I'm not sure whether this is a case of people just pulling fragments out of an overall bigger point I made to say, "you're wrong," or if I was really unclear.
I'm talking about a situation in which the Saints tell him what they will give him if they can work out a trade for 31 (which they would have to in order to get him to sign the tender), but the Patriots won't give him the same. I wasn't talking about an offer sheet.
(nitpick: I think you mean #32, as the Falcons have #31)
Firstly, I was responding to what I thought was the main thrust of your scenario, rather than just taking something out of context. But thank you for clarifying.
If the Saints make an implicit offer - telling him "sign your QO, we've worked out a trade with BB, and once acquired we'd like you to offer you X, will you take X?" - then the whole thing is kinda Bayesian from the perspective of the Patriots. The Patriots would probably have discussions with Butler about whether they'd be willing to offer him X, and given the discounting necessary to account for sending #32 back, X would probably be a fair offer for all sides. But suppose they think otherwise; then what the Patriots have proposed to them is, they have Butler on $3.9/1 fully guaranteed, which is a below-market asset worth roughly $10M in net value, not to mention an excellent way to spend cap money and roster space. Regardless of what the Saints intend to do once they acquire him, the choice for BB is, "what is a fair value for that asset?", and he might well conclude that the answer is well above what he paid for Cooks (who while a good WR is probably not as good as Butler is a CB, at least in my opinion).
I don't see any reason why Belichick would look at that situation and decide the best way to proceed is to take a trade that doesn't fully value the asset he's giving up. You say he'd need to consider the possibility that Butler would hold out if Belichick refused a trade for something below Butler's market value as-signed. I think that a holdout would be extremely unlikely for a couple of reasons:
1) Every game he sits, he loses a game check worth a fully guaranteed pro-rated amount of that $3.91, roughly $250k. That is meaningful money to him.
2) While waiting for his UFA status certainly poses risk, he maintains the same upside because he's hitting the truly open market at the earliest possible age for him. Any dollars he'd have lost by not playing under the Saints' offer could easily be recouped by a decent year on the field in 2017 - and perhaps exceeded.
3) His value also goes up with the generally high rate of increase in the cap, and the sparse number of pro bowl level players who actually hit UFA, especially at a premium position such as CB.
4) Meanwhile, sitting might well turn off plenty of suitors who would otherwise bid up his value to that amount. He'd be cutting off his nose to spite his face. Nobody is going to believe that the problem in this relationship is the Patriots, given how they run their organization in general (or at least, that Belichick deserves a majority of the fault). Several teams might reasonably think they were getting a malcontent.
5) Generally, holdouts are trying to force a team to sign them long-term, rather than punish their current team for not trading them. From Emmitt Smith to Logan Mankins, that's been the desired (And often achieved) outcome of an established, star or near-star-level player holding out. The team who is initially pissed off from being held out on, ends up being the one happy, because they get the star back on a long term deal. Butler would be trying to have the team he's holding out on
remain pissed off, and just tactically that strikes me as a gambit less likely to work.
