ASAS is a long term project to monitor bright variable stars over the whole sky. It has discovered 50,122 variables brighter than V < 14 mag south of declination +28 degrees, and among them 11,099 eclipsing binaries. We present a preliminary analysis of 5,384 contact, 2,957 semi-detached, and 2,758 detached systems. The statistics of the distribution provides a qualitative confirmation of decades old idea of Flannery and Lucy that W UMa type binaries evolve through a series of relaxation oscillations: ASAS finds comparable number of contact and semidetached systems. The most surprising result is a very small number of detached eclipsing binaries with periods P < 1 day, the systems believed to be the progenitors of W UMa stars. As many (perhaps all) contact binaries have companions, there is a possibility that some were formed in a Kozai cycle, as suggested by Eggleton and his associates.
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