Effective interaction with the world requires the brain to signal behaviourally relevant events and organise an appropriate and timely motor response to such events. Unilateral brain lesion typically results in a reduction and slowing of motor behaviour directed to contralesional space. Accumulator models of choice and reaction time can distinguish between two possible functional causes of this deficit: slowed extraction of evidence in favour of a motor response or an increase in the required amount of evidence for response generation. Three patients with unilateral damage to the right hemisphere were tested on a visually guided saccade task. All three patients showed a dramatic increase in the latency of their responses to targets in the contralesional visual field. We fit their saccade latency distributions with a number of competing accumulator models that embody the alternative functional causes of this deficit. The latency difference between the two hemifields was best accounted for as an increase in the amount of evidence required for a contralesional response.