The success of education and correction depends heavily on the character and sensitivity of the person receiving it. Gentle guidance offered to an insightful person achieves far greater results than harsh physical punishment inflicted upon a fool.
A single verbal warning is enough to awaken and correct an understanding person. Commentators offer different perspectives on exactly how this correction affects them. One approach suggests that a simple reprimand creates a profound sense of fear and submission [רש"י, מצודת ציון, מצודת דוד]. Another perspective views the correction as something that lands and penetrates deep into the person's heart [מלבי"ם, ביאור שטיינזלץ], though some consider this interpretation less likely [אבן עזרא]. A third view is that the rebuke simply causes the insightful person genuine sorrow and distress over their actions [ביאור שטיינזלץ].
The primary approach among commentators is that this single verbal correction has a much larger impact on a perceptive person than a hundred physical blows would have on a fool. While the insightful person requires no physical punishment at all, a fool remains completely unmoved even after severe beatings. This sharp contrast stems from the root of their behavior. A fool is not necessarily lacking knowledge; rather, he rebels on purpose because his physical desires overpower him [מלבי"ם]. Because his actions are driven by stubborn desire, no amount of hitting will change his path. Physical correction is only useful for those who act purely out of ignorance, similar to an animal that requires physical steering to find its way [מלבי"ם].
An interesting alternative view suggests that the insightful person learns his lesson without even being directly rebuked. Instead, he corrects his own behavior simply by observing the fool receive a hundred blows for his foolish actions [עמנואל הרומי].