The irony of the father
Coach Sweet's father urges him to go join a war, which is ironic, considering the likelihood of martyrdom. A father should teach their son about sacrifice and pride in one's community, but this father is completely imbalanced. Instead of teaching his son to thrive and to trust his own intuition, he urges his son to go stand in line, to take orders, and potentially to die. Why? Because it will build character? Sweet's approach to leadership is the opposite of his father's example.
The irony of politics in the school
Coach Sweet decides that he personally feels he should not be political with the students, because he doesn't see his own political opinion as a thing to be shared with them. But ironically, that makes him one of a kind—most of the men he reports to in the district are openly Republican, and they are openly interested in helping children reach Republican conclusions about life's questions.
The irony of hippies
The use of the word hippie verges on slur usage when the school leadership warns Coach Sweet about his coaching style. They don't want him to encourage freedom in their points of view, nor openness to new experience. As grown men, they see the world in a specific way, and they want Coach Sweet to eliminate rebellion and freedom from the team. Coach Sweet doesn't see the kids as hippies of course; he sees them as baseball players, and he's confused when the conversations start.
The irony of the plate
Instead of thinking about competition with the other team, Coach Sweet encourages his players to approach the plate in a new way. By seeing the plate as a portal toward excellence and fun, he teaches them to engage the game of baseball in a way that makes them natural and consistent, instead of the other way, which is when life's daily emotional turmoil manifests itself in the mind of the player when they should be focusing. By coming to plate with peace, they are not desperate, and they perform better.
The irony of success
The novel has a delightful irony as its climax. The reader learns that one of the players was the real life Steve Shartzer, who goes on to be a real life baseball star. The irony of Coach Sweet's hard work is that someone else gets to be famous. His sacrifice is that he used his entire life of wisdom and hard work to enable a young person to become excellent and successful, while he stays behind to teach English under the sharp eye of conservative school administrators.
