Confidence is a value from 0 to 100 on characters in The Elder Scrolls IV: Oblivion. It is used by the AI together with Responsibility to determine what their behavior will be. Confidence is relevant in fights. The lower a character's Confidence is, the more likely they are to escape from combat; specifically, when their Health drops below a certain level, they will then try to run away. Fleeing characters will run to the closest guard (even a dead one).
An extreme example of a low rating is that of deer. To emulate the behavior of real deer, deer in Oblivion have a Confidence of 0, but an Aggression of 100. As a result, they will enter combat with the Hero on sight, but then immediately flee, making it appear as though they were startled by the Hero.