Two main concepts in mathematical modelling of ship encounters have been proposed by Davis. The first, the ‘domain’, was an adaptation of a concept originally introduced by Goodwin, who defined the domain as the ‘area about own-ship that a navigator wished to keep free with respect to ships and other stationary objects’. The second, the ‘arena’, conceived by Davis, is the area around the domain which when infringed causes the mariner to consider whether to make a collision-avoidance manoeuvre. Thus, in a computer model, when a vessel enters the arena the computer analyses the situation and, depending on the severity of the threat, makes a collision-avoidance manoeuvre.

Goodwin's domain was divided into three sectors corresponding to the ‘giveway’, the ‘stand-on’ and the ‘overtaking’ regions as defined by the relative velocity of approach. The domain was derived from radar films of ship tracks and records of radar simulator experiments. Davis smoothed the sectored domain to a circle with own-ship off-centred astern and to port, and the weighting of each of the sectors retained. Davis's domain had a solid theoretical grounding; the arena, however, was simply a larger version of the smoothed domain. Its size and position were obtained by means of a well-distributed questionnaire. It served its purpose in the model, but lacked any real validation.

One problem with the Davis arena was its inability automatically to take into account different velocities, both of own-ship and of targets.