Quoth said Wikipedia article, in the "criticisms":

"EBM applies to groups of people but this does not preclude clinicians from using their personal experience in deciding how to treat each patient. One author advises that "the knowledge gained from clinical research does not directly answer the primary clinical question of what is best for the patient at hand" and suggests that evidence-based medicine should not discount the value of clinical experience.[26] Another author stated that "the practice of evidence-based medicine means integrating individual clinical expertise with the best available external clinical evidence from systematic research".[1]"

Which suggests that the precursor to EBM is a combination of Education and Intuition. Sorry if I'm not framing it terribly well - there's an intuitive category in my head for this method, but I've never really had to refer to it explicitly. It's the same technique I use to troubleshoot computer problems - I get a hunch as to what is causing it, and then proceed through a mixture of "safe, generalized advice" (try rebooting!) and "advice specific to the problem I think it is" (aha, you must not have your DNS configured correctly). If both of those fail, THEN I'll resort to actually collecting data, analyzing it, and seeing where that leads me - "have you had other problems?", "hmm, let me look up this error code..."

I've generally observed this path as the default human behavior, with "call someone else" occurring when they hit the limit of their abilities.