All indications are that you will do very well in a graduate program in Science. Your academic record shows that you have worked hard for many years, did well in a range of difficult classes, and acquired the research experience that is essential preparation for graduate studies in Science. Your personal statement was well-written and focused, your grades are excellent, your GRE scores are very high, and it is clear that your reference letter writers are impressed with your intellectual abilities, motivation, and maturity. You have clearly met or exceeded all of our criteria for acceptance to the graduate program in Science at Major Research University.
We regret that we cannot offer you admission to the Department of Science this year.
Why can't we accept you, and all other qualified applicants? We can't owing to factors that have nothing to do with the quality of an applicant's academic record. For example, we have to consider how many graduate students are interested in particular fields of Science relative to the number of faculty in those fields, the number of current advisees these faculty have, and their interest in (and funding level for) advising new grad students. As it turns out, you expressed interest in a field that had the highest number of applicants this year.
In addition, our budget is being slashed and we are no longer able to provide a guaranteed financial safety net for as many students as we used to, in the event that an adviser doesn't have sufficient funding to cover a student's graduate program in its entirety. We are therefore admitting fewer students overall than usual.
To some extent, it is random bad luck that you aren't getting an offer of admission and a few others, with similar excellent records, are. That may make you feel better, or worse, but we wanted you to know that the reason you aren't being offered admission has nothing to do with your academic qualifications.
We have no way of knowing if you were serious about wanting to join our Department or whether this letter is a disappointing blow to you, but either way, we hope you are soon able to launch an interesting and successful career in Science at another university. In fact, we hope that you will do so well that you will make us regret not accepting you into our graduate program.
The Admissions Committee
6 years ago