Daniel Q’s point, the importance of which can not be overstated, was that often the best way to protect your own child’s physical and emotional well-being is by eliminating the problem through peaceful means rather than hostile ones. In helping the bully change their situation and self image, you are removing the threat in a more profound and lasting way than with a baseball bat.
Not to impugn Daniel’s generosity of spirit, this approach demands not generosity, but rationality and objectivity.
Simply put, if you will act in a goal-oriented way, and your goal is the protection of your child, you will often find yourself helping the bully.
On a side note, as Daniel alluded, the halacha of yeihareig v’al ya’avor does not actually apply to halbonas panim; the Gemara indicates that “mutav”, it is preferable, (based on Tamar and Yehuda), but this directly indicates that it is not required.
Once more, I will point out that even in a small recreation area with a small number of children, it is impossible to supervise all actions of all children for every second of recess. This is true whether or not the supervisor is shmoozing. As a Rebbe who supervises recess on occasion, I can tell you that nobody understands this better than the bullies. They are shrewd enough to make sure that their actions take place under the radar.