The interplay between math and team personnel is part of what makes basketball interesting. Math can give you answers that are correct in absolute terms, but the construction of a team plays a role in dictating whether a specific roster can execute those mathematically optimal plans.

Math is winning out on offense in the NBA. Three-pointers and shots at the rim are good, and midrange shots are bad. You can’t get the ideal distribution of shot attempts every night, since some defenses are very good at forcing teams into “bad” shots within the confines of the shot clock. Not every roster will have enough players who are actually skilled at the best shots, especially 3-pointers, to chase the math as aggressively as other teams. But over a large sample size, almost any semitraditional group of 15 NBA players would come out ahead on offense by rejiggering its shot selection to match the math. There are still some unknowns, especially in regard to offensive rebounding, but smart teams have basically solved NBA offense.

The deeper mysteries involve defense, where we are still in the early stages of understanding how doing one thing impacts a team’s ability to take away something else — and how all the strategic stuff interacts with a team’s roster makeup. Forcing opponents into missing lots of shots is obviously a good thing. So is coaxing an opponent into taking lots of shots from the dead midrange zone; studies have shown that just limiting the number of corner 3-point attempts correlates more strongly with overall defensive ratings than a lot of traditional measures. The same is true of shots in the restricted area.

But the “how” of forcing empty trips is where things get fun, and two teams make for especially interesting case studies this season: Minnesota and Portland. Rick Adelman drew some laughs a couple of weeks ago, after another frustrating Minny loss, when he declared, “It almost takes an act of Congress for us to go out and foul somebody. You have to get after people in this league.”

That’s interesting: a coach calling for more fouls. Aren’t fouls an objectively bad thing? There are exceptions, of course — fouling a terrible free throw shooter, or breaking up a sure fast-break dunk with a hard foul. But it would seem strange for a coach to call for his team to foul more.

Minnesota, it turns out, is the league’s most foul-averse team, and it is on pace to be one of the half-dozen most foul-averse teams in NBA history, per Basketball-Reference and NBA.com. The Wolves allow the fewest free throws per opponent field goal attempt in the league, just ahead of the Spurs — the most consistently foul-averse team of the last decade. As a rule of thumb, it’s safe to assume whatever the Spurs are doing is smart. But the Wolves are like the Spurs in this one respect, and Adelman appears to wish at some level they were a bit different.

The Blazers over the summer reconstructed their base defense to play a more conservative style, aimed at forcing as many midrange jumpers as possible. Their big men mostly sag back against pick-and-rolls, and they stick very close to opposing shooters dotting the perimeter. Some teams have those defenders along the arc dart into the paint to provide help, or at least the threatening impression of help, but Portland’s guys stay close to home.

It’s working! Only four teams allow more midrange jumpers than Portland, and nobody, not even the Bulls, allows fewer corner 3-point attempts per game, according to NBA.com. Rejoice, hipster doughnut-eaters of the world!

But wait … the Blazers, despite this fairly healthy shot distribution profile, are not very good at defense. They’re tied for 20th in points allowed per possession. They can pile up all the wins in the world, but they’re not sniffing a championship with a bottom-10 defense. There are a few things behind the struggle, but here’s a big one: The Blazers almost never force turnovers. They simply don’t do the sorts of things that produce turnovers — aggressive help in the passing lanes, frenzied traps, packing the paint to force risky inside-out passes around the horn. Portland has forced turnovers on just 11 percent of opponent possessions, per Basketball-Reference. That would be the third-lowest turnover rate in the history of the league.

Conservatism can be healthy for an NBA defense. Coaches preach it all the time: Stay home, don’t gamble, don’t reach yourself into a foul. Let’s force them into a long jumper, clean the rebound, and move on with life. If they make it, they make it. What can we do?

The Blazers and Wolves raise an interesting question: At what point does playing it safe on defense turn into a liability? And the ways in which the two teams are playing it safe are very clearly related: Searching out turnovers can lead to an increase in fouls, since pursuing steals involves reaching, lunging, and all sorts of mean-spirited behavior that can end with one large human colliding into another. This is why Jeff Hornacek wasn’t all that broken up about Phoenix’s high foul rate when I asked him about it a few weeks ago. The Suns want to pressure teams, force some turnovers, and get out on the break. Play like that, and fouls will happen. “We play aggressive, tough defense,” Hornacek says. “We get after guys. We’re just playing really hard, and sometimes when you do that, you commit more fouls.”

The Wolves, interestingly, have managed to both force turnovers and avoid fouling, yet Adelman is still angry. Only four teams have forced more turnovers per possession than Minnesota, even though the Wolves play a conservative base system very similar to what Terry Stotts plays in Portland. The difference may come down to simple personnel: Ricky Rubio is a steals artist, and Corey Brewer has the guts and long arms to do crazy stuff Portland’s blander guys won’t risk. The Wolves are 11th overall in points allowed per possession — not great, but hardly enough to warrant much hand-wringing.

But Adelman wants some freaking fouls because Minnesota can’t stop anyone at the basket. Teams are shooting 66 percent against Minny in the restricted area, the worst mark for any defense, and both Kevin Love and Nikola Pekovic rank as awful rim protectors, per SportVU tracking data. Maybe this is when fouls start to have a positive value — when the alternative is a consistently easy path to the rim. Start knocking people around, and opponents will suddenly start shooting more free throws. But they’ll miss some of those free throws, negating an otherwise easy two points, and there is probably some difficult-to-quantify intimidation value in being known as a hard-hitting team. A lot of people around the league also suspect the officials might allow such a team more leeway once it gains a reputation as a respected, rugged defense.

Perhaps the Wolves are foul-averse because Pekovic and Love understand their central importance to the team. Minnesota has been awful with Love on the bench, and their backups have been unreliable for most of the season. Stotts has told me the Blazers allowed a ton of easy shots at the rim last season in part because LaMarcus Aldridge, aware of Portland’s historically terrible bench, was afraid to foul himself out of playing time. Stotts wanted Portland to foul more this season. “Not fouling can be a double-edged sword,” he told me over the summer. “Of course, you’d hope to play defense without fouling. San Antonio is an example of that. But other teams have defended well and had a top foul rate. I don’t think there is a perfect solution. But with more depth this season, we should have more willingness to take a foul and contest a shot.”

Portland still isn’t fouling very often. It has allowed a hair fewer than one made opponent foul shot for every attempted field-goal, the ninth-lowest such mark in the league. The Blazers are on pace to be only the 20th team to allow such a low free throw/field goal attempt ratio and force turnovers on fewer than 12.5 percent of opposing possessions. In other words: They might be the most “conservative” defensive team ever.

Take a look at those 20 teams. Some of them were really good, some awful. It’s hard to spot any universal truths going through that list. But I’ll try. The strong teams among this group featured one of the these two things, and generally only one:

A Great Offense

Not just a top-five offense, or a top-two offense in a down year for offenses. An all-time great offense. The list includes two of Mike D’Antoni’s peak Phoenix teams, which redefined the NBA and posted some of the greatest single-season scoring marks ever. The 1991-92 Cavs, one of the all-time great forgotten NBA offenses, are also on there. A conservative defensive system without much defensive talent will generally have a pretty low ceiling. If you’re gonna play that way and win, scoring the ball like hell is borderline essential — and particularly within the half-court, or after opponent misses, since such conservative teams won’t force many live-ball turnovers.

The Blazers, so far, fall into this category, with an offense that at its peak has rivaled those D’Antoni-era Phoenix teams. It may be that the Blazers simply don’t have enough good defensive players to get much better on that end as currently constituted. They’ve actually held opponents to a low shooting percentage in the restricted area, but they’re allowing a ton of close shots from that range — second-most in the league, behind only the porous Lakers. I’m not sure what Stotts’s next move is here, other than to keep the system intact and hope the players get better at it.

An Elite Rim Protector

This makes intuitive sense: If you’re going to allow a ton of shots without fouling or forcing turnovers, you’d better be able to challenge those shots — especially the ones near the basket. It helps if you have a big man scary enough to deter people from approaching the rim in the first place.

If your team has such a player, its perimeter defenders would be dumb to even risk fouling as an offensive player drives the ball from the 3-point arc toward the basket. Why bail that guy out when he’s heading toward Hibbert Mountain?

Sure enough, the list of good ultraconservative teams includes teams featuring peak Tim Duncan and Yao Ming. Broaden the criteria just a tad — by mere fractions of percentage points — and more Duncan/Yao teams pop up, along with the very best Dwight Howard–era Orlando teams. Adelman’s defenses in Houston may have been the best in the league over a three-year semi-healthy Yao stretch, and they all played the same way — low turnovers, low fouls, and a “passive” pick-and-roll defense in which Yao dropped back toward the rim and the Rockets’ perimeter defenders funneled ball handlers toward either Yao or the sidelines.

Adelman doesn’t have a rim protector anymore, which is why he might want to see one of his big men knock the heck out of somebody at some point. Almost everyone I’ve talked to in the league believes fouling too much, above some unknown threshold probably a bit higher than league average, is a universally bad thing. The days of the 1990s-era Knicks are over. Teams that play that way would suffer too much foul trouble, allow opponents to live in the bonus, and forgo healthy transition chances.

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For some teams, an uptick in fouling might be healthy. “The thing you’re striving for is to foul the appropriate amount,” says Jeff Van Gundy. “And that depends on each team’s individual situation. It’s a fine line you walk. There are trade-offs with everything.”

Other coaches around the league cite Adelman, D’Antoni, and Popovich in popularizing the low-risk/low-fouls paradigm, and several coaches, including Mike Brown (a Pop disciple) and Stan Van Gundy (as sharp a coaching mind as exists) incorporated those same principles.

The league’s overall turnover rate is on a general long-term decline, though not a particularly huge or continuous one. The number of free throws has dropped more severely, and league higher-ups have kicked around several possible causes — the increase in the number of 3-point attempts (which rarely draw fouls), more zone and zone-style defenses, the rise of “verticality,” and stricter rules about what should and should not constitute a shooting foul.

The decrease in free throws naturally means we’ll see more teams that meet these “conservative” forced turnovers/low free throws allowed. But coaching philosophy and roster makeup still determine the look and feel of each individual team defense, and we’re still in the early stages of learning which sort of system is the “best” — or whether such a judgment is even possible, given each team’s unique personnel. We’ve still got so much to learn about defense, and the interaction between defense and offense.