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Reading the draws and working out what chance predicts.
Loading…
Reading the draws and working out what chance predicts.
Gap Uniformizer
A five-draw wait for one game and a twelve-draw wait for another are not directly comparable. The geometric null transforms every completed wait to 0–1, where fair residuals fill the ruler evenly.
Cash Pop Night Owl1/15 era · since May 2022600 draws
Randomised geometric PIT + complete-draw simulationgeometric-gap-rpit-v1seed 20260827199 fair histories; two-test Bonferroni
For one ball, a fair completed gap is geometric with appearance probability :
A wait only feels meaningful relative to its opportunity to end. Uniformisation removes that changing scale: every correctly modelled wait becomes another point on the same ruler.
The ruler is a diagnostic, not a due-number engine. A residual near one says a completed wait was long under the model; the geometric law remains memoryless before the next draw. Discrete forecast residuals follow the model-checking approach described by Czado, Gneiting, and Held.
Because is discrete, its randomised probability-integral transform is
Under the null, is uniform. The laboratory checks the pooled uniform distribution and lag-one residual correlation. It does not pretend residuals from different balls are independent: every null run simulates complete -of- draws, recomputes both statistics, and corrects their minimum p-value.
The final open wait is censored. For every gap that does finish, the transform therefore uses the geometric law conditional on completion before the recorded history ends. Long unfinished waits are not silently discarded from an untruncated reference law.