With both Tatum and Brown, the big man needs to be mostly a spot up floor spacing big man. An uber talent like KP can do a bit more pick and rolls, but even KP had to adjust a fair amount to really make it work.
There aren't a lot of offenses you can run with 2 wings with the skill sets of Tatum and Brown, especially when they are both on the floor. Neither one has the ball handling or playmaker abilities of the other great wing duos in history (Lebron/Wade and MJ/Pippen). JT and JB really only work well in an offensive system similar to the one Boston runs. Now if you swapped one out for a similarly talented player that wasn't a wing, a lot more options would open up.
I don't think they need a spot up shooter next to the Jays. I think the Jays can make any type of center work with them. They have good versatility. More so than some other stars.
The Jays have a good track record with a variety of bigs. We have the high post facilitator in Horford to more of a spot-up shooter Horford towards the end. We have a versatile inside-outside scoring threat in Porzingis. We have rim runners in Queta and Kornet. We've had D Theis. We had Kanter who worked well on offense next to the Jays but couldn't play defense.
I have always liked having a passing big next to Tatum & Jaylen. We become too dribble-happy and perimeter orientated with them. Having a big inside the defense you can throw the ball to. Three ways to penetrate a defense - dribble behind them, pass it behind them, shoot and go for an offensive rebound. When we become too perimeter orientated it allows the opposition to put 5 defenders in between the ball and the rim. When you have a big man who can pass, you can move it inside to 17-20 feet, then the perimeter guys gotta turn their head because the ball has gone past them and is now inside the defense. Creates opportunities for off ball movement. Gets the defense off balance.
I have always liked having a good passing big because like you say the Jays are not top level ball-handlers / playmakers. Tatum is good. Jaylen is middling.
What we did differently in the 2024 season was having Jrue & D White together in the backcourt. That gave 2 more ball-handlers so now they had 4 dribble drive threats. With that extra driving capacity and passing quality from the guards, the passing of the big man was less important. We can re-create that but we have to replace Jrue.
If we don't re-create that dynamic and instead go back to a 1 guard 3 wings 1 big configuration, I like going back to involving the center more as a passer. Take some of the pressure of the Jays as ball-handlers / playmakers. Allow them to get it in more variety of situations instead of trying to create everything off the dribble from 25 feet against a set defense.
But ultimately, I believe just about any type of big man will work next to the Jays. It is just about talent in my eyes. Get the best talent center you can and the Jays will make it work.
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The players I am more worried about having specific types of centers are:
(1) The ball dominant heliocentric stars with strong playmaking ability like Luka or Harden who often love to have a rim runner next to them. Or Trae Young.
(2) Guys who are deficient shooters and hamper spacing and therefore need a center next to them who can shoot. Like Giannis.
The Jays I believe can work with anyone.