Tony says, “Deflection in my mind is how much the ball has veered off axis during the time the tip is in contact with the cue ball.”
If all shots could be played with center ball it wouldn’t matter if you used a baseball bat instead of a cue. However, playing often requires a more complicated shot. When you use english, that is, hit a ball off-center, you impart two distinct energy forms. When using english you have assigned rotational energy (or spin) as well as directional energy to the cue ball. The slower the cue ball is traveling the greater the effect of the rotating energy, because rotating energy is very weak and quickly dissipated, compared to the cue ball’s velocity. Therefore, more dramatic angles can be obtained coming off the rail by slowing ball travel and increasing spin, or english.
When executing a shot with right hand english you are bending the cue transversely. The tip of the cue bends into the ball first, compressing the left side of the tip and cue. This happens quickly, but your eye only sees the rebound of the flexing action, that is, the shaft recoiling to the right and the cue ball squirting to the left.
Under the best of stroke conditions, a stroke that accelerates through the ball, the tips contact time is dramatically increased. In doing this the tip is recoiling to the opposite direction holding the ball on line. The cue bends drastically different.
Tony’s hypothesis is: The longer the tip is in contact with the cue ball the more likely the ball will travel to the same line of sight with the cue. This is assuming you are playing with a cue engineered like a Black Boar. A softer cue allows a player to enjoy a tighter grip. Giving a Black Boar cue to a player with an excessively tight grip is like “giving an ice pick to a blind man.”
This is best exemplified by using the tip of your finger to contact the ball in an attempt to push it forward. The contact time is very short if you poke the ball, and you will have trouble controlling its path. But, if you address the ball smoothly with constant increasing speed you can keep your finger in contact with the ball all the way to the moon.