It doesn't happen. The weaknesses of the debate format as an illustrator of the skills of a would-be president are found in the format's very nature. Debating rewards speed, reaction, fact recall and other attributes that are important to the one half of the population that prefers to get its information through analytical means. For the other half of the population, which prefers information that reveals understanding of the spiritual, moral and emotional needs of humans, debates are lousy formats for communication. The emotional balance exemplified by Ronald Reagan and Harry Truman may make for a much more desirable constellation of presidential talents.
Effective leaders have clear visions of where they are going and sound principles for guidance.
Effective presidents are also good negotiators. Not good from the perspective of always getting everything they want, but from the perspective of finding ways to move the interests of the nation forward. Too often, good negotiators are thought of as compromisers - splitting differences down the middle. That's actually a refined and respectable form of surrender in a negotiation. A good negotiator finds ways to get what's needed without spending too much convincing the opponent to agree.