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.

Safer red ball cricket

We see that pitches for red ball cricket (3, 4 or 5 days) are prepared that are quite dangerous, to increase the chance of a result. I have an alternative solution.

Wickets fall at a very random rate. Runs are scored at a more even rate. So, instead of having a target of more runs in 20 wickets, the plan is to a target of least wickets to fall to score a set number of runs. You can have as many innings as needed to get those runs.

For example suppose the target for a test match is 500 runs. Then the two teams alternate innings (an innings always counts as 10 wickets) till one team has 500 or more runs. If it is the team batting 2nd then they win because the other team has already lost more wickets. If it is the team batting first that first exceeds 500 runs, then the team batting 2nd knows how many wickets they can afford to lose before they get to 500 to win. Ties will be more common, so maybe have a tie-breaker system, but I don't have a problem with ties.

One nice thing about this scheme is that you can play the game to a finish, however long that takes with rain, without the dangers of matches going for a long time, as used to happen before WWII. Let's have more ties and no draws.

The main objective is that pitches be prepared that don't have the ball rising sharply from just short of a length.

This can be combined with another idea I like: Let the captains make a bid (in runs) for the right to decide who bats first. The side losing the auction starts their innings with the runs they bid.