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A Pitcher's Stuff
A sphere of majesty, is the majesty someone has over a sphere, that sphere being a baseball, making this a pitcher's stuff, as in what he throws and how he throws it.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
As it gets closer baseball season in spring, that pitcher gets better at his pitches.