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            "guarantee_minus_random": 0.026348104818257556,
            "ci95": [
              0.016767905790203208,
              0.035928303846311904
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            "p": 7.025283177369229e-08
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        }
      },
      {
        "ids": [
          50001,
          50046
        ],
        "names": [
          "拳击手套-初级",
          "标靶"
        ],
        "positions": {
          "1": {
            "all": {
              "n": 100646,
              "a": 49844,
              "b": 50802,
              "matches": 90270,
              "rate": 0.4952407447886652,
              "ci95": [
                0.49215113930829524,
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              "p_half": 0.002534886710407435
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            "win": {
              "n": 94872,
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              "matches": 85136,
              "rate": 0.49476136267813475,
              "ci95": [
                0.49157831113743233,
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              "p_half": 0.0012566898461673888
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            "loss": {
              "n": 5774,
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              "matches": 5134,
              "rate": 0.5031174229303775,
              "ci95": [
                0.49027357604553296,
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              "p_half": 0.6342759880651514
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          },
          "2": {
            "all": {
              "n": 12284,
              "a": 6119,
              "b": 6165,
              "matches": 12124,
              "rate": 0.49812764571800716,
              "ci95": [
                0.48928395449628503,
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              ],
              "p_half": 0.6781737640130038
            },
            "win": {
              "n": 11548,
              "a": 5758,
              "b": 5790,
              "matches": 11402,
              "rate": 0.49861447869761,
              "ci95": [
                0.4894931662820542,
                0.5077357911131658
              ],
              "p_half": 0.765918992957226
            },
            "loss": {
              "n": 736,
              "a": 361,
              "b": 375,
              "matches": 722,
              "rate": 0.4904891304347826,
              "ci95": [
                0.45434963345115903,
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              "p_half": 0.6059900578953544
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          },
          "3": {
            "all": {
              "n": 12017,
              "a": 5889,
              "b": 6128,
              "matches": 11880,
              "rate": 0.49005575434800697,
              "ci95": [
                0.48111558843138985,
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              "p_half": 0.029250815601061683
            },
            "win": {
              "n": 11336,
              "a": 5553,
              "b": 5783,
              "matches": 11216,
              "rate": 0.48985532815808047,
              "ci95": [
                0.4806497405465063,
                0.49906091576965467
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              "p_half": 0.030780052087851815
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            "loss": {
              "n": 681,
              "a": 336,
              "b": 345,
              "matches": 664,
              "rate": 0.4933920704845815,
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              "p_half": 0.7299966630260115
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          }
        },
        "contrasts": {
          "2": {
            "guarantee_minus_random": -0.0028869009293419623,
            "ci95": [
              -0.012256861764320615,
              0.00648305990563669
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            "p": 0.5459238614319673
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          "3": {
            "guarantee_minus_random": 0.0051849904406582326,
            "ci95": [
              -0.004274825158060257,
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            "p": 0.28269291671783
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        }
      }
    ],
    "method": "Pair share A/(A+B); match-clustered CIs, contrast covariance includes shared matches across positions. No filtering on future pick or outcome in primary comparisons.",
    "seconds": 3.9096452000085264
  },
  "hero_matched_comparison": {
    "scope": "All 86 cached shards, first purple guarantee panels (upgrade2 + shop2); heroes 121 and 129; both book and watch eligible at tested position, all four profession pools nonempty initially. No task panels or rerolls.",
    "heroes": {
      "121": {
        "name": "凛",
        "points": [
          15,
          15,
          30,
          80
        ]
      },
      "129": {
        "name": "赛克斯",
        "points": [
          15,
          15,
          30,
          80
        ]
      }
    },
    "pair": [
      50029,
      50031
    ],
    "rows": 32897,
    "results": [
      {
        "position": 1,
        "crude": {
          "129": {
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            "matches": 17163,
            "rate": 0.5303191192086291,
            "ci95": [
              0.5230028528612898,
              0.5376353855559683
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            "p_half": 4.577033137253057e-16
          },
          "121": {
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            "b": 2605,
            "matches": 5690,
            "rate": 0.5509394931908291,
            "ci95": [
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            "p_half": 6.181450236298724e-15
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        },
        "exact_inventory_match": {
          "strata": 43,
          "min_per_arm": 10,
          "control_n": 1109,
          "control_dart": 605,
          "treatment_n": 2171,
          "treatment_dart": 1177,
          "matches": 3273,
          "standardized_control": 0.5479295429602523,
          "standardized_treatment": 0.5441502489387843,
          "difference_pp": -0.3779294021468038,
          "ci95_pp": [
            -4.42585385277414,
            3.669995048480532
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          "p_two_sided": 0.8548035519282703,
          "examples": [
            {
              "key": [
                8589934592,
                0
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              "control_n": 140,
              "control_dart": 71,
              "treatment_n": 65,
              "treatment_dart": 42,
              "control_rate": 0.5071428571428571,
              "treatment_rate": 0.6461538461538462,
              "example_control_owned": [
                50040
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              "example_treatment_owned": [
                50040
              ]
            },
            {
              "key": [
                268435456,
                0
              ],
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              "control_dart": 23,
              "treatment_n": 455,
              "treatment_dart": 253,
              "control_rate": 0.5348837209302325,
              "treatment_rate": 0.5560439560439561,
              "example_control_owned": [
                50032
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              "example_treatment_owned": [
                50032
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            },
            {
              "key": [
                2097152,
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              "treatment_n": 43,
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              "control_rate": 0.5813953488372093,
              "treatment_rate": 0.4883720930232558,
              "example_control_owned": [
                50025
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              "example_treatment_owned": [
                50025
              ]
            },
            {
              "key": [
                1099780063232,
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              "treatment_n": 136,
              "treatment_dart": 78,
              "control_rate": 0.6470588235294118,
              "treatment_rate": 0.5735294117647058,
              "example_control_owned": [
                50032,
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              "example_treatment_owned": [
                50032,
                50047
              ]
            },
            {
              "key": [
                562949953421312,
                0
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              "treatment_n": 55,
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              "control_rate": 0.5151515151515151,
              "treatment_rate": 0.5272727272727272,
              "example_control_owned": [
                50083
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              "example_treatment_owned": [
                50083
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            }
          ],
          "p_bonferroni_3_positions": 1
        }
      },
      {
        "position": 2,
        "crude": {
          "129": {
            "n": 3623,
            "a": 1774,
            "b": 1849,
            "matches": 3599,
            "rate": 0.48964946177201213,
            "ci95": [
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            "p_half": 0.21321606435573603
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          "121": {
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            "ci95": [
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            "p_half": 0.47730800710224125
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        },
        "exact_inventory_match": {
          "strata": 2,
          "min_per_arm": 10,
          "control_n": 54,
          "control_dart": 25,
          "treatment_n": 28,
          "treatment_dart": 9,
          "matches": 82,
          "standardized_control": 0.4431372549019608,
          "standardized_treatment": 0.29411764705882354,
          "difference_pp": -14.901960784313728,
          "ci95_pp": [
            -35.862496707305816,
            6.058575138678357
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          "p_two_sided": 0.1634782133239994,
          "examples": [
            {
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                8589934592,
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              "control_n": 42,
              "control_dart": 21,
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              "treatment_dart": 3,
              "control_rate": 0.5,
              "treatment_rate": 0.1875,
              "example_control_owned": [
                50040
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              "example_treatment_owned": [
                50040
              ]
            },
            {
              "key": [
                2097152,
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              "treatment_n": 12,
              "treatment_dart": 6,
              "control_rate": 0.3333333333333333,
              "treatment_rate": 0.5,
              "example_control_owned": [
                50025
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              "example_treatment_owned": [
                50025
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            }
          ],
          "p_bonferroni_3_positions": 0.4904346399719982
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      },
      {
        "position": 3,
        "crude": {
          "129": {
            "n": 3558,
            "a": 1791,
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            "matches": 3525,
            "rate": 0.5033726812816189,
            "ci95": [
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            "p_half": 0.6863693315299021
          },
          "121": {
            "n": 979,
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            "matches": 974,
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            "p_half": 0.26363505127020737
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        },
        "exact_inventory_match": {
          "strata": 1,
          "min_per_arm": 10,
          "control_n": 12,
          "control_dart": 7,
          "treatment_n": 14,
          "treatment_dart": 8,
          "matches": 26,
          "standardized_control": 0.5833333333333334,
          "standardized_treatment": 0.5714285714285714,
          "difference_pp": -1.1904761904761973,
          "ci95_pp": [
            -40.02481571010657,
            37.64386332915418
          ],
          "p_two_sided": 0.952088510001744,
          "examples": [
            {
              "key": [
                2097152,
                0
              ],
              "control_n": 12,
              "control_dart": 7,
              "treatment_n": 14,
              "treatment_dart": 8,
              "control_rate": 0.5833333333333334,
              "treatment_rate": 0.5714285714285714,
              "example_control_owned": [
                50025
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              "example_treatment_owned": [
                50025
              ]
            }
          ],
          "p_bonferroni_3_positions": 1
        }
      }
    ],
    "seconds": 1.2053897999867331,
    "matching": "Exact full owned inventory AND previous exclusion set. Shared initial profession vector means all four current profession scores, schools and initial eligible pools agree. Min 10 per hero per stratum; harmonic overlap weights. Match-clustered confidence intervals.",
    "limitations": "Characters were not randomly assigned. Ability, player choice, update/date distribution, preceding other candidates at random positions, source and match inclusion can still confound. Client recommendation evidence is not server source code."
  },
  "random_comparator_best_of_16": {
    "order": "all_id_reverse",
    "comparatorOutcomes": 2,
    "trials": 100000,
    "errors": 727,
    "counts": {
      "50085": 23993,
      "50046": 25848,
      "50065": 24081,
      "50001": 25351
    },
    "max_abs_error_pp": 2.262398980545524,
    "predicted": {
      "50085": 0.24168706496227574,
      "50046": 0.26037291106343113,
      "50065": 0.24257350941343567,
      "50001": 0.25536651456085746
    }
  },
  "probability_status": "Model estimates only. The within-profession uniform model conflicts with recorded frequencies; selection bias and server draw implementation remain unresolved. Client recommendation scores are not established draw weights."
}