I think CDC recommends a 10-day quarantine from the time you're infected. Let's say the positive test came a day or two after exposure they might not be able to play in the tournament. However, if only one or two players or coaches are positive and the other players have four or five days of consistent negative tests they should be able play.
"All Tier 1 travel party participants will be required to undergo and document seven consecutive negative COVID-19 tests prior to arrival into Indianapolis. The NCAA will work with IU Health to provide health related support including the administration of daily PCR tests for Tier 1 individuals upon arrival and throughout the tournament. Tier 1 participants include student-athletes, coaches, athletic trainers, physical therapists, medical staff, equipment staff and officials.
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All Tier 1 participants will wear KINEXON contact tracing devices throughout the tournament, including practices and games. These devices, coupled with video analysis, provide data that allows total time measurement of those who are within 6 feet of a newly infected individual with COVID-19. The data will be utilized to assist with contact tracing and the need to quarantine participants. If close contact time with another individual who has tested positive for COVID-19 is less than 15 minutes over 24 hours, then quarantine may not be required.
COVID-19 testing and contact tracing will not be required for asymptomatic Tier 1 individuals who are at least two weeks post-infection and within 90 days of the first known date of infection, or participants who are at least two weeks post their second COVID-19 vaccine (or singular COVID-19 vaccine for FDA approved vaccines that require one dose only). These groups will still be required to wear masks and physically distance."