I do not buy that any of the players coming in have a high BBIQ which consists of making the right play at the right time. Tim Duncan fits the definition as well as any player and currently, Al Horford certainly fits the bill. Admittedly, I haven't seen enough of Hayward to say much of anything, but Irving's defenses lapses have been pretty striking at times and it's pretty much a known of Tatum's game that he's a black hole on offense and raw on defense.
As for IT, Amir, Jae, and AB? IT has a pretty high basketball IQ from what I can see, but is limited defensively by his size. IT makes many good passes under intense pressure. Offensively, he’s outstanding, but it’s impossible to say he accomplishes his feats solely because of his ridiculous athleticism.
Amir is an advanced stats dream with amazing +/- stats throughout his career which generally indicates that he doesn't do dumb things and does many positive things not readily apparent to those who follow the ball with their eyes. Jae has decent +/- stats, but is nowhere in Amir's class. Certainly tough to make him out to be a high BBIQ guy though.
That leaves Avery, who cannot be one of the lowest BBIQ guys in the NBA. Too good a defender. On the other side of the ball, he definitely has issues, which I attribute to tunnel vision for a lack of a better term. The game speeds up when he has the ball in his hands, unlike high BBIQ guys where the game slow down. Avery is fine as a one or two dribble shooter, but in terms of creating a shot and dishing off if it's not there, he's brutal. Always was.
Nonetheless, that does not make him one of the lowest BBIQ players in the NBA. They cannot do anything right other than shoot the ball, if that. Think Gerald Green for his first stint through BOS, Michael Beasley, Kwame Brown, Michael Bennett, to name some famous ones. We've had a few like Fab Melo, the Brazilian center who has left this earth too early who didn’t know when to duck and Ricky Davis.