The quantity we're measuring tells us how improbable this event is, in the absence of optimization, relative to some prior measure that describes the unoptimized probabilities. To look at it another way, the quantity is how surprised you would be by the event, conditional on the hypothesis that there were no optimization processes around. This plugs directly into Bayesian updating

This seems to me to suggest the same fallacy as the one behind p-values... I don't want to know the tail area, I want to know the probability for the event that actually happened (and only that event) under the hypothesis of no optimization divided by the same probability under the hypothesis of optimization. Example of how they can differ: if we know in advance that any optimizer would optimize at least 100 bits, then a 10-bit-optimized outcome is evidence against optimization even though the probability given no optimization of an event at least as preferred as the one that happened is only 1/1024.