The Madden-Julian Oscillation (MJO) is a large area of organized tropical thunderstorms, flanked to the east and west by regions where these storms are unusually absent, that moves eastward along the equator from the Indian Ocean to the central tropical Pacific Ocean, over the course of 30 to 90 days. Its slow movement, and the atmospheric disturbances it drives in the extratropics, makes it a prime focus for improved prediction studies. In this work, we develop a data-driven method to characterize the MJO in terms of two east-west see-saw patterns, one that moves faster (once every 45 days), and one that move slower (once every 70 days). These patterns combine to yield nearly all of the observed MJO phenomenon as defined by past methods, and how they combine can be used ahead of time to identify when MJO forecasts will be particularly skillful. In such cases, operational weather models like that of the ECMWF predict the MJO more skillfully by approximately one week than typical forecasts.