This may not be related to the mental game as much but read this. http://www.fi.edu/learn/brain/exercise.html I've heard that stimulating the brain cures depression. How this relates is that when a pitcher is facing a hard situation, he becomes stressed which affects his performance (obviously becoming stressed leads to depression, if it's not taken care of, obviously pitchers don't usually go through depression, but this is how it relates I guess). This is why having a positive mindset which stimulates the brain is important for a pitcher. It mentions this in the article. 

Imagine Increased Muscle Strength!-Experiment
In a fascinating experiment, researchers at the Cleveland Clinic Foundation discovered that a muscle can be strengthened just by thinking about exercising it. For 12 weeks (five minutes a day, five days per week) a team of 30 healthy young adults imagined either using the muscle of their little finger or of their elbow flexor. Dr. Vinoth Ranganathan and his team asked the participants to think as strongly as they could about moving the muscle being tested, to make the imaginary movement as real as they could. Compared to a control group – that did no imaginary exercises and showed no strength gains – the little-finger group increased their pinky muscle strength by 35%. The other group increased elbow strength by 13.4%. What's more, brain scans taken after the study showed greater and more focused activity in the prefrontal cortex than before. The researchers said strength gains were due to improvements in the brain's ability to signal muscle. Pay attention to your breathing. Is it slow and deep, or quick and shallow? Is your belly expanding and contracting, or is your chest doing all the work? 

This is why visualization is very important and critical for a pitcher X).