This is something that Mrs. Olinski, the paraplegic teacher who teaches and selects the Souls, the four children who form her academic bowl team, is never really able to understand herself. However, as her team become more and more successful it becomes more and more important to have a number of good, acceptable responses up her sleeve to be able to explain her selection, even when those answers aren't necessarily the truth. Note how the novel begins by focusing on this:
Mrs. Eva Marie Olinski always gave good answers. Whenever she was asked hwo she had selected her team for the Academic Bowl, she chose one of several good answers. Most often she said that the four members of her team had skills that balanced one another. That was reasonable. Sometimes she said that she kenew her team would practice. That was accurate.
However neither of these answers, nor the other answers that she variously gives, such as wanting an ethnically diverse team, is the truth, and these various answers seem to highlight the intuition or the hunch that went in to her selection of the team that managed to triumph so spectacularly.