I was actually thinking about this last night. I know it would be an unpopular opinion, but I do think a lot of Gay minutes should come from Royce. Gay can obviously siphon minutes from Joe, Royce and Bojan, but I think the idea that he could take some Royce minutes probably isn't thought about much. I struggle with Royce not because of his pros/limitations, but because I believe that the dose is just too high, or that we're expecting/relying on him for things we shouldn't be. This has been a challenging discussion because it tends to be fairly polarized in terms of peoples' view on it. I think he's an important part of the team and rotation but I think we can correct the ways in which he's being overutilized. Overall his strengths are that he's an a-bit-above-average defender, he plays hard and makes hustle plays, and he hits open threes at a good clip. The fact that he's low usage has a lot of positive considering who he's playing with that, in some ways, makes him fit in reasonably in those situations. On the other hand, I believe there are some pretty important things to look at when we're comparing Gay vs. Royce in some of those minutes. Superficially, Gay would be considered a lesser three point shooter and less of a spacer. But Royce is only shooting when he's open (26.1% of shots are considered open or defender within 4-6 feet, and 63.2% of his shots are considered wide open at 6+ feet from the next defender -- 89.3% of all his shots are either open or wide open). This is looking at last year but...
Wide open threes:
Royce 39.8% and 63.2% of his threes were wide open.
Gay 39.1% and 17.5% of his threes were wide open.
Open threes:
Royce 26.1% and 5.8% of his threes were open.
Gay 39% and 21.7% of his threes were open.
The bottom line is that Royce is left wide open for threes, and those are generally the ones he takes. That's neither good nor bad in a vacuum as the defense is having to pick their poison on leaving Royce open to hit a high percentage shot or give attention elsewhere on the floor. But would our view of Gay be skewed because we look at his total percentage? What would it look like if Gay is surrounded by the same guys Royce is surrounded by and he's getting those wide open looks? More specifically, the answer is probably that Gay draws a bit more defensive attention and doesn't get as many open and wide open threes. So what that translates to is that Royce is getting open and wide open shots because the defense is crammed elsewhere. Royce shoots a higher percentage so we view him more as a spacer, but in reality he's not spacing things the way we think because he's getting those open looks. He's the opposite end of it where he's capitalizing on the space created from others (but facilitated by sagging off of him). In theory Gay would draw more attention and probably get up less open and wide open threes because the defense has to be a bit more honest, and the trade off is that the floor opens (and actually spaces) for others. Not to mention that Gay has a lot more tools to punish the defense, even while having lower usage in those lineups. Though Royce always tends to shoot a good percentage in the amalgam, there are times where the moment is big and he becomes a reluctant shooter or the nerves get the best of him.
Now pivoting to the defensive end, what does that look like? This is one area I believe people would get squeamish. We've always defaulted Royce as the man-to-man defender, even when there are numerous scenarios when that doesn't matter or becomes irrelevant (smaller quick guards, lengthy wings). Royce struggles to stay in front of anyone. Royce is good to great at a lot of things, but it's fair to say he struggles with his lateral quickness staying in front of guys (this is true of everyone else, too, but we can't ignore it here because we're having to justify his presence based on defensive acumen). Gay will be a longer defender. I don't know what his lateral quickness will look like this year, but he should be a guy who's a good team defender and can make the right rotations. He's a good secondary rim defender and rebounder when Rudy goes out to challenge (and that's one of the biggest holes in our defensive strategy right behind guys on the perimeter not staying in front of their man). If Rudy goes out to contest, the lane is open for lobs or offensive rebounds and we consistently get killed in these situations. Gay does give true size at the 4. My belief is that the biggest barriers we may have to face in a potential drop off from Royce to Gay may be our psychological perception of it. There may actually be enough other positives that would tilt the scale in Gay's favor.
tl;dr I believe that Gay may bring a number of things to the table offensively in a lower-usage role in the main unit that we may be neglecting and I believe he brings unique abilities on the defensive end when we're comparing it against those same units but with Royce. This isn't about Gay vs. Royce. Both guys can get theirs. The question and assumption is already out there about Gay possibly closing some games in place of Bojan, depending on the situation. But I don't think that discussion has been had in relation to the same idea with Royce, and I believe having that discussion would make many psychologically uneasy, but I do believe there are a few minutes to spare there where Gay is inserted into the Royce role with reasonably good success, and it should be explored without having to drastically change anyone's identities.