> the measure of success for a teacher in higher education is in how knowledgeable and influential their own students are.

this is exactly right, and if thought about carefully, probably impossible to measure without your later suggestion.

> only one was an actual teacher. The other was paranoid and egotistical.

Hot take. I approve.

> shouldn’t just be measured in novel research and publishing but the ability to replicate and/or filter out bullshit research as well.

Replication is the foundation of science. It is the only way to actually fight the tyranny of metrics because replication always necessitates variance from the original. Failure to replicate doesn't simply mean fraud, as many believe, but that there are confounding variables that were not uncovered in the original. That's just another piece of the puzzle. But whats destructive is that you can uncover there, formulate a better hypothesis, and then fail to get published due to lack of novelty. Generally associated with reviewers stating that your claim is obvious, despite it not being in the literature or not being able to get anyone to make similar claims prior to giving evidence. There's a reason scissors took a long time to invent, because despite what they look like, it isn't just slapping two knives together.

> I’d also go as far as to say professionals in industry should be able to link to their old professors and not just institutions.

At least this happens with the PhD level, but I do wonder if this could help at a lower level. Or if this would just end up making the tyranny of metrics worse as people try to extract too strong of a signal? I went to a low rank undergraduate school and I know for a fact that my math education was better than friends who went far more prestigious schools. I took more classes, went in more depth, and was able to solve more Putnam problems than them (only a few total btw, but I did physics not math).

With school rankings, I think it is quite silly how we quantify them. I mean if you take schools on csranking.org (at least the top 30) doing a linear regression of the rank against the number of faculty results in a extremely good fit. But I'm not sure why people would be surprised about this given that you're basically limited to teaching at universities ranked lower than the one you graduated from, which should result in homogenization. Yet we still care deeply. Tracking professors sounds like a lot of work, with similarly high variance. I can see utility given that it can help show that you took an easy or a hard professor, but that might just also end up with similar metric hacking where a professor becomes hard rather than successful (because people are likely to measure via failure rate than a more intangible and stochastic long-term outcome based metric which would be coupled with every other educator the student had). It seems easier to just not care. You should get nearly as good outcomes while exerting several orders of magnitude fewer resources. I'm not against it, I just think it would be likely to be far more abused than the current shitty metrics we already use. I think we just at the end of the day need to embrace the stochastic nature of things, and if we don't incorporate that into our models then we're going to end up with bad outcomes. Causal inference is crazy fucking hard because there are far more confounding variables than people assert and more often than not there are elements which are not distinguishable. That many different paths can lead to the same outcome. I'm certainly not saying to give up or abandon metrics, but rather that shits hard and when we start forgetting that we make big mistakes.