  A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically
`decadent' in that it is stable only in some regions of the moduli space and
decays on submanifolds in the moduli space. Using this fact, and from the
degeneracy of the system close to the decay, a new derivation for the
degeneracy of such dyons is given. The degeneracy obtained from these very
simple physical considerations is in precise agreement with the results
obtained from index computations in all known cases. Similar considerations
apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the
$\mathcal{N} =4 $ field theory dyons and those counted by the Igusa cusp form
in toroidally compactified heterotic string is elucidated.
