The activity of dozens of simultaneously recorded neurons can be used to control the movement of a robotic arm or a cursor on a computer screen. This motor neural prosthetic technology has spurred an increased interest in the algorithms by which motor intention can be inferred. The simplest of these algorithms is the population vector algorithm (PVA), where the activity of each cell is used to weight a vector pointing in that neuron's preferred direction. Off-line, it is possible to show that more complicated algorithms, such as the optimal linear estimator (OLE), can yield substantial improvements in the accuracy of reconstructed hand movements over the PVA. We call this open-loop performance. In contrast, this performance difference may not be present in closed-loop, on-line control. The obvious difference between open and closed-loop control is the ability to adapt to the specifics of the decoder in use at the time. In order to predict performance gains that an algorithm may yield in closed-loop control, it is necessary to build a model that captures aspects of this adaptation process. Here we present a framework for modeling the closed-loop performance of the PVA and the OLE. Using both simulations and experiments, we show that (1) the performance gain with certain decoders can be far less extreme than predicted by off-line results, (2) that subjects are able to compensate for certain types of bias in decoders, and (3) that care must be taken to ensure that estimation error does not degrade the performance of theoretically optimal decoders.