However, the calculation gets complicated. In part, that's because the amount a business makes on a single ticket — $250 in the video's example — is far less than the penalty they pay for bumping someone from their flight. Bumping someone from their flight often involves a refund, food, rebooking, or a hotel room.
Airlines create a binomial distribution that calculates the probability of different numbers of people arriving for their tickets. The airline uses that to help determine not just how much money the airline can make or lose on a given flight and number of passengers, but how likely different scenarios are.
Watch the video above from TED-Ed and Nina Klietsch to get a better understanding of why and how airlines come to these policies. You'll learn something and by the end of the video you'll remember that you're just a number in this game and that it still pisses you off when they ask how you feel about delaying your vacation a day or two.