CrossFit performance is only moderately related to aerobic and anaerobic capacity
CrossFit can be thought of as a "rainbow" training program, as it incorporates aerobic and anaerobic exercises, gymnastics, weightlifting, sprinting, full-body exercises and calisthenics. It develops 10 aspects of physical fitness: cardiorespiratory endurance, stamina, strength, flexibility, power, coordination, agility, dexterity, balance and accuracy. The training exercises are changed regularly and an attempt is made to use comprehensive and continuously varying training stimuli.
An interesting study conducted by David Bellar and colleagues at the University of Louisiana at Lafayette found that performance in two daily CrossFit workouts was only weakly related to maximal oxygen consumption and maximal power release (Wingate test). CrossFit experience was a good predictor of performance during CrossFit workouts, as measured by the total number of repetitions performed during each workout.
Franklin Henry of UC Berkeley proposed the theory of specificity. His work showed that the learning of motor skills involved the development of very precise motor patterns. CrossFit athletes perform better in CrossFit workouts because they have more practice in learning the necessary skills.
(Biology of Sport, 32: 315 - 320, 2015)