In a series of sophisticated experiments, Steve Lisberger and colleagues showed that movements of the eyes keep time. When following a predictable moving target, the brain learns what to expect, so it anticipates what will come next. The brain appears to keep time with eye movements by taking note of the distance covered by the eyes and its speed.
Pretty amazing stuff, this pacemaker in moving eyes. It also tells you why timing and coordinated movements are so abnormal in children with apparently mild eye movement abnormalities or amblyopia. It also tells us why visual problems present with "much more than eyes."
The second link below is neat article showing how lazy eye begets lazy brain. The brain registers visual information differently in people with lazy eye or significantly 'uneven' acuities (anisometropia). One more recent study found that altered motion processing occurs on the side of the 'lazy brain'. That definitely makes it harder to catch a ball.
Exploring the brain's internal stopwatch
Lazy eye causes lazy brain