@lander01 you should also consider that a large majority of kids who go to elite boarding schools like Andover or Exeter (non-elite boarding schools can be worse than public school, but that’s a different story) have parents who are alumni or very wealthy (and therefore big donors to the school).
So, once you take out the kids of big donors, alumni, and the athletic recruits, the matriculation stats to top colleges actually slim down to something very similar to that of a competitive public high school.
Also, considering that these elite boarding schools cost similarly or even more than college, are you sure your family can afford 4 years of BS AND College? Something to discuss with your parents, surely.
To be very blunt, your “dream” college right now is very unlikely to be your dream college in the future. Do you know what you want to study? Because that will have an effect on your “dream college.” Most kids in their second year of college haven’t even totally figured that out yet. Heck, a lot of people even change careers in grad school.
Want to study math? Calculus class in High school might make or break you. Biology? you might come to hate working in a lab after doing so in high school. These are just examples.
If you want to study liberal arts or the humanities (languages, history, etc.), a liberal arts college might be better than Stanford.
High school is a time to explore your interests, and dive deeply into what you like to do. As a middle school student you still have little idea of what great changes your high school experience may bring you.
For example, I thought about going to a boarding school while in middle school, and thought that it would be beneficial for college admissions. At the end due to family issues I ended up at a competitive high school in an upper-middle class neighborhood, and I absolutely love my experience here (im a rising senior).
By the end of high school, your world view will probably radically change.
Also, if you are more STEM-oriented, an elite boarding school might not serve your interests well as they are more liberal-arts based (harkness method and all that). I’m involved with my school’s robotics team and I can tell you that the robotics teams from these elite BS are some of the weakest in the league.
Where you go to high school is not going to be significant ten, twenty years down the line. The college you go to might not even matter. There’s a saying: The college doesnt make the student; the student makes the college.
In conclusion, dont go to a BS if you just want higher chances of going to stanford, cause you’re not going to get it. Instead weigh what you value most, and which is a more comfortable environment for you, for the next four years. Also consider finances carefully with your family.
Good luck.