In its brief, Harvard said that if it eliminated all consideration of race and other preferences, the African-American share of the class would decline to 5 percent from 14 percent and the Hispanic share would decline to 9 percent from 14 percent.

The plaintiffs say that Harvard could achieve levels of racial diversity close to what it has now if it were to eliminate preferences for the children of alumni, donors and staff, while allowing for a slight fall in SAT scores and a significant drop in the percentage of wealthy students.

Is statistical evidence enough?

The plaintiffs argue that statistical analysis shows that Asian-Americans as a group have better academic and extracurricular credentials than white applicants, but are penalized by a biased personal rating.

Harvard disputes the evidence offered by the plaintiffs but says that even if it were valid, it would not be enough to show that any disparate impact on Asian-Americans was intentional.

“Even though courts have recognized that statistical evidence generally cannot prove discriminatory intent, S.F.F.A. has repeatedly conceded that statistical evidence is the core of its intentional discrimination claim,” Harvard’s brief says, referring to the organization that filed the suit.

Where is the smoking gun?

Harvard says there is no evidence that the admissions committee — with about 40 members of diverse backgrounds — engaged in some kind of conspiracy to discriminate against Asian-Americans.

The plaintiffs say that in this day and age, discrimination is often subtle and insidious, and people know better than to leave proof of it behind.