Although this approach to measuring is plausible, I fear it is not what you want. Although of course things vary by field, the papercount per se, or even "impact factor", or ... any other easily-measurable thing is not quite what will affect things.
At least in mathematics (my field), a smaller number of very-good papers is much better than a large number of irrelevant papers. One might imagine that this would be measured by "impact factor", but it is absolutely not reliably so. As an extreme case, consider what happens when an important problem is finally and definitively solved: there may be fewer follow-ups, fewer citations, simply because there's little more to say.
And there's time-lag: I have many examples of 10-20 year (and longer) delays before people widely realized the interest of a given paper. Srsly, surely we're not trying so much to be of-the-moment-celebrities, but to make a long-term impact.
One could go on-and-on about the unreliability of appealing-but-fatally-flawed metrics... but the real point is that a less objectifiable judgement is necessary to evaluate the "merits" of a program. Stats on the students is probably not quite what you'd want, even though it might seem to be. E.g., at more elite places, there is vastly greater variance among students... so the "outcomes" are harder to interpret meaningfully... and, for you yourself, what those other kids did or didn't do is operationally irrelevant:
That is, your level-of-performance, that causes (or doesn't) respected experts to commend you to their peers, is what will get you a job, or not. The "published papers" thing is a side-effect.