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"padj_interceptionWon": 0.0, "padj_totalClearance": 1.358939, "padj_blockedScoringAttempt": 0.0, "mean_opp_possession": 0.530625, "duel_win_pct": 0.8 }, { "player": "Matheus Mendes", "team": "Alverca", "position": "G", "minutes": 900.0, "matches": 10, "p90_def_actions": 1.4, "padj_def_actions": 1.296296, "padj_totalTackle": 0.0, "padj_interceptionWon": 0.0, "padj_totalClearance": 1.296296, "padj_blockedScoringAttempt": 0.0, "mean_opp_possession": 0.54, "duel_win_pct": 0.727273 }, { "player": "Ignacio de Arruabarrena", "team": "Arouca", "position": "G", "minutes": 4320.0, "matches": 48, "p90_def_actions": 1.229167, "padj_def_actions": 1.292726, "padj_totalTackle": 0.065732, "padj_interceptionWon": 0.021911, "padj_totalClearance": 1.161262, "padj_blockedScoringAttempt": 0.0, "mean_opp_possession": 0.475417, "duel_win_pct": 0.666667 }, { "player": "Nico Mantl", "team": "Arouca", "position": "G", "minutes": 3330.0, "matches": 37, "p90_def_actions": 1.243243, "padj_def_actions": 1.284199, "padj_totalTackle": 0.0, "padj_interceptionWon": 0.027917, "padj_totalClearance": 1.256281, "padj_blockedScoringAttempt": 0.0, "mean_opp_possession": 0.484054, "duel_win_pct": 0.769231 }, { "player": "Lucas Fran\u00e7a", "team": "Santa Clara", "position": "G", "minutes": 3555.0, "matches": 40, "p90_def_actions": 1.316456, "padj_def_actions": 1.237852, "padj_totalTackle": 0.0, "padj_interceptionWon": 0.0, "padj_totalClearance": 1.237852, "padj_blockedScoringAttempt": 0.0, "mean_opp_possession": 0.53175, "duel_win_pct": 0.925926 } ] } }, "caveats": [ "NO RANKING IS PUBLISHED. Individual players could not be separated from their team by the pre-registered criterion: >= 20 players with shrinkage >= 0.2 AND positive walk-forward log-score gain. Only 0 of 786 players had a posterior meaningfully narrower than the population prior.", "Substitution timing is not in the source data. Exposure is minutes-weighted, so a substitute is credited with a fraction of the whole match rather than the specific minutes they were on the pitch.", "One static effect per player across the whole panel: 34 matches a season is too thin for a per-season defensive effect.", "Goals conceded is a team outcome. Every on-pitch player is in the model, not only defenders, because forwards pressing also matter.", "Players below the minutes threshold are pooled into a single replacement bucket pinned at zero.", "27% of the spread in the point estimates is between clubs rather than between club-mates, and the ratings correlate at r=-0.51 with their club's goals conceded per match: what is being measured is mostly the club, with player names attached.", "Averaged to club level the ratings reproduce club goals conceded at r=-0.985 across 23 clubs. The model is a club defence model that distributes its answer over whoever was on the pitch.", "Collinearity retains only 11% of the information the line-ups nominally carry: summed over players the model resolves 11 effective parameters against 105 if every other effect were known. The most-used player in the panel, Diogo Costa (8822 minutes), reaches shrinkage 0.028 where 0.324 was attainable.", "With the shared hierarchical mean removed, frequent team-mates have a median posterior correlation of -0.04 (players who never shared a pitch: -0.00); the data pins their combined effect better than the split between them.", "Walk-forward (fit 2023-24+2024-25, score 2025-26): adding player effects changed the out-of-sample log score by +2.34 nats over 612 team-matches (t = +1.70)." ], "what_the_model_could_distinguish": { "note": "Club-level defensive quality is identified; individual players inside a club are not. The club column below is the mean of that club's player ratings, which tracks the club's actual goals conceded almost perfectly -- the model is measuring the club.", "club_level_corr": -0.98468, "clubs": [ { "primary_team": "Porto", "club_gc": 0.7282, "mean_rating": 0.1317 }, { "primary_team": "Benfica", "club_gc": 0.8058, "mean_rating": 0.1281 }, { "primary_team": "Sporting CP", "club_gc": 0.7961, "mean_rating": 0.128 }, { "primary_team": "Famalicao", "club_gc": 1.068, "mean_rating": 0.1145 }, { "primary_team": "Santa Clara", "club_gc": 1.087, "mean_rating": 0.1119 }, { "primary_team": "SC Braga", "club_gc": 1.1456, "mean_rating": 0.108 }, { "primary_team": "Vitoria SC", "club_gc": 1.233, "mean_rating": 0.1047 }, { "primary_team": "Moreirense", "club_gc": 1.3204, "mean_rating": 0.0998 }, { "primary_team": "Gil Vicente", "club_gc": 1.3301, "mean_rating": 0.0997 }, { "primary_team": "Nacional", "club_gc": 1.4058, "mean_rating": 0.0963 }, { "primary_team": "Farense", "club_gc": 1.4265, "mean_rating": 0.0952 }, { "primary_team": "Rio Ave", "club_gc": 1.5146, "mean_rating": 0.0946 }, { "primary_team": "Alverca", "club_gc": 1.5429, "mean_rating": 0.0942 }, { "primary_team": "Estrela Amadora", "club_gc": 1.5631, "mean_rating": 0.0933 }, { "primary_team": "Casa Pia", "club_gc": 1.4757, "mean_rating": 0.0928 }, { "primary_team": "Tondela", "club_gc": 1.6176, "mean_rating": 0.0918 }, { "primary_team": "Arouca", "club_gc": 1.5825, "mean_rating": 0.0898 }, { "primary_team": "Estoril", "club_gc": 1.6408, "mean_rating": 0.0852 }, { "primary_team": "Boavista", "club_gc": 1.7794, "mean_rating": 0.0845 }, { "primary_team": "AVS", "club_gc": 1.8676, "mean_rating": 0.0822 }, { "primary_team": "Vizela", "club_gc": 1.9412, "mean_rating": 0.0788 }, { "primary_team": "Chaves", "club_gc": 2.1176, "mean_rating": 0.0765 }, { "primary_team": "Portimonense", "club_gc": 2.1176, "mean_rating": 0.0697 } ] } }