My gut feeling is that it does have an impact; especially for pitchers. I tend to have a lot better outings when my SPs (in particular) start with a full bar. There are just so many moving parts with this game, it's impossible to truly suss out.
My angle is this. In real life, there is an impact. I role play as though the game portrays a similar impact. Whether it does or not....who knows? From my immersion perspective, I roll with it as though it does and make strategic decisions accordingly. If it truly does, great. If it doesn't...well, I'd honestly not rather know that and keep that illusion alive.

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