  We uncover two precise interpretations of traditional electroweak fine-tuning
(FT) measures that were historically missed. (i) a statistical interpretation:
the traditional FT measure shows the change in plausibility of a model in which
a parameter was exchanged for the $Z$ boson mass relative to an untuned model
in light of the $Z$ boson mass measurement. (ii) an information-theoretic
interpretation: the traditional FT measure shows the exponential of the extra
information, measured in nats, relative to an untuned model that you must
supply about a parameter in order to fit the $Z$ mass. We derive the
mathematical results underlying these interpretations, and explain them using
examples from weak scale supersymmetry. These new interpretations shed fresh
light on historical and recent studies using traditional FT measures.
