Thanks that is very helpful.
Since we are on this topic, why is it that people always look for 'grains running straight through the toe'? What does that imply?
I think that the feeling generally is that there is strength in straightness. To get straight grains through the bat, across the width of the bat from face to back, the tree has to have reached a level of maturity. However quickly or slowly it has grown, it must have reached a circumference of at least 52-54 inches (around 140cm). If the grains curve from the face to back of the bat, then the cleft has either been cut from an immature tree, or has simply been incorrectly cut.
If you look at my drawings again, imagine the clefts I've drawn in red being positioned to the left of the position I've shown, closer to the core of the tree. In that case, the rings of the tree are much tighter, which would mean the grains on the bat curving from face to back. The core of the tree, known as the pith, is definitely to be avoided for batmaking, as it might literally fall out. Alternatively, imagine the clefts I have drawn being turned clockwise through 45 degress. Again, the grains would curve from face to back, this time because the cleft was cut incorrectly.
So, straight grain from face to back is a good indicator of a tree grown to maturity, gives security (to some extent) that the willow is OK and that whoever cut the cleft knows what they are doing.