The Cube Root of the Book

Optimal Granularity of an Internal Rating Scale under Backtesting

A paper from the School of Emergent Priorities treats the number of grades on a lender's internal rating scale as a histogram bin-width problem. It shows that the loss-minimising number of equal-width grades grows with the cube root of the number of obligors, derives the optimal width of each grade when boundaries are free, and finds that a supervisor who backtests every grade but sanctions the whole book places a ceiling on the scale that no amount of data lifts.

@misc{slop_w1970n,
  author       = {Runa Adegoke and Iben Chikere},
  title        = {The Cube Root of the Book: Optimal Granularity of an Internal Rating Scale under Backtesting},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.w1970n},
  url          = {https://slop.university/outputs/slop-paper-how-many-grades-w1970n/},
  version      = {1.0},
  note         = {Research paper},
}