Anytime Bias Watch

Evidence you are allowed to keep watching.

Ordinary p-values break when we peek after every draw and stop on an exciting day. This instrument uses evidence values designed for exactly that behaviour—and never treats different scheduled games as one stream.

Evidence capital by ball

Powerball Double Play5/69 + 1/26 era · since Aug 2021812 draws

Global evidence: 0.08×
Alarm line: 20×
Null inclusion rate: 7.25%
80% power scale: ±3.84 points

Beta-mixture e-processbeta-mixture-e-v1global value is the valid average across balls

20 is the 5% Ville threshold. Crossing it is a prompt to investigate data and machinery, not an allegation.

Every ball on its own

Powerball Double Play5/69 + 1/26 era · since Aug 2021812 draws

390.83×

80.49×

230.45×

50.19×

450.19×

120.14×

130.14×

410.12×

330.11×

460.11×

600.11×

690.11×

The reference line is the plain 20×, which is the right threshold for the global reading above and the wrong one for any single ball here.

Beta-mixture e-processbeta-mixture-e-v1per-ball e-processes averaged into one valid global e-process; the per-ball column is descriptive and needs 1380x before it is a claim

Descriptive; not anytime-valid on its own. Each ball’s e-process is a valid test for that ball, but this column shows the largest of 69 of them and picking the largest is a selection — Ville’s guarantee covers one process, not a maximum over many.

The maths, in plain language

Evidence safe under peeking

For one ball, $X_t=1$ when it appears and $p=k/N$ . With a $\operatorname{Beta}(1/2,1/2)$ alternative,

The story behind it

A statistic built for the monitoring room

A monitoring room must be able to look every day. Safe testing prices that freedom into the statistic itself. The result is less theatrical than repeated significance tests—and far harder to fool by choosing when to stop.