Schwartz told Henry that the Westish Harpooners had been crappy for too many years to count, but with Henry's help they were going to turn it around. (2.24)
Mike's number one goal is for his baseball team to win. With this being his priority, we're surprised he wants to go to law school instead of being a coach. Baseball always seems to be his number one priority.
"Doesn't this drive you nuts? […] Sitting on the bench." (5.15, 5.17)
Henry is a player—not with women, but with baseball. He doesn't want to sit on the sidelines, he wants to be in the game… at least as long as he's perfect. Notice that, once his streak ends, Henry avoids the field at all costs.
"This is America. Winners win. Losers get booted." (5.61)
There's no irony here. Both Mike and Henry believe in their own way that it's either go big or go home. For Henry, it's more of a personal win. He doesn't care if the team wins or loses, as long as his big streak survives. Still, when Henry later finds himself unable to go big, he wants to go home.
"You think these guys care what our record is? Hell no. They think they're going to walk all over us, because we're from Westish College. They see this uniform and their eyes light up. They think this uniform's some kind of joke." (21.26)
For Mike, it isn't just a championship trophy at stake, it's his school's reputation. That raises the stakes a bit above your typical college baseball game.
The Harpooners' arms were bare. Schwartz insisted on it: a psychological advantage could be gained by pretending to be impervious to the weather. By pretending to be impervious, you became so. (28.19)
This is one of those "fake it 'til you make it" situations, except a person can never be impervious, so they better be prepared to keep up the fakeness for a long, long time.
"It doesn't feel like much," [Henry] said. "You really only notice it when you screw up." (29.53)
Some people screw up all the time and it's not a big deal (like your average clumsy Young Adult heroine falling over every 3 minutes). But Henry, at least in baseball, is statistically perfect. His errors stand out like big red letters on a yellow background.
Everything that happened between [Henry and Owen] between then and now could be forgotten. Today was big, big was good. The sun shone overheard. Fans in the stands. A chance to do some winning. (46.7)
Baseball isn't all training until you puke, and winning or wishing you were dead. There is a sense of companionship that comes with this kind of sports competition. Henry and Owen are able to put their (honestly, extremely minor) differences behind them and play on the same team.
The other teams wanted to win, and the other teams had more talent. The Harpooners had to feel, like he did, that they would die if they lost. (63.25)
Mike's coaching tactic seems to be "win at all costs." This is motivating up to a point, but with Henry it ends up being a double-edged sword. Henry becomes amazing, but one mistake makes him feel like a loser, and he can't get that big L off his forehead.
If the Harpooners lost they would blame [Henry], rightly blame him forever, for dragging himself halfway across the country to jinx them. (75.20)
Why do you think Henry gets weirdly superstitious near the end of the book? Is it because he wants to put the blame for his failures on something else entirely, or is it to take some pressure off himself?
Deep down, [Henry] thought, we all believe we're God. We secretly believe that the outcome of the game depends on us, even when we're only watching—on the way we breathe in, the way we breathe out, the T-shirt we wear, whether we close our eyes as the pitch leaves the pitcher's hand and heads toward Schwartz. (75.109)
Here, Henry explains his personal belief about why people are superstitious regarding sports. It's a control thing. This isn't surprising coming from Henry, a guy whose desire to keep everything the same could be read as a crazy control issue.