Expected vs worst-case communication complexity 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?
The reason is that a lower bound on the worst-case complexity automatically implies a lower bound on the expected complexity, so there is no reason to prove the latter.

To see the implication, observe that every randomized protocol with expected complexity $c$ and error probability $\varepsilon$ can be transformed into a randomized protocol with worst-case complexity $c/\varepsilon$ and error probability $2\varepsilon$: The new protocol simulates the old protocol, but forces the simulation to halt after $c/\varepsilon$ bits have been transmitted. By Markov inequality, a forced halting occurs with probability at most $\varepsilon$, so it adds at most $\varepsilon$ to the original error probability.

Since error probability can be amplified, it follows that every randomized protocol with expected complexity $c$ and constant error probability can be transformed into a randomized protocol with worst-case complexity $O(c)$ and the same error probability. Thus, if we show that there is no randomized protocol with worst-case communication $O(c)$ and constant error probability that computes a function $f$, the same holds for protocols with expected communication $O(c)$.