A mathematician unpacks the science of “bracketology”

March Madness is upon us yet again as the NCAA basketball tournament kicks off in earnest: 68 teams facing off in a series of matchups until only one champion is left standing. Millions of sports fans take part by creating their own bracket predictions. The challenge is that there are so many variables and potential outcomes, it's almost impossible to devise the perfect bracket, correctly calling the outcome of every matchup. Online advice abounds, from amateur enthusiasts to professional sports analysts at media giants.