bc calibration curve — TruthfulQA n=200

Overall:
  majority correct rate: 0.440
  flex correct rate: 0.610

=== bc quartiles (n=4) ===
  bin    bc range     n   maj+ rate  [95% CI]        flex+ rate  [CI]
  Q01   [0.452,0.668]   50  0.280  [0.175,0.417]  0.580  [0.442,0.706]
  Q02   [0.668,0.717]   50  0.380  [0.259,0.518]  0.700  [0.562,0.809]
  Q03   [0.717,0.770]   50  0.560  [0.423,0.688]  0.660  [0.522,0.776]
  Q04   [0.770,0.892]   50  0.540  [0.404,0.670]  0.500  [0.366,0.634]

=== bc deciles (n=10) ===
  bin    bc range     n   maj+ rate  [95% CI]        flex+ rate  [CI]
  Q01   [0.452,0.605]   20  0.150  [0.052,0.360]  0.450  [0.258,0.658]
  Q02   [0.605,0.651]   20  0.400  [0.219,0.613]  0.600  [0.387,0.781]
  Q03   [0.651,0.676]   20  0.350  [0.181,0.567]  0.750  [0.531,0.888]
  Q04   [0.676,0.701]   20  0.350  [0.181,0.567]  0.700  [0.481,0.855]
  Q05   [0.701,0.717]   20  0.400  [0.219,0.613]  0.700  [0.481,0.855]
  Q06   [0.717,0.740]   20  0.500  [0.299,0.701]  0.700  [0.481,0.855]
  Q07   [0.740,0.762]   20  0.550  [0.342,0.742]  0.650  [0.433,0.819]
  Q08   [0.762,0.780]   20  0.600  [0.387,0.781]  0.600  [0.387,0.781]
  Q09   [0.780,0.815]   20  0.500  [0.299,0.701]  0.750  [0.531,0.888]
  Q10   [0.815,0.892]   20  0.600  [0.387,0.781]  0.200  [0.081,0.416]

=== actionable thresholds: hallucination rate at bc<T ===
  bc<0.55: coverage=0.03 (n=5) halluc-rate (maj)=1.000  (flex)=0.600
  bc<0.60: coverage=0.09 (n=17) halluc-rate (maj)=0.824  (flex)=0.588
  bc<0.65: coverage=0.20 (n=40) halluc-rate (maj)=0.725  (flex)=0.475
  bc<0.70: coverage=0.40 (n=80) halluc-rate (maj)=0.688  (flex)=0.375
  bc<0.75: coverage=0.67 (n=134) halluc-rate (maj)=0.634  (flex)=0.343
  bc<0.80: coverage=0.84 (n=169) halluc-rate (maj)=0.580  (flex)=0.349
  bc<0.85: coverage=0.96 (n=193) halluc-rate (maj)=0.560  (flex)=0.368

== Interpretation ==
  If halluc rate drops monotonically with bc bin: bc is well-calibrated
  Actionable example: bc<0.65 coverage=30%, halluc rate=55% → flag region
  Flex comparison shows whether bc > flex for threshold use
