As evidenced by threads in Town Square, there are many different ideas and perspectives around both of these.
There is a straight forward, business-like view of teacher performance that is generally overlooked. According to this view, a teacher's performance can only be properly seen when understanding three aspects to their work. First, and the most often considered, is the work output - usually thought of as the ability of students to demonstrate their competence. Normally, tests provide a proxy for this result.
Second, the input, or raw material that the teacher starts with. This includes the abilities, talents, inclinations, work habits, previous education, home life, health, and other aspects of the relevant students that impact their ability to gain and demonstrate competence.
The third aspect is the resources leveraged by the teacher during teaching. Some of these resources are practically unlimited or are renewable; others are more scarce. A teacher that requires significant use of scarce resources is not performing as well as one who does not. For example, expert parent time for any given subject is a scarce resource for our population overall; access to specific material on the internet is essentially unlimited.
There's plenty to be said about all three of these, but this posting is about output.
Some teachers look at the performance of their top students as demonstrating the quality of their output. A student winner of a national award, if taught by the teacher, gives the teacher prestige and proves that the teacher really knows the advanced material and can teach it.
But if you graph teacher output for all students, you see a broader view of the teacher's output. Consider a student performance graph with the students on the x-axis, ordered by performance best to worst. This graph is a descending curve. The teachers with the graphs starting with the highest performance are often considered the highest quality teachers. But even ignoring the teachers' inputs and resource use, I would argue that the area under the curve represents the best measure of teacher output.
It's how the whole set of students performs that matters, not just how well the very best students perform.