season HDI includes 0). Each season estimate carries its own posterior sd; when the delta is smaller than that sd the change is indistinguishable from zero. Treat the per-season series as descriptive, not as evidence that a player's finishing skill changed.",
  "n_players": 40,
  "players": [
    {
      "slug": "samu-aghehowa",
      "rank": 1,
      "player": "Samu Aghehowa",
      "player_id": 1503836,
      "team": "Porto",
      "position": "F",
      "minutes": 3741,
      "matches": 53,
      "goals": 32,
      "goals_per_90": 0.77,
      "sar": 0.426,
      "sar_sd": 0.0877,
      "skill_lo": 0.2853,
      "skill_hi": 0.5743,
      "xg_skill_per_90": 0.5241,
      "p_above_replacement": 1.0,
      "last_season": "2026-27",
      "seasons": [
        {
          "season": "2024-25",
          "team": "Porto",
          "minutes": 2263,
          "matches": 30,
          "goals": 19,
          "goals_per_90": 0.756,
          "sar_season": 0.4372,
          "sar_season_sd": 0.0883
        },
        {
          "season": "2025-26",
          "team": "Porto",
          "minutes": 1414,
          "matches": 20,
          "goals": 13,
          "goals_per_90": 0.827,
          "sar_season": 0.441,
          "sar_season_sd": 0.0915
        },
        {
          "season": "2026-27",
          "team": "Porto",
          "minutes": 64,
          "matches": 3,
          "goals": 0,
          "goals_per_90": 0.0,
          "sar_season": 0.423,
          "sar_season_sd": 0.0978
        }
      ],
      "skill_change": {
        "from_season": "2025-26",
        "to_season": "2026-27",
        "delta": -0.018,
        "delta_ref_sd": 0.1339,
        "within_noise": true
      },
      "recent": [
        {
          "season": "2026-27",
          "matchday": 9,
          "date": "2026-10-24",
          "opponent": "Gil Vicente",
          "is_home": false,
          "started": false,
          "minutes": 30,
          "goals": 0,
          "assists": 0,
          "rating": 6.3
        },
        {
          "season": "2026-27",
          "matchday": 8,
          "date": "2026-10-10",
          "opponent": "Maritimo",
          "is_home": false,
          "started": false,
          "minutes": 24,
          "goals": 0,
          "assists": 0,
          "rating": 6.5
        },
        {
          "season": "2026-27",
          "matchday": 7,
          "date": "2026-09-20",
          "opponent": "Benfica",
          "is_home": true,
          "started": false,
          "minutes": 10,
          "goals": 0,
          "assists": 0,
          "rating": 6.4
        },
        {
          "season": "2025-26",
          "matchday": 21,
          "date": "2026-02-09",
          "opponent": "Sporting CP",
          "is_home": true,
          "started": true,
          "minutes": 45,
          "goals": 0,
          "assists": 0,
          "rating": 6.4
        },
        {
          "season": "2025-26",
          "matchday": 20,
          "date": "2026-02-02",
          "opponent": "Casa Pia",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.2
        },
        {
          "season": "2025-26",
          "matchday": 19,
          "date": "2026-01-26",
          "opponent": "Gil Vicente",
          "is_home": true,
          "started": true,
          "minutes": 77,
          "goals": 1,
          "assists": 0,
          "rating": 6.9
        },
        {
          "season": "2025-26",
          "matchday": 18,
          "date": "2026-01-18",
          "opponent": "Vitoria SC",
          "is_home": false,
          "started": true,
          "minutes": 72,
          "goals": 0,
          "assists": 0,
          "rating": 5.9
        },
        {
          "season": "2025-26",
          "matchday": 17,
          "date": "2026-01-04",
          "opponent": "Santa Clara",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 1,
          "assists": 0,
          "rating": 7.1
        }
      ]
    },
    {
      "slug": "vangelis-pavlidis",
      "rank": 2,
      "player": "Vangelis Pavlidis",
      "player_id": 795236,
      "team": "Benfica",
      "position": "F",
      "minutes": 5581,
      "matches": 75,
      "goals": 49,
      "goals_per_90": 0.79,
      "sar": 0.4217,
      "sar_sd": 0.0755,
      "skill_lo": 0.3025,
      "skill_hi": 0.5491,
      "xg_skill_per_90": 0.5198,
      "p_above_replacement": 1.0,
      "last_season": "2026-27",
      "seasons": [
        {
          "season": "2024-25",
          "team": "Benfica",
          "minutes": 2275,
          "matches": 34,
          "goals": 19,
          "goals_per_90": 0.752,
          "sar_season": 0.4297,
          "sar_season_sd": 0.0743
        },
        {
          "season": "2025-26",
          "team": "Benfica",
          "minutes": 2667,
          "matches": 33,
          "goals": 22,
          "goals_per_90": 0.742,
          "sar_season": 0.4252,
          "sar_season_sd": 0.0766
        },
        {
          "season": "2026-27",
          "team": "Benfica",
          "minutes": 639,
          "matches": 8,
          "goals": 8,
          "goals_per_90": 1.127,
          "sar_season": 0.434,
          "sar_season_sd": 0.0852
        }
      ],
      "skill_change": {
        "from_season": "2025-26",
        "to_season": "2026-27",
        "delta": 0.0088,
        "delta_ref_sd": 0.1146,
        "within_noise": true
      },
      "recent": [
        {
          "season": "2026-27",
          "matchday": 8,
          "date": "2026-10-11",
          "opponent": "Vitoria SC",
          "is_home": true,
          "started": true,
          "minutes": 82,
          "goals": 0,
          "assists": 1,
          "rating": 7.9
        },
        {
          "season": "2026-27",
          "matchday": 7,
          "date": "2026-09-20",
          "opponent": "Porto",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.9
        },
        {
          "season": "2026-27",
          "matchday": 6,
          "date": "2026-09-13",
          "opponent": "Gil Vicente",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 2,
          "assists": 0,
          "rating": 8.1
        },
        {
          "season": "2026-27",
          "matchday": 3,
          "date": "2026-09-09",
          "opponent": "Moreirense",
          "is_home": false,
          "started": true,
          "minutes": 66,
          "goals": 1,
          "assists": 0,
          "rating": 6.8
        },
        {
          "season": "2026-27",
          "matchday": 5,
          "date": "2026-09-05",
          "opponent": "Maritimo",
          "is_home": false,
          "started": true,
          "minutes": 82,
          "goals": 0,
          "assists": 1,
          "rating": 7.1
        },
        {
          "season": "2026-27",
          "matchday": 4,
          "date": "2026-08-31",
          "opponent": "Estoril",
          "is_home": true,
          "started": true,
          "minutes": 80,
          "goals": 1,
          "assists": 0,
          "rating": 7.4
        },
        {
          "season": "2026-27",
          "matchday": 2,
          "date": "2026-08-17",
          "opponent": "Casa Pia",
          "is_home": false,
          "started": true,
          "minutes": 59,
          "goals": 3,
          "assists": 1,
          "rating": 10.0
        },
        {
          "season": "2026-27",
          "matchday": 1,
          "date": "2026-08-09",
          "opponent": "Academico Viseu",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 1,
          "assists": 0,
          "rating": 7.5
        }
      ]
    },
    {
      "slug": "pedro-goncalves",
      "rank": 3,
      "player": "Pedro Gonçalves",
      "player_id": 895764,
      "team": "Sporting CP",
      "position": "F",
      "minutes": 5467,
      "matches": 73,
      "goals": 29,
      "goals_per_90": 0.477,
      "sar": 0.3499,
      "sar_sd": 0.0745,
      "skill_lo": 0.2274,
      "skill_hi": 0.4767,
      "xg_skill_per_90": 0.448,
      "p_above_replacement": 1.0,
      "last_season": "2025-26",
      "seasons": [
        {
          "season": "2023-24",
          "team": "Sporting CP",
          "minutes": 2591,
          "matches": 32,
          "goals": 11,
          "goals_per_90": 0.382,
          "sar_season": 0.3439,
          "sar_season_sd": 0.0756
        },
        {
          "season": "2024-25",
          "team": "Sporting CP",
          "minutes": 882,
          "matches": 14,
          "goals": 5,
          "goals_per_90": 0.51,
          "sar_season": 0.3489,
          "sar_season_sd": 0.0792
        },
        {
          "season": "2025-26",
          "team": "Sporting CP",
          "minutes": 1994,
          "matches": 27,
          "goals": 13,
          "goals_per_90": 0.587,
          "sar_season": 0.3755,
          "sar_season_sd": 0.082
        }
      ],
      "skill_change": {
        "from_season": "2024-25",
        "to_season": "2025-26",
        "delta": 0.0266,
        "delta_ref_sd": 0.114,
        "within_noise": true
      },
      "recent": [
        {
          "season": "2025-26",
          "matchday": 34,
          "date": "2026-05-16",
          "opponent": "Gil Vicente",
          "is_home": true,
          "started": true,
          "minutes": 73,
          "goals": 0,
          "assists": 1,
          "rating": 7.7
        },
        {
          "season": "2025-26",
          "matchday": 33,
          "date": "2026-05-11",
          "opponent": "Rio Ave",
          "is_home": false,
          "started": true,
          "minutes": 82,
          "goals": 0,
          "assists": 0,
          "rating": 6.7
        },
        {
          "season": "2025-26",
          "matchday": 32,
          "date": "2026-05-04",
          "opponent": "Vitoria SC",
          "is_home": true,
          "started": true,
          "minutes": 78,
          "goals": 0,
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          "rating": 6.9
        },
        {
          "season": "2025-26",
          "matchday": 26,
          "date": "2026-04-29",
          "opponent": "Tondela",
          "is_home": true,
          "started": true,
          "minutes": 75,
          "goals": 0,
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          "rating": 7.0
        },
        {
          "season": "2025-26",
          "matchday": 31,
          "date": "2026-04-26",
          "opponent": "AVS",
          "is_home": false,
          "started": true,
          "minutes": 74,
          "goals": 0,
          "assists": 0,
          "rating": 6.2
        },
        {
          "season": "2025-26",
          "matchday": 30,
          "date": "2026-04-19",
          "opponent": "Benfica",
          "is_home": true,
          "started": true,
          "minutes": 68,
          "goals": 0,
          "assists": 0,
          "rating": 6.2
        },
        {
          "season": "2025-26",
          "matchday": 29,
          "date": "2026-04-11",
          "opponent": "Estrela Amadora",
          "is_home": false,
          "started": true,
          "minutes": 67,
          "goals": 0,
          "assists": 0,
          "rating": 6.1
        },
        {
          "season": "2025-26",
          "matchday": 28,
          "date": "2026-04-03",
          "opponent": "Santa Clara",
          "is_home": true,
          "started": true,
          "minutes": 45,
          "goals": 1,
          "assists": 0,
          "rating": 7.2
        }
      ]
    },
    {
      "slug": "jalen-blesa",
      "rank": 4,
      "player": "Jalen Blesa",
      "player_id": 1499082,
      "team": "Rio Ave",
      "position": "F",
      "minutes": 1863,
      "matches": 22,
      "goals": 10,
      "goals_per_90": 0.483,
      "sar": 0.2952,
      "sar_sd": 0.1008,
      "skill_lo": 0.143,
      "skill_hi": 0.4705,
      "xg_skill_per_90": 0.3933,
      "p_above_replacement": 1.0,
      "last_season": "2026-27",
      "seasons": [
        {
          "season": "2025-26",
          "team": "Rio Ave",
          "minutes": 1077,
          "matches": 13,
          "goals": 7,
          "goals_per_90": 0.585,
          "sar_season": 0.3082,
          "sar_season_sd": 0.1045
        },
        {
          "season": "2026-27",
          "team": "Rio Ave",
          "minutes": 786,
          "matches": 9,
          "goals": 3,
          "goals_per_90": 0.344,
          "sar_season": 0.2969,
          "sar_season_sd": 0.105
        }
      ],
      "skill_change": {
        "from_season": "2025-26",
        "to_season": "2026-27",
        "delta": -0.0113,
        "delta_ref_sd": 0.1481,
        "within_noise": true
      },
      "recent": [
        {
          "season": "2026-27",
          "matchday": 9,
          "date": "2026-10-25",
          "opponent": "Famalicao",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.8
        },
        {
          "season": "2026-27",
          "matchday": 8,
          "date": "2026-10-11",
          "opponent": "Nacional",
          "is_home": true,
          "started": true,
          "minutes": 78,
          "goals": 1,
          "assists": 0,
          "rating": 8.1
        },
        {
          "season": "2026-27",
          "matchday": 7,
          "date": "2026-09-19",
          "opponent": "Alverca",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.9
        },
        {
          "season": "2026-27",
          "matchday": 6,
          "date": "2026-09-14",
          "opponent": "Estrela Amadora",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 1,
          "assists": 0,
          "rating": 8.0
        },
        {
          "season": "2026-27",
          "matchday": 5,
          "date": "2026-09-06",
          "opponent": "Santa Clara",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.7
        },
        {
          "season": "2026-27",
          "matchday": 4,
          "date": "2026-08-28",
          "opponent": "Sporting CP",
          "is_home": true,
          "started": true,
          "minutes": 86,
          "goals": 0,
          "assists": 0,
          "rating": 6.7
        },
        {
          "season": "2026-27",
          "matchday": 3,
          "date": "2026-08-22",
          "opponent": "Estoril",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 1,
          "assists": 1,
          "rating": 8.6
        },
        {
          "season": "2026-27",
          "matchday": 2,
          "date": "2026-08-15",
          "opponent": "Porto",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.8
        }
      ]
    },
    {
      "slug": "yanis-begraoui",
      "rank": 5,
      "player": "Yanis Begraoui",
      "player_id": 930246,
      "team": "Estoril",
      "position": "F",
      "minutes": 5286,
      "matches": 75,
      "goals": 33,
      "goals_per_90": 0.562,
      "sar": 0.2681,
      "sar_sd": 0.0679,
      "skill_lo": 0.1606,
      "skill_hi": 0.3849,
      "xg_skill_per_90": 0.3662,
      "p_above_replacement": 1.0,
      "last_season": "2026-27",
      "seasons": [
        {
          "season": "2024-25",
          "team": "Estoril",
          "minutes": 1930,
          "matches": 34,
          "goals": 11,
          "goals_per_90": 0.513,
          "sar_season": 0.2683,
          "sar_season_sd": 0.0706
        },
        {
          "season": "2025-26",
          "team": "Estoril",
          "minutes": 2726,
          "matches": 34,
          "goals": 20,
          "goals_per_90": 0.66,
          "sar_season": 0.2838,
          "sar_season_sd": 0.0715
        },
        {
          "season": "2026-27",
          "team": "Estoril",
          "minutes": 630,
          "matches": 7,
          "goals": 2,
          "goals_per_90": 0.286,
          "sar_season": 0.2657,
          "sar_season_sd": 0.0757
        }
      ],
      "skill_change": {
        "from_season": "2025-26",
        "to_season": "2026-27",
        "delta": -0.0181,
        "delta_ref_sd": 0.1041,
        "within_noise": true
      },
      "recent": [
        {
          "season": "2026-27",
          "matchday": 7,
          "date": "2026-09-20",
          "opponent": "Casa Pia",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 7.0
        },
        {
          "season": "2026-27",
          "matchday": 6,
          "date": "2026-09-14",
          "opponent": "SC Braga",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 5.9
        },
        {
          "season": "2026-27",
          "matchday": 5,
          "date": "2026-09-07",
          "opponent": "Arouca",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 7.1
        },
        {
          "season": "2026-27",
          "matchday": 4,
          "date": "2026-08-31",
          "opponent": "Benfica",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 1,
          "assists": 0,
          "rating": 7.7
        },
        {
          "season": "2026-27",
          "matchday": 3,
          "date": "2026-08-22",
          "opponent": "Rio Ave",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 7.0
        },
        {
          "season": "2026-27",
          "matchday": 2,
          "date": "2026-08-16",
          "opponent": "Nacional",
          "is_home": false,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.4
        },
        {
          "season": "2026-27",
          "matchday": 1,
          "date": "2026-08-07",
          "opponent": "Famalicao",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 1,
          "assists": 0,
          "rating": 8.3
        },
        {
          "season": "2025-26",
          "matchday": 34,
          "date": "2026-05-16",
          "opponent": "Benfica",
          "is_home": true,
          "started": true,
          "minutes": 90,
          "goals": 0,
          "assists": 0,
          "rating": 6.5
        }
      ]
    },
    {
      "slug": "goncalo-paciencia",
      "rank": 6,
      "player": "Gonçalo Paciência",
      "player_id": 138890,
      "team": "Santa Clara",
      "position": "F",
      "minutes": 1115,
      "matches": 20,
      "goals": 8,
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      "sar": 0.2679,
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      "skill_lo": 0.1091,
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      "xg_skill_per_90": 0.366,
      "p_above_replacement": 1.0,
      "last_season": "2026-27",
      "seasons": [
        {
          "season": "2025-26",
          "team": "Santa Clara",
          "minutes": 507,
          "matches": 12,
          "goals": 3,
          "goals_per_90": 0.533,
          "sar_season": 0.2706,
          "sar_season_sd": 0.1087
        },
        {
          "season": "2026-27",
          "team": "Santa Clara",
          "minutes": 608,
          "matches": 8,
          "goals": 5,
          "goals_per_90": 0.74,
          "sar_season": 0.276,
          "sar_season_sd": 0.1098
        }
      ],
      "skill_change": {
        "from_season": "2025-26",
        "to_season": "2026-27",
        "delta": 0.0054,
        "delta_ref_sd": 0.1545,
        "within_noise": true
      },
      "recent": [
        {
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