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argella42 comments on Request for advice: high school transferring - Less Wrong Discussion
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I went to the public middle school, which is the exact same group of kids, so I know a lot of students there and have talked to them about it. It genuinely is the exception to the rule that a public school can be almost as good as a private school (and better, when you throw in the commute and the snobbery involved with the private school). I went to school in a different district when I was younger and it was terrible, even though the school was considered really good, so I know exactly what you're talking about.
I don't know what you mean by "base rate", but people seem to do pretty well at both schools.
Here's a link to the base rate fallacy article on Wikipedia: https://en.wikipedia.org/wiki/Base_rate_fallacy.
A thing to avoid in your situation is focusing excessively on the specifics that lead you to conclude that the local public school will be as good as the private school you are attending. Generally speaking, public schools are lower quality than private schools. But getting a little more narrow might be worthwhile: How are the public schools in your general area compared to public schools in the country, using objective statistics on things like SAT rates? Now, can you compare that to your private school or your brand of private school (Catholic, secular, whatever)? Think about other metrics that matter for you: percent getting into Ivy League colleges, or number of assaults on campus per 100 students, or whatever.
Compare those rates before mentally inserting yourself into the situation. Once you mentally place yourself there, a lot of what you know about the statistics of the places can slip away. That is what the base rate fallacy teaches. It helps you focus on the idea that the median experience at each school is likely to be your experience, which helps defeat the "grass is greener on the other side of the fence.".