Maths for better Batting

If we look at the bowler's delivery, then at any time the ball is at a specific point and travelling in a specific direction in 3D space. Let's imagine an arrow in space starting at the position of the ball and going in the direction of the ball at that point in time. (This is called a tangent vector of our moving point).

Now imagine the bat moving through space. We'll start by considering the line in the middle of the bat. At any moment in time our bat gives us a line in space, and the motion of the bat defines it's direction. There's a bit of subtlety here, but for our purposes we can pick out a flat plane that the bat is moving in at a particular moment (a tangent plane). When we add the width of the bat, then we get a thickened plane that the bat is moving in.

Now consider the moment when the ball meets the bat. If the ball's arrow is moving across that thickened plane from one side to the other, then any error by the batsmen will result in a miss or an edge. If, at the other extreme, the arrow for the ball is wholly within the plane then an error by the batsman will just mean that the ball hits higher or lower on the bat.

Consider, for example, the sweep shot where the batter uses a horizontal bat to hit the ball close to where it pitches so he doesn't have to worry about the spin. Looks great when it works, but it fails catastrophically. The alternative is to play with an angled bat pointing to the point where the ball pitches, and with the angle of the bat being the angle that the ball bounces up. Now the ball is staying in the bat's thickened plane and though it looks awkward it has a much higher margin for error.

This is harder with leg spin with the ball moving away. Then you have to angle the bat with the handle more away from you than the blade. But if you get the bat handle in front and the blade behind and back cut, then suddenly all is good. Indeed when the batter gets in a muddle, and is forced to back cut the ball to stop it hitting the stumps, they often find that surprisingly easy. It would be exciting to see a batsmen practice this and then do it deliberately and repeatedly.

When the ball is spinning (or swinging) in, then this theory recommends hitting into the spin with a straight bat. I think that is best for defensive shots. Alternatively if attacking then an angled bat hitting to the leg side is your best chance to hit the ball with the balls tangent vector within the bat's thickened plan. This is the slog that even weaker players often succeed with. Not just luck after all.