I think Beasley gets a bigger bump offensively from playing alongside S.Nash at the PF position than the SF position. No Haslem + J.Noah clogging the paint. More space for Beasley to attack from in one-on-one situations and off pick and rolls.
I also think your team in general gets a bigger bump offensively from Beasley playing the PF spot than the SF position. The spacing will be better in the halfcourt with the added shooting ability, there will be more movement and cutting without the ball and you'll be much more dangerous in transition.
Without that offensive boost from Beasley, I don't think you can justify him as a starter in this league.
His negative defensive contributions are just harmful. His value as an offensive player fails to make up for that. Too inefficient and difficult to play alongside. He needs to create that offensive boost to be a worthwhile starter.
Otherwise, your team would be better off with a Jared Dudley type ... even if your squad does have a lack of recognizable shot-creators. Just let Nash do his thing and have intelligent scrappy shooters around him who'll compete.
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I also think Beasley has more potential defensively at the PF position than at the SF position. He has the athleticism and quickness (relative to his position) to become a quality team defender there. I haven't seen that capacity from him at the SF position.