In Harper Lee's To Kill a Mockingbird, Jem is convinced that Atticus will win the case for two reasons. First, Atticus proves that Bob Ewell could well have beat Mayella up, as Scout observes at the end of Chapter Seventeen:
Jem seemed to have a quiet fit. He was pounding the balcony rail softly, and once he whispered, "We've got him."
I didn't think so: Atticus was trying to show, it seemed to me, that Mr. Ewell could have beaten up Mayella. That much I could follow. If her right eye was blacked and she was beaten mostly on the right side of the face, it would tend to show that a left-handed person did it.
Though Bob Ewell cannot read, he makes his mark with his left hand.
Scout is unsure as to Tom's innocent. Seeing how large a man he is from the back, she is certain Tom would have had the strength to harm Mayella, and Scout believes that Jem is premature in his summation of what Atticus has proved—he's "counting his chickens."
However, Jem's certainy seems greatly supported very soon after (the second reason)—when Scout sees that Tom has no use of his arm, as described at the start of Chapter Nineteen, she begins to understand that Tom was innocent:
Thomas Robinson reached around, ran his fingers under his left arm and lifted it. He guided his arm to the Bible and his rubber-like left hand sought contact with the black binding. As he raised his hand, the useless one slipped off the Bible and hit the clerk's table. He was trying again when Judge Taylor growled, "That'll do, Tom."
Injured when he was young, Tom has no use of his left arm; there was no way he could have beaten or held down Mayella. Jem is certain that Tom will be acquitted, but when he is not, Jem must come to understand that:
In the secret courts of men's hearts, Atticus had no case.