The constant reassurance Mihashi gets throughout the series that he is in fact a skilled pitcher and deserving of being up on the mound is this. Seeing his self-esteem build piece by piece throughout the series is one of the show and manga's major strengths.
The first meeting of Abe and Mihashi. After meeting the team and Abe, they want him to try throwing pitches. Mihashi sees the team standing around him expectantly and resigns himself to the fact that he'll throw once and they'll realize how bad he is. When he wills himself to throw, someone in the team mentions aloud that "it's so slow!" and Mihashi turns around to walk away. Then Abe calls his name and throws the ball back.
Even better: Once they've completed a short game of catch for the team, the stoic Abe runs up to Mihashi with stars in his eyes asking what pitches he can throw.
In episode three, Abe is frustrated with Mihashi and his lack of spirit and emotional strength in the eve of competing against his old school. Before the game, one of Mihashi's old team members finds him in the woods behind the field and threatens to break his arm before Abe intervenes. Mihashi breaks down and admits to his guilt for ruining his old team's games. Abe takes Mihashi's hand (thanks to the suggestion of Momoe) and tries to tell Mihashi that he's a good pitcher. When Mihashi doesn't budge in his thinking and breaks down more, Abe notices all the calluses on Mihashi's hands from practicing so hard and realizes that he sincerely wants to help Mihashi, breaking down himself.
Mihashi becomes worried that Abe will get injured, because without Abe as his catcher he'll "go back to being a useless pitcher." Abe immediately denies this claim, but when Mihashi keeps saying that he's only good with Abe, Abe realizes it's the first positive thing he's heard Mihashi say about himself, and promises that he won't get hurt for three years. This backfires tragically, but the fact that he'd promise something so absurd and mean it for Mihashi's sake is heartwarming enough.
The team unanimously deciding Hanai should be Captain. They don't argue over anything; they all just turn to him.