“… then you would have to have a draft number that was of those selected, much less than the total”
At the peak of the Vietnam war, they were taking just about everybody. I registered at 18 and was in the army before I was 20.
“Then you would have to pass your physical…”
It was hard to fail a physical. Unless you had something obvious wrong with you (e.g., missing limb) they were likely to keep you overnight to reexamine you and if you failed again they could call you back again a month or two later and repeat the process again, and again.
“…and [pass] basic training.” It was hard (or, at least, dangerous) to fail basic training. The DIs were intimidating enough that I remember one guy who peed in his pants. I don’t know that they ever actually beat anyone up but I do know that they (and the company commander) would punish a whole platoon if one guy gave them trouble. Then they would encourage the platoon to solve it’s problem by holding a blanket party for the troublesome recruit.
“Then you would have to select”
Select?!?!?! There was no selection for draftees. Among the guys I went through basic training with, at least half (including anyone who had been to college) were sent on to Advanced Infantry Training at Ft. Polk and the rest were sent to learn to be cooks, truck drivers, etc.
“And then you would have to be stationed in Vietnam, which was not likely, as then as now the majority of soldiers are stationed in the US and Europe.”
It was highly likely. Ft. Polk was on the way to Vietnam. Europe and Korea were filled with guys who enlisted or reenlisted (probably to avoid Vietnam).
“Even you would probably not be sent to a “hot” combat area.”
Fat chance. Damn near the whole country was “hot.”
“…and only if there was a ‘slot’ available”
There was no shortage of slots. Besides guys being wounded or killed, they rotated out every year.
I’d have to say, in contrast to your experience, that in my experience the chances of a healthy, non-deferred, 19 year old American being sent into combat in Vietnam in 1968 was probably over 50%. Why do you think W joined the Guard?