Unpredictable movement can provide an advantage when animals avoid predators and other threats. Previous studies have examined how varying environments can elicit unpredictable movement, but the intrinsic causes of complex, unpredictable behavior are not yet known. We addressed this question by analyzing >200 hours of flight performed by hummingbirds, a group of aerial specialists noted for their extreme agility and escape performance. We used information theory to calculate unpredictability based on the positional entropy of short flight sequences during 30-min and 2-hour trials. We show that a bird’s entropy is repeatable, with stable differences among individuals that are negatively correlated with wing loading: birds with lower wing loading are less predictable. Unpredictability is also positively correlated with a bird’s overall acceleration and rotational performance, and yet we find that moment-to-moment changes in acceleration and rotational velocities do not directly influence entropy. This indicates that biomechanical performance must share an underlying basis with a bird’s ability to combine maneuvers into unpredictable sequences. Contrary to expectations, hummingbirds achieve their highest entropy at relatively slow speeds, pointing to a fundamental trade-off whereby individuals must choose to be either fast or unpredictable.