By being mentally ready on the field they’ll put themselves in a position to use all that training and find greater success.
Anyone who has seen a gladiator movie, or a movie with gladiators in it, is familiar with this scenario: Two warriors do battle until one bests the other. The victor stands over the fallen loser, weapon at the ready, and looks to the Emperor (or highest-ranking official in attendance). The Emperor holds out his hand with his thumb extended sideways, then either turns it up to spare the fallen warrior or down to indicate he should be killed.
Never mind that this is just a dramatic fiction of the movies. In reality, gladiators were too expensive to acquire and train to be wasted in such a manner. The idea of the thumbs-up/thumbs down creates a scenario to help fastpitch softball as well as baseball catchers.