Consider college football programs, for instance. The best high school players generally want to play for the top programs, such as Alabama, LSU, Texas, Ohio State, USC, and Notre Dame ("2013 Team Rankings"), which makes it easier for them to recruit and get more of the best players, which is why they tend to remain top programs. This is true even if they don't have great coaching. Because of the talent they attract, the win in spite of themselves. Their status, in other words, helps them reproduce their own success.
A similar process occurs in most industries. Take the venture capital (VC) industry, for instance. Most entrepreneurs hope to receive funding from top VC firms, such as Kleiner Perkins and Sequoia Capital, not just because these VC firms are seen as being more "wise," but also because their ties with the top lawyers, accountants, and investment bankers raise the probability the entrepreneurial companies will succeed. What this means for VC firms is that the top (i.e., the high status) VC firms will have their "pick" of the entrepreneurial company litter, while lower status VC firms will not. Moreover, top VC firms will generally be able to command better terms with their investments, such as getting a larger stake in the start-up's equity (Note: VCs don't make loans; they invest in companies hoping they'll cash in on their investment if and when the company goes public or is acquired by another firm). In other words, if you have two VC firms, X and Y, with X being a high status firm and Y being a low status one, if both invest $1 million dollars in entrepreneurial company Z, all else being equal, X will get a greater share of the company Z's equity than will Y.
What does this have to do with high schools? Well, imagine two high schools, School A and School B. Available teachers have been randomly assigned to both schools so that the overall quality of teaching at both schools will be the same. The schools differ, however, in that most of the best students attend School A and most of the worst students attend School B. So, which school do you think will score better in various standardized tests? Which school do you think will enjoy a higher graduating rate? Which school do you think will send more students to college? School A, of course. But note that it will score higher, have a higher graduation rate, and send more students to college, not because of its teaching, but because it attracts more of the best students.
Now consider a slightly different scenario. Imagine the same two schools, but this time let's say that their average performance on standardized scores is a combination of innate student ability and teaching quality. More precisely, imagine that on their own (i.e., without teaching) students can score between 0 and 50 (out of 100) and that teaching can raise their scores from 0 to 50 points. So, for instance, a student with an innate ability of 50 who receives the best possible teaching (50) will score 100 out of 100, and a student with no innate ability who receives the worst possible teaching will score of 0. Now, imagine that the average student ability at School A is 45, while the average student ability at School B is 30. This means that in order for School B to score as high (or higher) than School A, the quality of teaching at School B has to 15 points better than School A. Put differently, School B could have the best teachers in the state (i.e., 50), but that will only raise the school's average standardized score to 80, while School A could have teachers who are 20% worse (i.e., 40), but their school's average standardized score will still be higher (85) than B's.
Granted, these two examples are stylized, but they illustrate an important point. School performance is not necessarily an indicator of teacher quality. To be sure, at one time School A may have had some of the best teachers in the district, and that's why it initially attracted better students, but that doesn't mean that it still has the best teachers. Unfortunately, a lot of parents interpret scores and graduation rates in just that way, and consequently (if they possess the requisite resources) they send their kids to schools they think are better but actually might not be. In Silicon Valley, the divide between School A and School B type schools tends to lie between private and public schools, and among public schools, between those in wealthier and poorer neighborhoods. I suspect, however, that if parents paid less attention to test scores and more to teacher quality, they'd realized that their local public high school is probably better than they initially thought it was.
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