Gretchen and her brother Raymond help Squeaky realize that winning is not always important. 

Throughout most of the story, Squeaky pits herself against others, feeling that because they are seemingly antagonistic to her, she must defeat them by winning races. For instance, she distrusts Gretchen's and any other girl's smile, declaring,

"...girls never really smile at each other because they don't know how...."

In addition, she has fought with Rosie and finds her antagonistic when she tells Squeaky that she will not win the race, 

"I don’t think you’re going to win [the May Day race] this time....”

Squeaky is also very defensive of her brother and resents anything that others say to him if it is derogatory. When one of the girls asks Raymond, “What grade you in now, Raymond?” Squeaky quickly retorts, 

“You got anything to say to my brother, you say it to me, Mary Louise Williams of Raggedy Town, Baltimore.”

It is not until she enters the competition of the May Day Race that Squeaky undergoes a change. For, until this day Squeaky has felt that she must be a winner in order to be superior to the others lest they tease her brother and ridicule her. However, when she sees that Raymond can run quickly in his own inimitable manner, Squeaky realizes that Raymond has his own talent and she no longer has to defend him by proving her superiority; instead, she can help train him. Further, when she recognizes Gretchen's smile as genuine, as well as being praise for Squeaky's winning run, Squeaky understands that Gretchen is truly a friend, and not a rival.