Hurray! A portion of what physicians do has solid research to support it! There are ways that work; we just have to do those more often and other things not at all.
What if the 15% of doctors who can at least follow the numbers started a medical sub-community dedicated to making decisions based on solid research and standardizing the practice of medicine, then commissioned an independent study of their success rate? That could take objective models for treatment, spread them to those who understand how they work, then spread them to everyone else who can see them working better than an average physicians choices.
Individual doctors could be certified by their sub-community as users of the research-supported ways, and their value would increase, and more would join them.
A feature in Scientific American magazine casts some light on the troubled state of modern medicine.
Health Care Myth Busters: Is There a High Degree of Scientific Certainty in Modern Medicine?
Short excerpt:
Scientific American often gates its online articles after some time has passed, so I don't know how long it will be available.