{
  "date": "2026-11-03",
  "modelSha256": "b1d01303fe03316068677c8b921f131a0b5a26bf5d3be3b3800baf6b4e0faadf",
  "note": "Recorded coordinates are from an archived local snapshot. Scores were recalculated for this article; no database records were changed.",
  "examples": [
    {
      "id": "straight-pool",
      "title": "A short, straight pool shot",
      "game": "pool",
      "size": 9,
      "cue": [
        1.27,
        0.8
      ],
      "object": [
        1.27,
        0.3
      ],
      "pocketId": 1,
      "source": "Constructed example",
      "explanation": "The pocket and the first-contact windows are symmetric. Both sides of the straight shot count toward the cue-ball tolerance.",
      "R": 0.028575,
      "table": {
        "l": 2.54,
        "w": 1.27,
        "cushion_height": 0.036
      },
      "pocket": {
        "center": [
          1.27,
          0
        ],
        "normal": [
          0,
          -1
        ],
        "width": 0.1472,
        "isSidePocket": true
      },
      "result": {
        "compl": 2.6144971769668377,
        "df": 2.6144971769668377,
        "valid": true,
        "cutAng": 0,
        "cutAngRaw": 0,
        "alphaPocketDeg": 9,
        "alphaCueDeg": 1,
        "deltaB": 0.01912297046050136,
        "angularTolerance": 0.297942892411007,
        "cueAngularTolerance": 0.03824827231827927,
        "pocketWidthUsed": 0.1472,
        "isSidePocket": true,
        "potType": "object"
      },
      "detail": {
        "L": 0.5,
        "d": 0.3,
        "x": 0,
        "h": 0.3,
        "a": 0.0736,
        "lower": -0.14897144620550348,
        "upper": 0.14897144620550348,
        "delta": 0,
        "gammaLower": -0.14897144620550348,
        "gammaUpper": 0.14897144620550348,
        "betaLower": 0.019124136159139625,
        "betaUpper": -0.019124136159139625,
        "objectWindow": 0.29794289241100697,
        "reachableWindow": 0.29794289241100697,
        "cueWindow": 0.03824827231827925,
        "ghost": [
          1.27,
          0.35714999999999997
        ],
        "end": [
          1.27,
          0
        ]
      }
    },
    {
      "id": "cut-pool",
      "title": "Same pocket, same distances, a thinner cut",
      "game": "pool",
      "size": 9,
      "cue": [
        1.7030127018922192,
        0.55
      ],
      "object": [
        1.27,
        0.3
      ],
      "pocketId": 1,
      "source": "Constructed example",
      "explanation": "The object ball has the same pocket window as in the first diagram. The thinner contact compresses the corresponding cue-ball window.",
      "R": 0.028575,
      "table": {
        "l": 2.54,
        "w": 1.27,
        "cushion_height": 0.036
      },
      "pocket": {
        "center": [
          1.27,
          0
        ],
        "normal": [
          0,
          -1
        ],
        "width": 0.1472,
        "isSidePocket": true
      },
      "result": {
        "compl": 6.851185555736903,
        "df": 6.851185555736903,
        "valid": true,
        "cutAng": 66,
        "cutAngRaw": 66,
        "alphaPocketDeg": 9,
        "alphaCueDeg": 0,
        "deltaB": 0.0072590652588025665,
        "angularTolerance": 0.297942892411007,
        "cueAngularTolerance": 0.014596013957943979,
        "pocketWidthUsed": 0.1472,
        "isSidePocket": true,
        "potType": "object"
      },
      "detail": {
        "L": 0.4999999999999999,
        "d": 0.3,
        "x": 0,
        "h": 0.3,
        "a": 0.0736,
        "lower": -0.14897144620550348,
        "upper": 0.14897144620550348,
        "delta": 1.0471975511965974,
        "gammaLower": 0.8982261049910939,
        "gammaUpper": 1.1961689974021008,
        "betaLower": -0.09596714611161375,
        "betaUpper": -0.11056316006955774,
        "objectWindow": 0.29794289241100697,
        "reachableWindow": 0.2979428924110069,
        "cueWindow": 0.014596013957943993,
        "ghost": [
          1.27,
          0.35714999999999997
        ],
        "end": [
          1.27,
          0
        ]
      }
    },
    {
      "id": "straight-snooker",
      "title": "The same metric position with snooker equipment",
      "game": "snooker",
      "size": 12,
      "cue": [
        1.7845,
        0.8
      ],
      "object": [
        1.7845,
        0.3
      ],
      "pocketId": 1,
      "source": "Constructed example",
      "explanation": "Distances remain 0.50 m and 0.30 m. A 52.5 mm ball and a nominal 90 mm entrance leave only 18.75 mm of clearance per side. The same geometric formula produces the score; there is no separate snooker multiplier.",
      "R": 0.02625,
      "table": {
        "l": 3.569,
        "w": 1.778,
        "cushion_height": 0.036
      },
      "pocket": {
        "center": [
          1.7845,
          0
        ],
        "normal": [
          0,
          -1
        ],
        "width": 0.09,
        "isSidePocket": true
      },
      "result": {
        "compl": 6.834036006678248,
        "df": 6.834036006678248,
        "valid": true,
        "cutAng": 0,
        "cutAngRaw": 0,
        "alphaPocketDeg": 4,
        "alphaCueDeg": 0,
        "deltaB": 0.007316255559830215,
        "angularTolerance": 0.12483761999191469,
        "cueAngularTolerance": 0.014632641663327438,
        "pocketWidthUsed": 0.09,
        "isSidePocket": true,
        "potType": "object"
      },
      "detail": {
        "L": 0.5,
        "d": 0.3,
        "x": 0,
        "h": 0.3,
        "a": 0.045,
        "lower": -0.06241880999595735,
        "upper": 0.06241880999595735,
        "delta": 0,
        "gammaLower": -0.06241880999595735,
        "gammaUpper": 0.06241880999595735,
        "betaLower": 0.00731632083166372,
        "betaUpper": -0.00731632083166372,
        "objectWindow": 0.1248376199919147,
        "reachableWindow": 0.1248376199919147,
        "cueWindow": 0.01463264166332744,
        "ghost": [
          1.7845,
          0.3525
        ],
        "end": [
          1.7845,
          0
        ]
      }
    },
    {
      "id": "recorded-cut",
      "title": "A recorded side-pocket cut",
      "game": "pool",
      "size": 9,
      "cue": [
        0.474265625,
        1.006078125
      ],
      "object": [
        0.9663906250000001,
        0.936625
      ],
      "pocketId": 4,
      "source": "Recorded position, recalculated",
      "explanation": "The half-window is about 0.224 degrees. The score comes from the reconstructed position, not from whether the player made the shot.",
      "R": 0.028575,
      "table": {
        "l": 2.54,
        "w": 1.27,
        "cushion_height": 0.036
      },
      "pocket": {
        "center": [
          1.27,
          1.27
        ],
        "normal": [
          0,
          1
        ],
        "width": 0.1472,
        "isSidePocket": true
      },
      "result": {
        "compl": 12.804698801076434,
        "df": 12.804698801076434,
        "valid": true,
        "cutAng": 61,
        "cutAngRaw": 61,
        "alphaPocketDeg": 4,
        "alphaCueDeg": 0,
        "deltaB": 0.0038616792725460892,
        "angularTolerance": 0.13321466772818635,
        "cueAngularTolerance": 0.007809633131830751,
        "pocketWidthUsed": 0.1472,
        "isSidePocket": true,
        "potType": "object"
      },
      "detail": {
        "L": 0.49700176277078295,
        "d": 0.45090746635300966,
        "x": -0.30360937499999996,
        "h": 0.333375,
        "a": 0.0736,
        "lower": -0.8077685735872142,
        "upper": -0.6745539058590279,
        "delta": 1.7109994248036282,
        "gammaLower": 0.903230851216414,
        "gammaUpper": 1.0364455189446002,
        "betaLower": -0.09692149012710101,
        "betaUpper": -0.10473112325893177,
        "objectWindow": 0.13321466772818635,
        "reachableWindow": 0.13321466772818624,
        "cueWindow": 0.007809633131830765,
        "ghost": [
          0.9278060884883707,
          0.8944662993299991
        ],
        "end": [
          1.271502491711716,
          1.27
        ]
      }
    },
    {
      "id": "recorded-distance",
      "title": "A recorded shot with a long cue-ball approach",
      "game": "pool",
      "size": 9,
      "cue": [
        2.5003125,
        0.835421875
      ],
      "object": [
        0.92075,
        0.55959375
      ],
      "pocketId": 0,
      "source": "Recorded position, recalculated",
      "explanation": "A modest cut can still demand a narrow aiming window when the cue ball starts a long way from the contact point.",
      "R": 0.028575,
      "table": {
        "l": 2.54,
        "w": 1.27,
        "cushion_height": 0.036
      },
      "pocket": {
        "center": [
          0.04525483399593905,
          0.04525483399593905
        ],
        "normal": [
          -0.7071067811865476,
          -0.7071067811865476
        ],
        "width": 0.128,
        "isSidePocket": false
      },
      "result": {
        "compl": 43.56385833102092,
        "df": 43.56385833102092,
        "valid": true,
        "cutAng": 21,
        "cutAngRaw": 21,
        "alphaPocketDeg": 2,
        "alphaCueDeg": 0,
        "deltaB": 0.0036804142868705867,
        "angularTolerance": 0.06682290845097058,
        "cueAngularTolerance": 0.0022954807914429397,
        "pocketWidthUsed": 0.128,
        "isSidePocket": false,
        "potType": "object"
      },
      "detail": {
        "L": 1.6034646381966975,
        "d": 1.0153995795807238,
        "x": -0.25537603344290394,
        "h": 0.9827611041121233,
        "a": 0.064,
        "lower": -0.2876929875143903,
        "upper": -0.22087007906341982,
        "delta": 0.6125182056417897,
        "gammaLower": 0.3248252181273994,
        "gammaUpper": 0.3916481265783699,
        "betaLower": -0.01177186513327667,
        "betaUpper": -0.01406734592471961,
        "objectWindow": 0.0668229084509705,
        "reachableWindow": 0.0668229084509705,
        "cueWindow": 0.0022954807914429397,
        "ghost": [
          0.9700271325277894,
          0.5885400228142791
        ],
        "end": [
          0.045218719416380115,
          0.04529094857549809
        ]
      }
    },
    {
      "id": "recorded-thin",
      "title": "A recorded position beyond the old 200 ceiling",
      "game": "pool",
      "size": 9,
      "cue": [
        1.68671875,
        1.11125
      ],
      "object": [
        1.53590625,
        0.30559375
      ],
      "pocketId": 2,
      "source": "Recorded position, recalculated",
      "explanation": "Only part of the pocket window is reachable by a first contact. The result is a very narrow cue-ball window and a score well above 200. This illustrates sensitivity near a tangential contact, not a verified rating of the player.",
      "R": 0.028575,
      "table": {
        "l": 2.54,
        "w": 1.27,
        "cushion_height": 0.036
      },
      "pocket": {
        "center": [
          2.494745166004061,
          0.04525483399593905
        ],
        "normal": [
          0.7071067811865476,
          -0.7071067811865476
        ],
        "width": 0.128,
        "isSidePocket": false
      },
      "result": {
        "compl": 1945.5687369345824,
        "df": 1945.5687369345824,
        "valid": true,
        "cutAng": 89,
        "cutAngRaw": 89,
        "alphaPocketDeg": 2,
        "alphaCueDeg": 0,
        "deltaB": 0.000042026622272984924,
        "angularTolerance": 0.05839907973741376,
        "cueAngularTolerance": 0.00005139885222331386,
        "pocketWidthUsed": 0.128,
        "isSidePocket": false,
        "potType": "object"
      },
      "detail": {
        "L": 0.819650171304998,
        "d": 0.9935534298818622,
        "x": 0.49391408665880365,
        "h": 0.8620889124852567,
        "a": 0.064,
        "lower": 0.492264884880788,
        "upper": 0.5506639646182019,
        "delta": 0.9704486714031045,
        "gammaLower": 1.4627135562838927,
        "gammaUpper": 1.5010148396026752,
        "betaLower": -0.06973008833999811,
        "betaUpper": -0.06978148719222144,
        "objectWindow": 0.05839907973741387,
        "reachableWindow": 0.038301283318782575,
        "cueWindow": 0.00005139885222332774,
        "ghost": [
          1.4808878900584244,
          0.32105669180740587
        ],
        "end": [
          2.487607809558412,
          0.038117477550289824
        ]
      }
    }
  ]
}