Sports and exercise are a big deal to Squeaky, who prides herself on being the fastest runner around. Early in the story, we learn that there is intense rivalry between her and Gretchen, who will attempt to beat Squeaky in the May Day races. Throughout the story, Squeaky is close with her brother, Raymond, and spends a lot of time taking care of him due to his mental disability.
The animosity between Gretchen and Squeaky seems to taper off after the big race, and Squeaky isn’t even sure who has won, partly because she has become so distracted by the idea of Raymond being a runner. The realization that winning isn’t everything melts away the animosity that she has felt towards Gretchen, and she exchanges a respectful smile with her former rival, while considering her as somebody who could potentially help her coach Raymond. The end of the animosity between Squeaky and Gretchen results in the two former rivals becoming closer.
While Squeaky has always been close to Raymond, the realization that he has potential as a runner makes his sister see him in a whole new light, and with new respect. She sees him as a potential runner with a talent of his own, and that, for Squeaky, is more important than whether or not she was successful in beating Gretchen. I would argue that sport brings Squeaky and Raymond closer by giving them common ground and giving Squeaky a new project to work on with Raymond.