"Researchers have since determined that rogue waves probably claimed 22 supercarriers and more than 500 lives in the second half of the 20th century alone...More information at Quanta Magazine.
... two schools of thought surfaced regarding how monstrous waves could develop. The first is the simplest. It starts with the observation that swells travel at different speeds. When one overtakes another, the two are combined... Others, however, hold that the most extreme waves form from less straightforward behavior. In wave tanks, for instance, when one wave travels right next to another of similar length, energy leaks from one to the other. The individual swells affect one another in complicated nonlinear ways...
Standard arithmetic suffices for simple casino games, but this thinking captures the spirit of a branch of probability known as large deviation theory (LDT). It specializes in identifying instances of rare events that are much more common than the next most likely way they might play out. In the exceptional cases when LDT can be used, it allows calculations that are impossible with standard statistics, Vanden-Eijnden said, just as calculus can solve problems that are intractable in algebra.
The chaotic ocean, the group reasoned, should be the perfect arena to witness LDT in action..."