Found a great video from May of this year in which Don Bishop, Associate Vice President of Undergrad Enrollment, gave an hour talk on the admissions process. The first half an hour is talking about the admissions process in general, and what one should anticipate or consider in the application process to all schools. The second half an hour is Don talking about the process at Notre Dame, including specifically what ND is looking for, holistic admissions, admission stats, and answering specific questions from people in attendance.
If you are considering applying to ND, this is a treasure trove of information, straight from the horses mouth.
A couple of stats that I found interesting. They had 1500 applications from children of alumni, only 500 of those were admitted. Being a legacy is a plus, but it is certainly not a golden ticket.
Here are some admission stats that revolve around test scores. The percentages for scores at 30 or below on the ACT kind of surprised me that they were that high. Of course some of those could be legacies.
If you scored in the top 1% (1500+ on the SAT, 33-36 on the ACT) you had a 50% chance of getting accepted
1430 to 1490 on the SAT or 31-32 on the ACT had a 14% chance of getting accepted
1380-1420 on the SAT or 29-30 on the ACT had a 8% chance of getting accepted
1300-1370 on the SAT or 27-28 on the ACT had a 8% chance of getting accepted
below 1300 on the SAT or below 27 on the ACT had a 4% chance of getting accepted
Performance in the classroom is more important than test scores was mentioned several times.
Here is the link to the video on youtube