I think this is the most insightful reply to the original post. Indeed, thinking about "numbers of students teached" is a really crappy metric for the performance of a teacher; it's far better, for example, to use something like (average increase in standardized test scores per student) * (number of students) / (hours taught) or somethng similar (assuming we do believe in standardized tests), the only problem with this metric being how you evaluate which teacher is responsible for which proportion of the increase in test scores, but this can be solved with proper randomization.
The idea behind this is that one should consider that a bad teacher is far more likely to fail his students (as lon as he doesn't control the exams), while a good teacher will send his students to the best univerisities/high schools/jobs availiable.
The idea behind this is that one should consider that a bad teacher is far more likely to fail his students (as lon as he doesn't control the exams), while a good teacher will send his students to the best univerisities/high schools/jobs availiable.