  A nonnegative martingale with initial value equal to one measures evidence
against a probabilistic hypothesis. The inverse of its value at some stopping
time can be interpreted as a Bayes factor. If we exaggerate the evidence by
considering the largest value attained so far by such a martingale, the
exaggeration will be limited, and there are systematic ways to eliminate it.
The inverse of the exaggerated value at some stopping time can be interpreted
as a $p$-value. We give a simple characterization of all increasing functions
that eliminate the exaggeration.
