The issue of whether visually-mediated, simple reaction time (VRT) is faster in elite athletes is contentious. Here, we examined if and how VRT is affected by gaze stability in groups of international cricketers (16 females, 28 males), professional rugby-league players (21 males), and non-sporting controls (20 females, 30 males). VRT was recorded via a button-press response to the sudden appearance of a stimulus (circular target-diameter 0.8°), that was presented centrally, or 7.5° to the left or right of fixation. The incidence and timing of saccades and blinks occurring from 450 ms before stimulus onset to 225 ms after onset were measured to quantify gaze stability. Our results show that (1) cricketers have faster VRT than controls; (2) blinks and, in particular, saccades are associated with slower VRT regardless of the level of sporting ability; (3) elite female cricketers had steadier gaze (fewer saccades and blinks) compared to female controls; (4) when we accounted for the presence of blinks and saccades, our group comparisons of VRT were virtually unchanged. The stability of gaze is not a factor that explains the difference between elite and control groups in VRT. Thus we conclude that better gaze stability cannot explain faster VRT in elite sports players.