I have no idea what strategy works, nor do I know if anything leaked post-negotiation has any validity.
For instance, it's really easy to come out and say "we don't know why Tony left, our offer was just as good" but I personally have no idea. Now, if it was about attempted playing time, then it makes sense. But Doc makes it seems like it was about money.
Now, I could easily see the C's starting with a below market offer. That just makes sense. But i don't know if the initial offer was made in a "this is our best offer, nothing higher is possible" way, but they were secretly ready to match the Griz offer? Or if it was a "here's a deal you can sign right now, but tell us if you get a better offer so we can still work something out" kind of thing, I don't know...and i don't even know which works better.
However, we do know that something in the negotiations of Powe and TA upset each of them enough to apparently sign for the same money elsewhere. I could see it as one of three things:
1. Player: Yeah, it's the same money, but you guys should show me home-town respect. So even though it's the same, both are low-ball offers, so i'm going to switch teams simply because you disrespected me and should have valued me more.
2. Team: Oh, we have no idea why he left. We offered him the same amount of money, i guess they just wanted to move on (spinning it to appease fans who developed emotional attachments)
3a. Team: you are terrible you are only worth this much good luck finding a better offer.
Player: okay then I'm going to this other team for X amount.
Team: oh, okay, we'll give you that!
Player: No Way.
3b. Team: here is the most we can afford. Tough luck, there is no way we can go higher; we will not budge.
Player: Okay, i have a better offer with X. Goodbye
Team: Hey! We were bluffing! We had a better offer for you!
If pressed, I would guess it's mostly #1, possibly with a little of the others thrown in.
Regardless, I have to give Ainge the benefit of the doubt so far. The Posey deal was Awful Awful. He's been terrible and it's quite high money. Powe was a talented player, but he'd already had his injury when he became a free agent, so the negotiations were based on ability to come back and stay on the court, not actual talent. TA is mercurial at best, so I do legitimately wonder if the team was surprised that he just chose a new city for the same contract just because it's Tony. Clearly the Davis deal was handled right; he hit the RFA market, no one bit, and Ainge didn't bid against himself so they found a mutual contract that would work.
It's the mid-level contracts for bench players that kills teams; Ainge seems to know this and avoid them...with some luck. The Sheed contract could have been such a deal, but he voided 2 years of it. We'll see, but if Perk extends for more than 7 million per year and Davis for more than an average of 5 per year, they'll become those clogging contracts, I bet. We'll see what happens there.