I’m confused how we can do thing like playing sports if our brains are mashing reality this much. How does a batter hit a 90 mph pitch if his vision can be delayed by half a second?
To see this in action, look around normally - notice your eyes move and then stop, taking in "still frames".
Next, look at your finger and move your finger around. Notice that your eyes smoothly follow the finger around.
When the batter is watching the ball, he is similarly tracking it.
It's also why pitchers can't wear white sleeves or use white gloves (e.g., Eddie Butler getting his sleeves cut off before he pitches [1]).
90mph is 132 feet per second. The distance from the pitching mound to home plate is 60 feet, 6 inches. The ball will take under half a second to travel that distance. I think about 450ms.
The actual swing takes about 150ms. That gives the batter about 300ms total to identify the pitch and decide to swing.
They're basically watching the pitcher and determining where to swing based on the release. Once the bat is in motion, it's up to the baseball gods. That's why batting averages are so low. Even great batters are hitting the ball only about a third of the time.
Also as soon as the pitcher starts moving his body the brain probably starts creating all types of predictions of what will happen next.