You are right that "mastering out" is not the same thing as failing out, so I may be overcounting here. Universities do also use the trick of admitting aspirin

You are right that "mastering out" is not the same thing as failing out, so I may be overcounting here. Universities do also use the trick of admitting aspiring PhD students as MS students first, so that it doesn't affect their numbers when they fail to enter the doctoral program later. So there is also a possibility of undercounting as well. I need to think a little more about this, but you're certainly correct in pointing out that it is more complicated that what I wrote - especially in engineering or CS, where an MS makes sense as a terminal degree goal.