Like all accident stats, there are thousands of close calls for every midair. The reason we don't report the close calls is mainly because we don't even see the other guy. I am convinced that the vast majority of close calls go unnoticed by either crew, so for every one you do see, there must have been dozens you did not see. I base this on the fact that whenever I have been able to identify the other airplane and have asked the crew, they did not see me. Maybe I am paranoid and have a more energetic look out going when I fly, but I sure see a lot of other airplanes and I don't call it a close call unless I have had to maneuver to avoid the other guy or we pass within 100 feet or so. If we were clearly going to miss each other, I don't worry about it.
Don't rely on TCAS. The other guy might not have a transponder or might not have it turned on. There is plenty of light airplane traffic around close to and sometimes inside your protected airspace, in VFR or marginal VFR especially. I was flying out of LAX in a Cessna 310, the transponder was inop and I was VFR. As I climbed I saw a FEDEX Dash 8 or similar flying at around 8000 crossing my path left to right, very close. I had to level off or I would have flown right into him, and intended to pass a few hundred feet below him. I was looking up, to make sure I had clearance, and as I passed under him I saw the FO look around and see me. I could almost see the surprise on his face, and before he totally disappeared his airplane rotated violently up, to avoid what must have been a frightening sight, since he had no idea I had him in sight and was already leveled off. I was glad he was not flying passengers, or else there would have been stories in the LA Times the next day. So what value your TCAS there? How effective is your electronic protections? Do you seriously think that replacing the Mk 1 eyeball with a box of tricks is a good idea? BTW, birds don't have TCAS.
A buddy of mine told me a story about a French glider instructor he was flying with in the south of France. Trying to impress the instructor, he called every other airplane that he was able to see as traffic. In every case the instructor replied "and what about the other one?" So my buddy intensified his efforts to see the "other one" and when he saw it, he called it too.
On the ground, he remarked to the French chap that he must have exceptional eyesight, since he was able to see more airplanes than my buddy could, and the instructor replied that he did not actually see the "other one", but knew that there must always be one out there. It is not the airplane you can see that is going to get you; it is the one you don't see!
We NEED to improve our lookout. We MUST be more vigilant. As a group, we are doing a pisspoor job and HAVE TO do better.
After 30 years in the airline business I know that lookout is worse there than any other field of aviation, and most of the readers of this forum are airline pilots, so yes, I am pointing at you.