It is neither pure luck nor a mistake that gets an applicant with a 28 ACT or an equivalent 1250-1280 SAT Critical Reading and Math score into Harvard. You get into Harvard if they deem you, for whatever reason, as one of their most special or extraordinary applicants! Of course, Harvard must be convinced that you can hang academically with the special and extraordinary applicants they admit with high test scores. That’s why they look closely at teacher and school evaluations, the quality of your courses, and at your academic strengths and accomplishments. If all you can show is high test scores, you will not stand-out in Harvard College admissions. Please consider what the Harvard Admissions Office says about test scores:
“Harvard does not have clearly defined, required minimum scores; however, the majority of students admitted to the College represent a range of scores from roughly 600 to 800 on each section of the SAT Reasoning Test as well as on the SAT Subject Tests. We regard test results as helpful indicators of academic ability and achievement when considered thoughtfully among many other factors.”
Harvard College Admissions § Applying: Frequently Asked Questions 
