Understanding the organisational principles of sperm motility has both evolutionary and applied impact. The emergence of computer aided systems in this field came with the promise of automated quantification and classification, potentially improving our understanding of the determinants of reproductive success. Yet, nowadays the relationship between sperm variability and fertility remains unclear. Here, we characterize pig sperm motility using t-SNE, an embedding method adequate to study behavioural variability. T-SNE reveals a hierarchical organization of sperm motility across ejaculates and individuals, enabling accurate fertility predictions by means of Bayesian logistic regression. Our results show that sperm motility features, like high-speed and straight-lined motion, correlate positively with fertility and are more relevant than other sources of variability. We propose the combined use of embedding methods with Bayesian inference frameworks in order to achieve a better understanding of the relationship between fertility and sperm motility in animals, including humans.