I've interviewed and worked with many people, MANY!, including e.g., Stanford MS CS graduates, who can't write real-world apps. I assume these people can score well on an algebra test. As far as I know, the ability to write non-trivial programs in a commercially relevant time frame can only be judged based on a candidate having already done so. If there's otherwise some way to predict who these people are, I'd love to know what it is.

Social factors in a workplace also seem to be important and hard to predict. Excellent work for one employer isn't necessarily reproducible for another.