We present a method for classifying human skill at fetal ultrasound scanning from eye-tracking and pupillary data of sonographers. Human skill characterization for this clinical task typically creates groupings of clinician skills such as expert and beginner based on the number of years of professional experience; experts typically have more than 10 years and beginners between 0-5 years. In some cases, they also include trainees who are not yet fully-qualified professionals. Prior work has considered eye movements that necessitates separating eye-tracking data into eye movements, such as fixations and saccades. Our method does not use prior assumptions about the relationship between years of experience and does not require the separation of eye-tracking data. Our best performing skill classification model achieves an F1 score of 98% and 70% for expert and trainee classes respectively. We also show that years of experience as a direct measure of skill, is significantly correlated to the expertise of a sonographer.