In this paper we develop an efficient mathematical solution method for an articulated raft wave energy converter. Representative of Pelamis and the Cockerell raft design, it is comprised of a series of floating pontoons connected via hinges. Power is generated through the relative motions of adjacent elements which are excited by the incident wave as it passes along the length of the device. Using an efficient semi-analytic solution we are able to generate results more quickly than would be possible using a panel-based numerical code such as WAMIT. This allows us to explore the parameter space quickly and thus to develop an understanding as to what elements of raft-type wave energy converter design allow it to generate power so successfully. We find that the capture factor increases proportionately to the number of pontoons, a focusing effect that allows the device to absorb far more power than that which is directly incident upon its frontage. Hinge position and device proportions are also significant with results favouring long, narrow rafts made up of pontoons of increasing length from fore to aft.