hand-eye coordination

This term describes a specific neurological and physical synergy. It is most frequently employed in sports science, occupational therapy, and gaming contexts to describe the precision of motor skills. While it sounds like a general ability, in professional contexts it refers to the specific latency and accuracy between visual perception and manual response.

Because it describes a singular physiological capability, it is treated as an uncountable noun. You would not refer to "three hand-eye coordinations"; instead, you would describe the level of coordination as "poor," "exceptional," or "developed."