PBL, I see others have answered your question (back on page 1) already, but let me add my tuppence worth to agree with them
Those crediting TCAS with all these "saves" need to explain why, before the advent of TCAS, there were a statistically-negligible number of collisions in the history of airline flying, and upon the introduction of TCAS there are suddenly almost 60 per year.
The answer, as already given, is GPS and IRS. Anyone who remembers reading Ernest K. Gann's classic "Fate is the Hunter" will remember the incident that is described in the very first pages of the book - where he and his co-pilot see, far too late to avoid it, another aircraft pass 50' overhead and disappear into the night.
I know it won't fix crossing conflicts, but offsetting, which others here on PPrune have been calling for for years now, (ever since the 1996 New Delhi mid-air, I think) WILL help mitigate the problem (because it is a problem) of ultra accuracy in GPS when the conflict is between opposite direction traffic on the same air route, as in the recent Brazilian tragedy.
I find myself wondering how it is that some ambulance chasing lawyer hasn't latched on to this fact years ago and tried sueing (sp?) someone - (ICAO?, the FMS manufacturers?, the tea lady at Boeing?) over their not doing sometrhing to fix what everyone should recognise is a quantum leap in loss of separation standards.
I think Ernest K. Gann's incident proves these really close calls have been happening for many years, and we've in many cases been totally unaware that many such incidents have occurred. It's only now, with ultra accurate GPS and RVSM-compliant altimiters that many such incidents now have such potential to be "hits" rather than the rather confusing, almost contractory term "near misses".