Here's a speculative answer, Matt:
I've been reading "Thinking Fast and Slow" by Daniel Kahneman, and here's one of my takeaways so far: Modern psychology - as Popovich likely knows from the advanced psychological methods of the U.S. military - has identified dozens of heuristics that cloud and guide the judgment of experts and novices alike. These heuristics all exploit the tension between the intuitive and rational minds and thereby allow - to use the simplest examples - irrational methods of advertisement and rhetoric to pierce into the rational mind, even to the point of predictability. What's more, the heuristics may be based on absolutely nothing: When you are asked to make an estimate of a quantity and an experimenter puts a totally random number on the sheet of paper before your estimate, your estimate is going to be heavily weighted by this, again, totally random number. This is just one example of how the mind is led astray by diversions to the fickle intuition, both in the random ether-streams of words and numbers of the Internet and deliberate attempts to sow the mind with messages by advertisers and public figures. Complicating matters even further is that (according to Kahneman) this tension between the intuitive and rational is also central to the great power of the mind.
I speculate then that Popovich deliberately tries to navigate this reality of the mind, and so gravitates toward incredibly intelligent, driven, attentive role players like Matt Bonner, TJ Ford, and Kawhi Leonard and gives them simple expectations and tasks that they can focus on with every fiber of their being while on the floor. It's no coincidence that the Spurs' execution seems so crisp: Popovich makes a constant effort to ameliorate the diversions to the intuition and to highlight the strengths of the prepared player's intuition. Popovich has incorporated the power and the frailty of human intuition into his every decision as a leader and demanded in turn that his players do the same.
This is why (for example) Popovich will stress repetition and practice and patience: there are all sorts of perfectly valid short-term reasons why his players may fail to execute or fail to learn or fail to be attentive in a small sample. Popovich doesn't - can't - control these myriad short-term factors, and in fact it's his counterpart's job on the other team to create as many of these short-term problems as possible for the Spurs. So he ignores them to some extent, chooses his battles, makes his rotations when he sees something disturbing, and then goes back to the film room.
Crucially, Popovich recognizes that he himself is subject to the same forces, and that he's not just playing a game of rationality: while his performance as a coach must not be guided unaided by his own brilliant intuition, he is subject to the same flaws as a decision-maker. He recognizes that the lifers in the coaching profession (such as Larry Brown and Hubie Brown) - for all their intelligence and experience - have a fatal flaw: They will often stress most about the things they can't control, whether or not those things are actually the most germane to focus on in scouting and winning games. And this stress will guide their intuition and advice and decision-making, creating an irrational bias: Coaches would rather lose on the randomness of 3-point shots than of a long train of creative mistakes such as turnovers and other "easy stuff" such as missing foul shots and layups, even if the probability of winning is higher for a given team with the latter mistakes. This isn't because the coaches are wrong or misguided: It's just that they're coaches by calling and approach their duty with a solemn conviction that if their players listen and execute the coach's best-laid plans, their teams will either win or only botch games for want of talent or luck.
Popovich (I imagine) has no such faith, and while he regards various coaches as being elite (take his effusive praise for Rick Carlisle, for example), he will also acknowledge at every stage of the game that it's a players' league, and will credit Tim Duncan et al. with the vast majority of his own success, and when Popovich actually brings up his own role, it's usually to apologize to his team for failing to give them a good or clear enough gameplan in some sense. What's more, he effusively acknowledges the power of random chance in determining outcomes: While he'll give credit to a team that wins on good shooting, he won't put much stock in the victory (or loss) if the shooting was pretty demonstrably a fluke.
And so with this fundamental skepticism and self-effacing attitude, we have finally that Popovich has no mystical beliefs about his role or the power of his intuition as a coach, which is minimal: to tinker with lineups, to bring the very best players to the front of the rotation, and to find an offense and a system of roles that allows his players to maximize their strengths and minimize their weaknesses while allowing Popovich himself maximal flexibility to handle various game situations. That's the whole endgame: He uses games as practices for his players so that he can see what situations various players are most comfortable in, what tandems are most germane to winning, and how to approach his potential opponents in the playoffs.
And just as surely, Popovich uses these games as practices for himself, for his own intuition as a coach, because he realizes that his view of the game is as susceptible to the transient short-term stimuli of the moment as his most cherished theories of work and and basketball and effort. As much as any doubt he could ever cast towards his players, Popovich therefore has no problem casting the same amount on himself. After all, he is just a person that - like his players - is trying to maintain focus as a lot of people and things deliberately conspire to obscure this focus on the simple truths of a simple game.
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With this speculation established, we come to Matt Moore's question. As part of Popovich's belief in the long haul and the approach of gradually developing the intuition, we might also suppose that the coach (before every season) gets his staff together and considers a whole lot of possible game and pre-game situations - for example, down by 12 against an inferior team with 15 minutes left or facing a mid-level non-divisional West team on a back-to-back on the road. Then Popovich and his coaching staff - along presumably with an in-house statistician - build a reasonable model for how they should respond to a large proportion of game situations. Then, an hour before tip-off and the media session, Popovich defines the sample space of the game before him and then draws from the I Ching 10-15 times, with more draws for back-to-backs and injuries and near the end of the season. Then - guided by this psychological anchor - the coach uses his intuition and what he knows about the situation to make slight tweaks to the result of the drawing and calls this a game-plan, which he then explains to the media as condescendingly as possible as if it were the product of incredibly simple and obvious planning.
There are 64 separate hexagrams in the I Ching. For Popovich, that great historian - who even encourages his team to discuss the State of the Union in team meetings - the I Ching is an obvious, well-trodden device for introducing randomness, with none of the dull silvery novelty of the Twitterverse. By weighting the hexagrams by the various distributions established before the season (and re-weighting at a mid-season team meeting), Popovich manages to maintain in a powerful tension the placidity and focus of a rational mind and the relentless unpredictability of an unhinged, creative intuition.
• • •
Or maybe it's that Tim Duncan's 35 and Tony's been logging a lot of minutes recently and Pop wanted to give them a lighter load especially on a back-to-back against a Portland team that's historically especially dangerous at home so that when the Spurs come back from All-Star Weekend the Big Three and Tiago are mostly healthy and ready to dominate or slog through the stretch run.
Whatever, something like that. He probably knew what he was doing.