The Arizona Cardinals are a nearly textbook example of how to build a successful N.F.L. team.

Using conventional wisdom, the Cardinals were not supposed to risk the first pick in the 2019 draft on the 5-foot-10 Kyler Murray, the type of undersized scrambler who gives old-school football types the willies. Instead, they should have been patient with Josh Rosen after selecting him 10th overall in the 2018 draft, despite his nearly disastrous rookie season.

Rebuilding teams are supposed to focus their resources upon the offensive line. The Cardinals prefer to use their top draft picks on skill-position weapons and speedy defenders who lack natural positions. The Cardinals were expected to commit to the development of their youthful nucleus after finishing 8-8 in 2020. Instead, they signed defensive lineman J.J. Watt, 32, and wide receiver A.J. Green, 33, aging stars of the kind usually courted by teams on the verge of reaching the Super Bowl.

And Coach Kliff Kingsbury, the bonny prince plucked from Texas Tech in 2019, was scheduled to receive his comeuppance by now. For evidence of what happens when college-to-N.F.L. coaching transitions go awry (as they nearly always do), witness Jacksonville Jaguars Coach Urban Meyer’s effort to cram all seven deadly sins into his first four weeks of the season.

Every decision the Cardinals made over the last three seasons had the potential to have backfired by now. Instead, they are 4-0 and coming off a convincing upset of the Los Angeles Rams, who shocked Tom Brady and the Tampa Bay Buccaneers the previous week, making the Cardinals the reigning kings of the N.F.L. according to the transitive property of succession. That only goes to show that the league’s team-building textbook is as outdated as a 1957 edition of “Computers 101: Punchcards, Vacuum Tubes, and You.”

Now, if you think you have heard much of this before, it’s because the Cardinals also mixed blowouts and impressive upsets while starting 6-2 in 2020. Trend Watch profiled them in this space last October, casting them as the league’s mischievous young bohemians while offering a note of caution. “The Cardinals do not appear quite ready to be Super Bowl contenders this season. Their offensive line and defense are still rather shaky, and Murray’s passing remains a little too scattershot. For now, they must settle for wreaking havoc on the playoff picture and leading the N.F.L. in sheer delight.”

That disclaimer proved accurate. Kingsbury became a tentative, predictable play-caller once games started having playoff implicationsand the Cardinals lost six of their last eight games.

Expectations were low entering this season. Watt and Green looked like antique-shop luxuries for a team that still needed to stock up on necessities. Kingsbury’s stale game plans suggested that opponents had “figured out” his collegiate scheme. Experts (and oddsmakers) remained justifiably skeptical after the Cardinals’ first three wins, one of which came courtesy of a missed last-second field goal by the Minnesota Vikings, another against the lowly, winless Jaguars.

There’s mounting evidence, however, that the Cardinals are much better than they were last season. They lead the league in both points (35) and yards (440.5) per game. They rank second to the Buffalo Bills in Football Outsiders’ Defense-adjusted Value Over Average, a metric that accounts for both situational success on a play-by-play basis and strength of schedule. They also pass the eyeball test: This year’s Cardinals appear deeper and better equipped to handle tough opponents than last year’s daring young gate-crashers.

The 2020 Cardinals relied on Murray’s sandlot tactics and 115 receptions by All-Pro receiver DeAndre Hopkins to generate most of their offense, especially after Kingsbury ran low on fresh ideas. But so far this season, eight different skill-position players have generated at least 100 yards from scrimmage. Thanks to upgrades at skill positions, better play calling and more experience, Murray operates much more efficiently from the pocket than he did last season.

On defense, former All-Pro lineman Chandler Jones has returned to form after an injury-marred 2020 season; Watt’s presence has also helped a bit. Cornerback Byron Murphy has intercepted three passes this season after picking off just one in his first two seasons. And linebacker Isaiah Simmons, the eighth overall pick in the 2020 draft who could not find a role as a rookie, is beginning to thrive as an all-purpose pass rusher, coverage defender and run-stuffer.

Most revealingly, the Cardinals rushed for 216 yards and allowed three sacks against the Rams despite the absences of starting offensive linemen Kelvin Beachum and Justin Murray. Veteran center Rodney Hudson did not generate Watt-level headlines when the Cardinals traded for him in March, but he has become a stabilizing influence on a once-shaky unit.

With their lack of playoff pedigree and a roster and coaching staff that do not quite fit the mold, the Cardinals still look like shaggy misfits among the top N.F.C. contenders. Oddsmakers give them steep +1600 odds to win the Super Bowl, while the Rams team they just beat are at +800 and the Buccaneers, who barely escaped Brady’s return to New England with their dignity intact, are at +500.

Analytics, on the other hand, are blind to such preconceptions. Football Outsiders’ simulation-based playoff odds give the Cardinals a 43.7 percent chance of winning the tightly contested N.F.C. West, while the Rams’ chances stand at just 24.7 percent. (The Buccaneers have the best Super Bowl odds among N.F.C. teams because even the laws of mathematics grovel before Brady).

In many ways, the 2021 Cardinals resemble the early 2010s Seahawks, who tossed away the team-building manuals and staked their fortunes upon the too-small Russell Wilson, the too-collegiate Pete Carroll, some square-peg athletes like Richard Sherman and game plans and philosophies that aren’t supposed to work in the N.F.L.

Those Seahawks won one Super Bowl, reached another and settled in as perennial contenders. After a false start in 2020, the Cardinals may be following the same path.