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The channel estimation overhead of reconfigurable intelligent surface (RIS) assisted communication systems can be prohibitive. Prior works have demonstrated via simulations that an adaptive transmission scheme where neighbouring RIS elements are grouped together can help to reduce the pilot overhead and improve achievable rate. In this letter, we present an analytical study of RIS element grouping. We derive a tight closed-form upper bound for the achievable rate and then maximize it with respect to the group size. Our analysis reveals that more coarse-grained grouping is important when the channel coherence time is low (high mobility scenarios) or the transmit power is large. We also demonstrate that optimal grouping can yield significant performance improvements over simple ‘On-Off’ RIS element switching schemes that have been recently considered.