Say it with me everyone: sign-and-trades ONLY HAPPEN when the player being signed WANTS to go where they are being traded. You can put together a million reasons why Memphis might want Nate, or why the Cs might want to move Nate, but until you put together an actual reason why Nate would want to play in Memphis, then you really don't have a leg to stand on.
In fact, Memphis tried to trade for Nate back in January. They actually had an offer that the Knicks would accept--but Nate had a no-trade clause and he wouldn't waive it to go to Memphis. Does anyone really think he's changed his mind since then?
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Nate is an asset and he will be resigned this summer. He will provide good depth behind Rondo and will represent a nice trading asset as we move forward, if we need to make an upgrade at some other position.
Sign-and-trades rarely bring back more value than they send out (the Grant Hill S&T to Orlando is the exception), and GMs usually only make them as a favor to a player (or agent), or because that player was going to leave anyway and the GM wanted to get a little value back in exchange for getting more $ for the player. But, as Baby showed last season, and as Nate will show this season, when there's some mutual interest between the player and team going forward AND there isn't another suitor willing to pay the player more, both sides will come to an agreement that benefits both parties.
This is about maximizing your assets. The Cs could try to work a sign-and-trade with Nate this summer, and maybe only get 60% value for him (unless they get lucky or find the perfect situation). Or they could sign him to a reasonable contract, coach him up, and possibly flip him down the road (to any team, not just one that Nate wants to go to) for something MORE VALUABLE than Nate.
Believe me, Danny knows this, which is why he ended up bringing Baby back last season. Ainge could have easily done the short-sighted thing and S&T'ed Baby to NJ for Yi (or other ballast from other teams)--instead he signed Baby to a smart contract and now he could probably move Baby TO ANY TEAM HE WANTS for much, much more than that this summer. And that's how you MAXIMIZE your assets in the NBA.