Let $S$ be the set of 81 points $(x, y)$ such that $x$ and $y$ are integers from $-4$ through $4$.  Let $A$, $B$, and $C$ be random points chosen independently from $S$, with each of the 81 points being equally likely.  (The points $A$, $B$, and $C$ do not have to be different.)  Let $K$ be the area of the (possibly degenerate) triangle $ABC$.  What is the expected value (average value) of $K^2$ ?