In court papers that Florida State University fought to keep confidential, the former director of the school’s Victim Advocate Office testified that in 2014, a total of 113 students reported being sexually battered, which is the same as rape in Florida. But the college reported only 14 cases to the federal government, records show.

The former official, Melissa Ashton, who ran the advocate office in 2014, also testified that in the nine years she worked in that office, an estimated 40 football players had been accused of either sexual assault or “intimate partner” violence, and that to the best of her recollection, only one person had been found responsible. She said most of the women chose not to pursue the cases “based on fear.” No names were mentioned.

Ms. Ashton said the number of sexual battery cases was so much higher than the total that university reported because most of the encounters occurred off campus, and the federal Clery Act, which requires colleges to report sexual misconduct cases as part of its overall crime statistics, did not require that those off-campus cases be included.

“I think we could do a better job,” she said.

In a statement, Florida State said, “We have no way to confirm or deny Ms. Ashton’s claims, given that her communications with such victims are confidential.”