In the set disjointness problem of 2-party communication complexity, Alice and Bob are both given an $n$-bit string as input; denoted by $X$ for Alice's input, and $Y$ for Bob's input. They need to output "no" if and only if there exists an index $i$ such that $X[i]=Y[i]=1$, otherwise they should output "yes".
The seminal paper An information statistics approach to data stream and communication complexity shows a lower bound of $\Omega(n)$ bits for this problem on the worst case length of the transcript $\Pi$ sent between Alice and Bob. At the end of their argument, the authors show this by using that $|\Pi| \ge H[\Pi]$, where $|\Pi|$ is the transcript length and $H[\Pi]$ is the entropy of the transcript.
I was wondering why the authors didn't show the significantly stronger statement that the expected communication complexity is at least $\Omega(n)$. This holds because even the expected length of the transcript is at least as long as $H[\Pi]$ (by the converse of Shannon's coding theorem, right?).
Actually, all lower bounds that I've seen in communication complexity seem to be shown only for the worst case length.
Is there some reason why the expected communication complexity isn't considered that I'm missing?