Traditional boys schools frequently used CP and often put great store on sports so sports-related punishment is likely. The lack of first hand reports may be because it was considered an in-house matter and kept private.
In 1783, the boys of Eton organized a cricket match and traveled to Harrow to play it. In defiance of their notoriously nasty Head Dr Heath.
They won it-he subsequently birched the entire XI on their return.
And that is genuinely how the phrase “It’s not cricket” entered the English language.