  Let $B$ be a $p$-block of a finite group, and set $m=$ $\sum \chi(1)^2$, the
sum taken over all height zero characters of $B$. Motivated by a result of M.
Isaacs characterising $p$-nilpotent finite groups in terms of character
degrees, we show that $B$ is nilpotent if and only if the exact power of $p$
dividing $m$ is equal to the $p$-part of $|G:P|^2|P:R|$, where $P$ is a defect
group of $B$ and where $R$ is the focal subgroup of $P$ with respect to a
fusion system $\CF$ of $B$ on $P$. The proof involves the hyperfocal subalgebra
$D$ of a source algebra of $B$. We conjecture that all ordinary irreducible
characters of $D$ have degree prime to $p$ if and only if the $\CF$-hyperfocal
subgroup of $P$ is abelian.
