A major analytics challenge in Mixed Martial Arts (MMA) is capturing the differences between fighters that are essential for both establishing matchups and facilitating fan understanding. Here, we model ~18,000 fighters as mixtures of 10 data-defined prototypical martial arts styles, each with characteristic ways of winning. By balancing fighter-level data with broader trends in MMA, fighter behavior can be predicted even for inexperienced fighters. Beyond providing an informative summary of a fighter's performance, style is a major determinant of success in MMA. This is reflected by the fact that champions of the sport conform to a narrow subset of successful styles.