{"id":"W4388582911","doi":"10.1002/cjs.11798","title":"Football group draw probabilities and corrections","year":2023,"lang":"en","type":"article","venue":"Canadian Journal of Statistics","topic":"Sports Analytics and Performance","field":"Economics, Econometrics and Finance","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Football; Competition (biology); Group (periodic table); Distribution (mathematics); Computer science; Symmetry (geometry); Mathematical economics; Operations research; Mathematics; Geometry; Mathematical analysis; Political science; Law; Physics; Ecology","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003014005,0.00006096673,0.0001736247,0.0003391342,0.0001314814,0.00008365988,0.00007665126,0.00003288071,0.0003084584],"category_scores_gemma":[0.0001173265,0.00006722385,0.00002848349,0.0001878668,0.00008927462,0.00009005379,0.000005804776,0.0001104104,0.00005589367],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006757722,"about_ca_system_score_gemma":0.0001277396,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003832764,"about_ca_topic_score_gemma":0.01903025,"domain_scores_codex":[0.9993396,0.000002720048,0.000371134,0.00007908085,0.0000222179,0.0001852039],"domain_scores_gemma":[0.9993615,0.00004117888,0.0001999528,0.00007572434,0.00006583748,0.0002558769],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.000002707975,0.000006110091,0.2990629,0.00003462608,0.00004167279,0.00008135362,0.001047119,0.0004206833,5.217843e-7,0.6617208,0.03541745,0.002164053],"study_design_scores_gemma":[0.0003074462,0.0001973591,0.3709376,0.00003409829,0.00001546556,0.00006173342,0.0005121636,0.01221134,0.000001180801,0.1644575,0.4510417,0.0002224712],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9230901,0.003766705,0.0433162,0.001988313,0.005434532,0.0002478843,0.004205633,0.00002874702,0.01792188],"genre_scores_gemma":[0.9959406,0.0004454867,0.001357462,0.0001039312,0.0001243568,0.000001158182,0.00001409307,0.00001193216,0.002001011],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4972633,"threshold_uncertainty_score":0.9988699,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03307046812853445,"score_gpt":0.190247631054488,"score_spread":0.1571771629259536,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}