Something I did as I did when younger that annoyed more ambitious friends: go to Wikipedia and find the incoming freshman class size for the top schools (say Harvard, Yale, Princeton, Stanford, MIT). Add them together. Now look up the number of high schools in the US and assume there’s 1 valedictorian per school. There just aren’t enough spots to even fit them.
Now complicate things more: all the elite high schools like Groton or something are gonna be sending way more than their top 1 student to these programs.
My conclusion was that it frankly doesn’t matter how much you compete with your personal classmates unless you have some other angle.
However outcompeting your classmates might get you a full scholarship to the state flagship, which is actually massive if you don’t use it completely imprudently.
Now complicate things more: all the elite high schools like Groton or something are gonna be sending way more than their top 1 student to these programs.
My conclusion was that it frankly doesn’t matter how much you compete with your personal classmates unless you have some other angle.
However outcompeting your classmates might get you a full scholarship to the state flagship, which is actually massive if you don’t use it completely imprudently.