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How much treadmill time factors into formal training for competitive athletes? And how much road work?
Treadmills are discouraged for competitive track and field training, except for bad-weather training, or situations that prevent an athlete from otherwise being able to train (mothers of small children who can't get a babysitter, for instance). Pete Pfitzinger, a former world-class runner and now exercise physiologist and coach, explains that treadmills, "are a necessary evil. Running on a treadmill is not quite the same as running on the road, but it’s a hell of a lot more specific to running than any other form of cross-training. Unless you are a treadmill veteran, you should limit your treadmill runs to general aerobic runs and recovery runs of up to 40 minutes."
As for roadwork, that all depends on a variety of factors (too many to discuss here in detail), including the specific event for which one is training, the experience and age of the runner, the conditions, the time of the year, whether or not the athlete is tapering for a big event. For a detailed training program for middle and long-distance competitive runners, I highly recommend Bob Glover's The Competitive Runner's Handbook: The Bestselling Guide to Running 5Ks through Marathons.
For sprint training, you might read Explosive Running : Using the Science of Kinesiology to Improve Your Performance, by Michael Yessis Ph.D., or Sports Speed by George B. Dintiman, Robert D. Ward and Tom Tellez.