Found this excellent excercise on YouTube done by young star Francisco lindor. It involves a cable machine with a stick at the end that you grip at either end and then you tilt your spine forward and rotate from low to high until the top hand and shoulder is down and shoulders are all the way open.
I did this excercise with a rubber band attached to a fence and the other end to a broomstick. Works just as well if you don’t have a machine.
Excellent excercise for separation, maintaining spine tilt and finishing rotation.
The formula says that off a Tee the exit velocity is around 1.1 times or a little more the batspeed. That means an 80 mph batspeed with a wood bat would lead to around a 90 mph exit speed off a Tee ( if you hit the ball in the sweet spot of course it can be much less if you don’t hit it on the screws).
Pitch velocity also plays a role but only to a much smaller degree.
Batted ball velocity has a very high correlation with performance. Better hitters tend to have higher batted ball speeds. Home runs in MLB usually are hit at a velocity upward of 100 mph. The hardest hit balls in MLB are around 120 mph, anything above 110 is really smoked.
Batspeed is not everything of course, you also need to make flush contact in the sweet spot and hit the ball in the right trajectory ( home runs usually have a launch angle of around 20-40 degrees). Do increase the chance to make such contact swing quickness and “shortness” ( elite swings take less than 150 milliseconds) is needed as well as a good swing plane, timing and barrell accuracy.
But if you want to become a really good batter increasing swing speed really helps.