{
  "schemaVersion": "football-1x2-scoring-benchmark/1.0.0",
  "title": "Football 1X2 Scoring Conformance Benchmark",
  "datePublished": "2026-07-14",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "caseCount": 54,
  "synthetic": true,
  "empirical": false,
  "description": "Synthetic mathematical fixtures with expected scoring outputs for testing football 1X2 metric implementations. This is not match data or model-performance evidence.",
  "truthBoundary": {
    "proves": "Reproducing these outputs under the declared conventions supports implementation conformance for these cases.",
    "doesNotProve": [
      "football model accuracy, calibration or profitability",
      "real pre-match publication or a complete prediction archive",
      "statistical superiority of one scoring rule",
      "independent replication or peer review"
    ]
  },
  "conventions": {
    "probabilityScale": "0-1",
    "inputSumTolerance": 1e-12,
    "derivedDecimalPlaces": 12,
    "brierSum": "sum_i((p_i - y_i)^2)",
    "brierClassAverage": "brier_sum / 3",
    "rpsOrder": [
      "H",
      "D",
      "A"
    ],
    "rpsNormalized": "((p_H-y_H)^2 + ((p_H+p_D)-(y_H+y_D))^2) / 2",
    "logLossExact": "-ln(p_observed); positive infinity when p_observed = 0",
    "logLossClipped": "-ln(min(1-1e-15,max(1e-15,p_observed)))",
    "topPick": "unique argmax only; tied maxima are blank"
  },
  "fields": [
    {
      "name": "benchmark_version",
      "description": "Semantic release of this immutable benchmark."
    },
    {
      "name": "case_id",
      "description": "Stable test-case identifier within the release."
    },
    {
      "name": "family",
      "description": "Synthetic scenario family; never a match or league label."
    },
    {
      "name": "pair_id",
      "description": "Optional identifier for a declared comparison or symmetry pair."
    },
    {
      "name": "p_home",
      "description": "Input home-win probability on the 0–1 scale."
    },
    {
      "name": "p_draw",
      "description": "Input draw probability on the 0–1 scale."
    },
    {
      "name": "p_away",
      "description": "Input away-win probability on the 0–1 scale."
    },
    {
      "name": "outcome",
      "description": "Synthetic observed result: H, D or A."
    },
    {
      "name": "unique_top_pick",
      "description": "Unique maximum-probability label, blank for a tie."
    },
    {
      "name": "top_pick_hit",
      "description": "Boolean hit for a unique top pick, blank for a tie."
    },
    {
      "name": "brier_sum",
      "description": "Sum of the three squared probability errors."
    },
    {
      "name": "brier_class_average",
      "description": "Summed multiclass Brier divided by three."
    },
    {
      "name": "rps_normalized_hda",
      "description": "Two-boundary H-D-A RPS divided by two."
    },
    {
      "name": "log_loss_nats_exact",
      "description": "Negative natural log of the observed-outcome probability; blank at zero."
    },
    {
      "name": "log_loss_exact_status",
      "description": "Finite or positive_infinity for the exact log score."
    },
    {
      "name": "log_loss_nats_clipped_1e15",
      "description": "Separate log loss after clipping to [1e-15, 1−1e-15]."
    }
  ],
  "invariants": [
    "The 18 declared probability vectors crossed with H, D and A create exactly 54 rows.",
    "Home and away mirror cases retain equal Brier, exact log loss and normalized RPS after reversing both labels and outcomes.",
    "The ordinal near and far pairs can hold Brier and exact log loss equal while normalized H-D-A RPS changes.",
    "A one-hot forecast that misses has summed Brier 2 and class-averaged Brier 2/3; normalized RPS is 0.5 for an adjacent miss and 1 for an opposite miss.",
    "The uniform forecast has outcome-invariant Brier and exact log loss; normalized RPS is 5/18 for H or A and 1/9 for D under the declared order.",
    "A tied maximum leaves unique top pick and hit blank while every proper score remains defined."
  ],
  "citations": [
    "https://doi.org/10.1175/1520-0493(1950)078%3C0001:VOFEIT%3E2.0.CO;2",
    "https://doi.org/10.1198/016214506000001437",
    "https://doi.org/10.1175/1520-0450(1969)008%3C0985:ASSFPF%3E2.0.CO;2",
    "https://doi.org/10.1515/1559-0410.1418",
    "https://doi.org/10.1007/s10994-018-5726-0",
    "https://doi.org/10.1007/s10994-024-06625-9"
  ],
  "rows": [
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      "brierSum": 0.666666666667,
      "caseId": "uniform-h",
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      "logLossExactStatus": "finite",
      "logLossNatsClipped1e15": 1.098612288668,
      "logLossNatsExact": 1.098612288668,
      "outcome": "H",
      "pairId": "uniform",
      "probabilities": {
        "A": 0.3333333333333333,
        "D": 0.3333333333333333,
        "H": 0.3333333333333333
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      "rpsNormalizedHda": 0.277777777778,
      "topPickHit": null,
      "uniqueTopPick": null
    },
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      "caseId": "uniform-d",
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      "outcome": "D",
      "pairId": "uniform",
      "probabilities": {
        "A": 0.3333333333333333,
        "D": 0.3333333333333333,
        "H": 0.3333333333333333
      },
      "rpsNormalizedHda": 0.111111111111,
      "topPickHit": null,
      "uniqueTopPick": null
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      "outcome": "A",
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      "probabilities": {
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        "D": 0.3333333333333333,
        "H": 0.3333333333333333
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      "family": "ordinal_distance",
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        "H": 0.6
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      "rpsNormalizedHda": 0.14125,
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        "H": 0.6
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        "H": 0.6
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      "caseId": "ordinal-away-near-h",
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      "logLossNatsClipped1e15": 2.995732273554,
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      "pairId": "ordinal-away",
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      "rpsNormalizedHda": 0.63125,
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