In 2010, Kim Clijsters won the U.S. Open, but had her world ranking drop from #3 to #5 by the Women's Tennis Assocation (WTA). How can a tennis player win a tournament but drop in the rankings? The WTA uses a moving window to determine the rankings. We explain how discounting older results in the window can prevent such counterintuitive behavior and consider geometric and arithmetic discounting methods. We examine real data from the WTA, and comment on discounting methods already in use by the Federation Internationale de Football Association (FIFA) for ranking national teams for the World Cup and by the Professional Golf Association for ranking golfers. This talk is based on joint work with Alex Webb (undergraduate at Macalaster College) and Jennifer Wilson (Eugene Lang College, New School University).