Coach Andy Reid’s Chiefs did it again.

Earning their fourth Super Bowl berth in six years, in a league designed for parity, quarterback Patrick Mahomes and friends got the details right at a high rate Sunday night.

Kansas City’s poise and precision, more than any factor, led to the 32-29 homefield victory in an entertaining AFC championship game at Arrowhead Stadium.

The Buffalo Bills did a lot right, too.

They had no turnovers, and got a first-rate touchdown pass from Josh Allen to Mack Hollins leading into halftime.

Buffalo, pursuing the franchise’s fifth Super Bowl berth, played well enough to win many of these adrenalized duels.

The Chiefs were sharper, especially early and late. Moving to within one victory of perhaps supplanting Bill Belichick as the NFL’s greatest coach, Reid hit the Bills with a few key fourth-quarter play designs that Bills players said they’d not seen in film studies.

Every NFL game produces random outcomes that add to the thrills and the agony.

On balance, the Chiefs benefited by a smidge from apparent randomness Sunday.

On the one hand, the Bills recovered each of the game’s five fumbles. So, Buffalo may have benefited from a good-luck bounce or two by the oblong football.

On the other hand, the Chiefs welcomed a large officiating decision that appeared wrong, when Allen was ruled short on a fourth-and-1 sneak. Allen, said former NFL official Gene Steratore of CBS, seemed to advance one third of the football beyond the line to gain on the critical fourth-quarter play.

I agreed with Steratore. The NFL can eliminate such controversies, if it desires, by adopting chip-sensor technology that yields precision instead of guesswork.

Another bummer for the Bills was the first-quarter concussion to cornerback Christian Bedford. Buffalo’s pass defense suffered, and Mahomes exploited it.

That Benford was playing Sunday, however, drew barbs from a brain scientist who, rather than chalk up the injury to bad luck, noted Benford had been concussed eight days earlier. “Christian Benford was cleared from #concussion protocol 3 hours before the game after only one week off,” Chris Nowinski of Concussion Legacy Foundation, posted on social media. “This seemingly modest hit forced him off on a cart. When this impacts his career earnings, who will make him whole? They failed him.”

In becoming the first team to reach a Super Bowl after winning the previous two Super Bowls, Chiefs coaches and players hit several high notes.

Critically, K.C.’s offense came out hot against a heady Bills defense overseen by former Reid protege Sean McDermott.

The clever, quick-passing game Reid devised was fundamental to the three first-half touchdowns, creating a 5-point lead.

Here’s why that mattered a lot: nearly 80% of NFL games are won by the team that leads at halftime.

Despite Tyler Bass’ 53-yard field goal, the slight edge in special teams went to Dave Taub’s Chiefs units.

Nikko Remigio’s long punt return led to a short-field touchdown. A gotta-have-it kick, from 35 yards, by Harrison Butker, a three-time Super Bowl champion, snapped a 29-29 tie.

Late-game chess victories by Steve Spagnuolo’s defense have become a hallmark of this astounding Chiefs dynasty.

Near game’s end, “Spags” struck again.

An intricate blitz fooled the Bills, creating a crucial fourth-and-5 incompletion by Allen.

The Chiefs, up 32-29, still needing two first downs, closed out the Bills with more detailed mastery. True to his elevated status in Hall of Fame coach Bill Walsh’s West Coast offense coaching tree, Reid sprang different running backs for “extended handoff” completions that sent the Chiefs toward New Orleans for Super Bowl 59, Feb. 9 against the Philadelphia Eagles.

Isaah Pacheco caught the first key pass.

Pacheco lined up behind fellow running back Kareem Hunt, whose deft blitz pickup, minutes earlier, had enabled a big gain.

Pacheco and Mahomes sprinted right. Pacheco ran uncovered, caught Mahomes’ flip-pass and, several yards later, bowled over a defender.

The clincher came via third-string back Samaje Perine’s catch-and-run, set up by another Reid gem.

The Chiefs did have one big error.

The Bills exploited it with their own opportunism.

Lineman Ed Oliver wrested the ball from Mahomes as the QB tried to recover his first-quarter fumble, and Allen and Co. pounced, mustering a long TD drive for a 10-7 lead.

Much later, Bills running back James Cook made the game’s best play.

Cook, scoring from the 1, overcame direct hits from two top-tier tacklers. The fourth-down rush moved Buffalo ahead, 22-21, late in the third quarter.

It was that kind of game. And the drama may have soared higher, had a former San Diegan made a difficult catch inside of two minutes.

Bills tight end Dalton Kincaid, the former University of San Diego star, couldn’t make a diving grab of Allen’s fourth-and-5 desperation throw. As drops go, Kincaid’s didn’t warrant harsh criticism. Allen did well to launch the blitz-induced wobbler, but it was a change of pace and well underthrown. Kincaid had to stop his sprint, wheel backward, find the ball and dive. His dive went inches too far, causing the descending ball to bounce off his right forearm.

So instead of defending at their 35, up three points, with the clock running toward 1:50, the Chiefs took over on downs.

Next comes another potential thriller: a rematch of Super Bowl 57. That night in Glendale, Ariz., Mahomes overcame a high ankle sprain and guided the Chiefs to a shootout victory despite a fine game by counterpart Jalen Hurts, who this time can lean on the NFL’s best rushing attack and a much-improved defense.