Sports sponsorship, whether it's by Dave's Ice Cream Parlor or Nike, yields name recognition. Every time athletes wearing gear emblazoned with a logo, spectators, both in the arena and on TV, see it, which reinforces the ubiquity of that brand, which yields sales. For example, before 2010, every time Tiger Woods participated in a tournament, millions of spectators saw AT&T's logo emblazoned on his golf bag.
Recognition, however, has drawbacks. If the athlete or athletes sporting that logo become involved in some sort of scandal, the brand that sponsors them becomes associated with that scandal, which is why companies often cease sponsorship of athletes and teams associated with scandal. For example, after scandal erupted surrounding Tiger Woods, AT&T ended sponsorship of him to avoid their company and logo from being associated with his behavior.
By attaching their names to athletes, companies enjoy the benefit of recognition, whether local or international, at a relatively low cost. This recognition often yields high profits. The idea behind sports sponsorship is that when consumers think of, say, buying a pair of sneakers, the name that pops into their head is "Nike" or "Adidas" or whichever brand is advertised by their favorite athlete or team.
Sports sponsorship is also a risky financial investment. For example, BMW sponsors a sailboat team, which was in 2007 eliminated from the qualifying competition for America's Cup, meaning that it could not participate in either the qualifying competition or in the main competition. BMW lost an estimated $200 million because of the disqualification, according to German press reports. This risk is inherent. If the sponsored team or athlete is disqualified, does not participate, or is involved in scandal, then the sponsoring company can suffer financially. And the greater the investment, the greater the financial downfall if something does go wrong.