I have found that being mindful of your breathing while you are playing (or practicing) can change how you phrase your ideas and how strong your sound is. It doesn't matter the instrument; saxophone, piano, voice, everything. We breath to prepare ourselves for what is to come. It is easy to play an idea not knowing when to stop. Rather than stop too early, the tendency is to play on and on, rather than putting some effort into creating clear statements that have shape. It is one of the many mental disciplines that are within our capacity. The breath is a powerful thing.