A coach doesn’t need to tell a player the math behind the analysis, just the end result.
I'm thinking of the scenario where the end result is counter-intuitive and fails the "eye test". On something as simple as allocation of playing time, will players trust in the coach if they don't really understand why his personnel rotations are they way they are (especially if they think they deserve more minutes), or do they need to understand the process of reaching those decisions to be able to accept them?
If Jared Sullinger begins the season as the starting power forward and midway through the season, Stevens determines that the team would be better off starting Olynyk and having Sullinger come off the bench, even though Olynyk doesn't appear to be statistically better, would Sullinger accept that or would he need to understand why that decision was made to feel comfortable with his new role?
There are some players in the league who would probably complain about losing his starting job because of some number-crunching nerd who doesn't know what it's like to be an NBA floor, when they might accept the demotion more readily from a coach with a stronger resume.
But I think that happens to every player on every team, regardless of the method the coaches uses to determine that, whether it's detailed statistical analysis or a hunch/gut-feeling/instinct or just a general observation. Just about every non-veteran thinks they should be playing more. Remember Gerald Green asking to be traded from Minnesota because he wasn't playing enough? You think that was Minnesota's advanced stats keeping him on the bench and Green disagreed with it or couldn’t understand it?
Usually every team but the top few experiment with dozens of different lineups and strategies. You experiment till you find something that works. The Hawks had 29 different starting lineups last year, the Mavs had 24, the Raptors had 22, the Bucks 20, etc. You think all those changes made sense to every player? Most of the league experiments and changes things up, this won’t be unique to Stevens.
In your Olynyk/Sullinger scenario, if Stevens is right, the team would win more games, how could anyone argue with that? Sully, we started 5-15 with you in the starting lineup, when we moved you to the bench we went 13-7. If he's wrong, he'd alter it again till he finds something that works. And there are a lot of good players that come off the bench while an inferior player starts: JR Smith, Jamal Crawford, Manu Ginobili, James Harden, etc. They seem to handle it okay.
I feel like you think Stevens is this guy who knows nothing about basketball and is just some math geek who doesn't understand the nuances of the game. He can coach basketball without stats, but he uses stats to tighten up or adjust things. His moves aren’t going to be that counter-intuitive, he's not going to play 4 centers or 3 point guards at once. It's not like Stevens is going to start and play Pressey, Crawford, Bogans, Iverson, and Melo 48 minutes a game, while sitting Rondo, Green, and Sullinger because his analysis tells him it's the best lineup because they have the highest rating based on a them playing together for 5 minutes at the end of a blowout.
It’s more like: Rondo's averaging 10 shot attempts per game, the analysis tells me we'd be better if he takes a couple more/less, let's run a couple more/fewer plays for him. The team performs best when we keep Green's minutes under 35 per game and Bogans and Olynk play at least 10mpg. I’ll cut Green down from 38mpg, and try bumping up Bogans and Olynyk from their 5mpg and 8mpg. And it’s not like he’s blind to anything outside of the stats: Green’s played his 35mpg, the stats tell me that's the best, I don’t care if it’s a triple overtime game, I can’t play Green anymore.
It's not Perk is shooting 60%, if he shoots every time, the team will shoot 60% and therefor win the game. Let's get Perk the ball!
This is not what Stevens does and it's not going to be any more counter-intuitive to NBA players than any other decision that cuts their minutes/shots.