{
  "run": "511-moneyball-salary",
  "as_of": "2026-08-15",
  "source": "Lahman Baseball Database, maintained release, via r-universe CSV endpoints (cdalzell/Lahman); Batting + Salaries tables joined on playerID+yearID, summed across in-season stints/trades",
  "window": [
    1985,
    2016
  ],
  "n_total": 7892,
  "n_players": 1494,
  "salary_table_ends": 2016,
  "naive": {
    "obp": {
      "n": 7892,
      "slope": 3.7018860169246595,
      "intercept": 4.8735900353836055,
      "r2": 0.05220255010850825,
      "p": 5.449259538809054e-94,
      "se": 0.17758098039605577,
      "ci": [
        3.353780290022464,
        4.049991743826856
      ]
    },
    "RBI": {
      "n": 7892,
      "slope": 0.007775243963308231,
      "intercept": 5.645652445094479,
      "r2": 0.11076851337094112,
      "p": 1.9690276547290375e-203,
      "se": 0.00024801318846086605,
      "ci": [
        0.00728907246533615,
        0.008261415461280312
      ]
    }
  },
  "horse_race": {
    "obp": {
      "n": 7892,
      "slope": 0.265784172035825,
      "intercept": -6.534587150381597e-17,
      "r2": 0.07064122610476911,
      "p": 1.0272213872660947e-127,
      "se": 0.010853084893142032,
      "ci": [
        0.24450925285567185,
        0.28705909121597817
      ]
    },
    "RBI": {
      "n": 7892,
      "slope": 0.35547908450178356,
      "intercept": -1.0797033341547833e-16,
      "r2": 0.1263653795182264,
      "p": 8.879673892950604e-234,
      "se": 0.010522681281585827,
      "ci": [
        0.33485184385744754,
        0.3761063251461196
      ]
    },
    "HR": {
      "n": 7892,
      "slope": 0.3104858008510711,
      "intercept": -9.583779169163739e-17,
      "r2": 0.09640143253013107,
      "p": 6.0857254171813215e-176,
      "se": 0.010701613582359574,
      "ci": [
        0.2895078055342008,
        0.33146379616794136
      ]
    },
    "avg": {
      "n": 7892,
      "slope": 0.16249071723573816,
      "intercept": -1.0975133187702698e-16,
      "r2": 0.02640323318778464,
      "p": 7.873964065524353e-48,
      "se": 0.011108388492778376,
      "ci": [
        0.14071533542195191,
        0.1842660990495244
      ]
    },
    "slg": {
      "n": 7892,
      "slope": 0.25455869125895986,
      "intercept": -8.472676271515517e-17,
      "r2": 0.06480012729547462,
      "p": 5.818637277339361e-117,
      "se": 0.010887137750741243,
      "ci": [
        0.2332170194641898,
        0.2759003630537299
      ]
    },
    "BB": {
      "n": 7892,
      "slope": 0.3401070049167128,
      "intercept": -1.0284197220690745e-16,
      "r2": 0.11567277479341702,
      "p": 6.450895746628178e-213,
      "se": 0.010586880139028084,
      "ci": [
        0.31935391751848236,
        0.36086009231494326
      ]
    }
  },
  "multi_obp_rbi": {
    "n": 7892,
    "r2": 0.141604596574035,
    "terms": {
      "intercept": {
        "coef": -6.710797485632136e-17,
        "se": 0.010409993261610288,
        "ci": [
          -0.02040634269376202,
          0.02040634269376189
        ],
        "p": 0.9999999999999949
      },
      "obp": {
        "coef": 0.13709680000424218,
        "se": 0.01158453761928575,
        "ci": [
          0.11438803942514507,
          0.15980556058333928
        ],
        "p": 0.0
      },
      "RBI": {
        "coef": 0.2958442329836106,
        "se": 0.011584537619285747,
        "ci": [
          0.2731354724045135,
          0.3185529935627077
        ],
        "p": 0.0
      }
    }
  },
  "multi_obp_rbi_hr": {
    "n": 7892,
    "r2": 0.14169604838899852,
    "terms": {
      "intercept": {
        "coef": -6.710797485632138e-17,
        "se": 0.0104100985229843,
        "ci": [
          -0.020406549430894903,
          0.02040654943089477
        ],
        "p": 0.9999999999999949
      },
      "obp": {
        "coef": 0.1370803122266464,
        "se": 0.011584668717383373,
        "ci": [
          0.11437129421880776,
          0.15978933023448505
        ],
        "p": 0.0
      },
      "RBI": {
        "coef": 0.27977792375286875,
        "se": 0.02100781965785434,
        "ci": [
          0.23859703489415,
          0.32095881261158754
        ],
        "p": 0.0
      },
      "HR": {
        "coef": 0.018703177040720692,
        "se": 0.020401228748045362,
        "ci": [
          -0.021288633025129955,
          0.05869498710657134
        ],
        "p": 0.35929267918249574
      }
    }
  },
  "multi_kitchen_sink": {
    "n": 7892,
    "r2": 0.15838133776967367,
    "terms": {
      "intercept": {
        "coef": -6.710797485632138e-17,
        "se": 0.01030972371224186,
        "ci": [
          -0.020209789011766805,
          0.020209789011766673
        ],
        "p": 0.9999999999999947
      },
      "obp": {
        "coef": -0.009792527010446877,
        "se": 0.03361089793966394,
        "ci": [
          -0.07567878883626701,
          0.05609373481537326
        ],
        "p": 0.7707914978071149
      },
      "avg": {
        "coef": 0.017572511234616017,
        "se": 0.02596105684976778,
        "ci": [
          -0.03331803599055293,
          0.06846305845978497
        ],
        "p": 0.498502166465699
      },
      "HR": {
        "coef": -0.022495863665509413,
        "se": 0.022169633734512778,
        "ci": [
          -0.06595421742436315,
          0.02096249009334433
        ],
        "p": 0.3102727513874104
      },
      "RBI": {
        "coef": 0.25519637063871997,
        "se": 0.025874613930163545,
        "ci": [
          0.20447527443042826,
          0.3059174668470117
        ],
        "p": 0.0
      },
      "BB": {
        "coef": 0.21874392313839647,
        "se": 0.0256157498784971,
        "ci": [
          0.16853026903165186,
          0.2689575772451411
        ],
        "p": 0.0
      }
    }
  },
  "era": {
    "pre_2004": {
      "n": 4574,
      "years": [
        1985,
        2003
      ],
      "multi_obp_rbi": {
        "n": 4574,
        "r2": 0.16708581284691482,
        "terms": {
          "intercept": {
            "coef": 3.3583808325521755e-18,
            "se": 0.013470714435111336,
            "ci": [
              -0.026409108030516385,
              0.026409108030516392
            ],
            "p": 0.9999999999999998
          },
          "obp": {
            "coef": 0.15413754753061878,
            "se": 0.014926581107597483,
            "ci": [
              0.12487423748899745,
              0.18340085757224012
            ],
            "p": 0.0
          },
          "RBI": {
            "coef": 0.3184731378480227,
            "se": 0.014926581107597479,
            "ci": [
              0.2892098278064014,
              0.34773644788964403
            ],
            "p": 0.0
          }
        }
      },
      "multi_obp_rbi_hr": {
        "n": 4574,
        "r2": 0.16728273787004022,
        "terms": {
          "intercept": {
            "coef": 3.358380832552176e-18,
            "se": 0.01347059547268658,
            "ci": [
              -0.02640887633725095,
              0.026408876337250958
            ],
            "p": 0.9999999999999998
          },
          "obp": {
            "coef": 0.15396620368437974,
            "se": 0.014927359238585337,
            "ci": [
              0.1247013664340263,
              0.1832310409347332
            ],
            "p": 0.0
          },
          "RBI": {
            "coef": 0.2949677387572524,
            "se": 0.027092954253713677,
            "ci": [
              0.2418524566639046,
              0.3480830208506002
            ],
            "p": 0.0
          },
          "HR": {
            "coef": 0.027438951575172364,
            "se": 0.026394153886363746,
            "ci": [
              -0.02430634412646851,
              0.07918424727681324
            ],
            "p": 0.2985880078441283
          }
        }
      },
      "obp_alone": {
        "n": 4574,
        "slope": 0.290062539295108,
        "intercept": -6.037143568951281e-18,
        "r2": 0.08413627670232617,
        "p": 2.257791257089869e-89,
        "se": 0.014153450090090556,
        "ci": [
          0.2623149411568773,
          0.3178101374333387
        ]
      },
      "rbi_alone": {
        "n": 4574,
        "slope": 0.3842593608879569,
        "intercept": -4.082990170956495e-17,
        "r2": 0.1476552564300215,
        "p": 7.46859476714958e-161,
        "se": 0.013653831303603906,
        "ci": [
          0.35749125688165156,
          0.4110274648942623
        ]
      }
    },
    "post_2004": {
      "n": 3318,
      "years": [
        2004,
        2016
      ],
      "multi_obp_rbi": {
        "n": 3318,
        "r2": 0.11016700083034192,
        "terms": {
          "intercept": {
            "coef": -1.8576718398093442e-16,
            "se": 0.016351591479750592,
            "ci": [
              -0.032060236072309796,
              0.03206023607230942
            ],
            "p": 0.9999999999999909
          },
          "obp": {
            "coef": 0.11411407467435739,
            "se": 0.018307801752855686,
            "ci": [
              0.07821833652015604,
              0.15000981282855874
            ],
            "p": 5.149864978903906e-10
          },
          "RBI": {
            "coef": 0.2648892049928403,
            "se": 0.018307801752855686,
            "ci": [
              0.22899346683863897,
              0.30078494314704163
            ],
            "p": 0.0
          }
        }
      },
      "multi_obp_rbi_hr": {
        "n": 3318,
        "r2": 0.110175655467044,
        "terms": {
          "intercept": {
            "coef": -1.8576718398093442e-16,
            "se": 0.016353978810178128,
            "ci": [
              -0.032064920396970745,
              0.03206492039697037
            ],
            "p": 0.9999999999999909
          },
          "obp": {
            "coef": 0.11415246605420167,
            "se": 0.01831172329735264,
            "ci": [
              0.07824903504966019,
              0.15005589705874314
            ],
            "p": 5.125344593182035e-10
          },
          "RBI": {
            "coef": 0.2599243364688996,
            "se": 0.0331665742150928,
            "ci": [
              0.19489529525568167,
              0.3249533776821176
            ],
            "p": 6.217248937900877e-15
          },
          "HR": {
            "coef": 0.00575637982668932,
            "se": 0.032062760508523,
            "ci": [
              -0.057108435845755784,
              0.06862119549913442
            ],
            "p": 0.8575288065698508
          }
        }
      },
      "obp_alone": {
        "n": 3318,
        "slope": 0.2323233663274934,
        "intercept": -1.5125004441225108e-16,
        "r2": 0.05397414654173872,
        "p": 6.61340466151403e-42,
        "se": 0.016890567505114546,
        "ci": [
          0.19920637446564782,
          0.265440358189339
        ]
      },
      "rbi_alone": {
        "n": 3318,
        "slope": 0.31581368088937023,
        "intercept": -2.0459689213416305e-16,
        "r2": 0.09973828103689297,
        "p": 9.648026681552899e-78,
        "se": 0.016476961645500117,
        "ci": [
          0.2835076376165946,
          0.34811972416214587
        ]
      }
    }
  },
  "era_diff": {
    "obp_coef_shift": {
      "point": -0.0400234728562614,
      "ci": [
        -0.08754386312156011,
        0.00574955621271593
      ],
      "excludes_zero": false
    },
    "rbi_coef_shift": {
      "point": -0.053583932855182426,
      "ci": [
        -0.10015636428198406,
        -0.007294640699418506
      ],
      "excludes_zero": true
    }
  },
  "spearman": {
    "obp_vs_salary": {
      "rho": 0.26689222284955405,
      "p": 8.344731762518872e-129
    },
    "rbi_vs_salary": {
      "rho": 0.3707783478734638,
      "p": 1.0002489985479702e-255
    }
  },
  "hatteberg_2002": {
    "year": 2002,
    "salary": 900000,
    "obp": 0.374,
    "rbi": 61,
    "hr": 15,
    "obp_percentile_in_year": 84.1,
    "salary_percentile_in_year": 31.4,
    "n_qualifiers_that_year": 258
  },
  "caveats": [
    "Lahman's Salaries table runs 1985-2016 only (source discontinued); no seasons after 2016 in this fit -- the 'does the market still misprice today' question is not tested",
    "standardized coefficients compare a player to his OWN season's qualifiers, not across seasons -- appropriate for the era-split question, not a claim about real dollar amounts",
    "OLS, uncorrected for arbitration-eligibility and free-agency status, both of which compress rookie/pre-arb salaries regardless of performance and are a real confound this run does not model",
    "RBI and HR are both counting stats that scale with playing time and batting-order slot (context), not just individual skill -- OBP and AVG are rate stats and do not; the multivariate models mix rate and counting stats on purpose, to match how the market actually sees a stat line",
    "no causal claim: this is what teams paid, not what they should have paid, though the run-value literature this replicates (Hakes & Sauer 2006) makes exactly that comparison"
  ]
}