The curveball never breaks, but instead follows a gradual and steady parabolic path. Our eyes just have trouble handling it.

Batters will use their foveal, or central, vision when the ball leaves the pitcher's hand. About 20 feet in, the batter will switch to peripheral vision, which occurs outside of the very center of the gaze. By the time the ball crosses home plate, the batter reverts back to central vision. Humans constantly switch focus like this.

The problem is peripheral vision processes first and second order motion in conjunction, while foveal vision distinguishes between the two.

During the peripheral stage, batters do not notice that the curveball has been gradually changing direction ever since it left the pitcher's mound.

Once they switch back to the foveal vision, batters accurately register the changed direction, but consider it a result of the ball's immediate "break," instead of their temporary impaired vision.