This is assuming a differentiation of 20 times as many boys caned as girls – which seems to be borne out by figures for England and Wales – but the numbers above of improvements and side effects were just made up to illustrate the mathematical argument).
If boys schools had no cane policies then other punishments could be just as effective,
The evidence is that that is not true. There are some boys for whom nothing else seems to work anywhere near as well, if at all, There’s a larger group that while alternatives can be found that are just as effective, they have higher risks of side effects, and are much more difficult to put in place. For a lot of boys, there are plenty of workable alternatives – but there’s a lot for whom that isn’t really true.