Integrity
Integrity is the unspoken premise of this novel, because Coach Sweet has integrity, which causes him to scrutinize those around him, because of how unlikely his experience of integrity really is. For instance, he specifically avoids pushing any agenda on the children, which shows his integrity for his role, even when the leadership at the school seems purposefully trying to create little Republicans out of the school. He teaches his team to play with integrity.
Hard work for the right reasons
Coach Sweet's point of view is not the most active. Instead, he prefers neutrality. Instead of actively participating in a war by going to the army the way his father urged him to, he decides to try and find something more rewarding. In his coaching, he teaches his players to get their heads on straight: If they think of baseball as an obligation, they will never thrive. He urges them to execute with discipline, but not for wrong emotional reasons. He teaches them to play because they want to.
Political independence
What does political opinion have with baseball? Well, the school administration feels there is a specific connection: A coach in any competitive endeavor will be instilling impressionable young people will ideas that will guide their opinions about competition for their whole lives. So, if Coach Sweet teaches them to be politically independent by divorcing themselves from competition, that poses a threat, leading to the counter-plot of this novel. Coach Sweet becomes a rebel in the eyes of the staunchly Republican community around him.