If you just look at cost of the program v. ticket sales, then yes, they lose money. However, most schools feel there is a huge value for the sports. Most athletes do not have a full scholarship, or even half, so the school is attracting tuition paying students. Many non-athletes wouldn’t attend a school without sports. The athletic department takes the budget ‘hit’ for athletic and work out facilities all students use like the pools and gyms, but if the school doesn’t have athletics they still often have a gym, pool, athletic fields.
Often the athletic facilities are money makers for school too. Personally, I’ve written a lot of checks to U of Denver as my kids have gone to day camp, sports camps, played on their youth teams, had birthday parties, gone to free (ha, ‘free’) skate, taken hockey and skating lessons, gymnastic lessons. We’ve been to many games and matches and paid to park on campus. They rent out their fields to local youth groups, their gym for high school graduations, concerts and robotics competitions. The public can buy a membership to the work out center, pool, or ice rinks.
Even my kids’ first high school made money off the athletic facilities. They had a $40 MILLION athletic center, and it was run as a business. There were baseball fields, soccer fields and a $10M pool that were rented out about 15 hours per day. You’d drive by and the lights would be on Sunday nights, there were 3-4 groups that used the pool for swim team, they even had a driving and putting set up for golf.