By Vahe Gregorian

The Kansas City Star

KANSAS CITY, Mo. — True to the cliche, football often amounts to a game of inches. The 37-31 overtime loss to New England in the AFC Championship Game on Sunday at Arrowhead Stadium was vivid, wrenching testimony to that for the Chiefs and their fans.

“We were this close, on an offsides, to being in Atlanta” for the Super Bowl, Chiefs coach Andy Reid said Monday, adding, “With an interception. With the ball in our hand. Game over.”

But while Reid quibbled over the fact that officials in a game of this magnitude normally first issue a warning about a player lined up over the line of scrimmage, as Dee Ford was with just over a minute left in regulation and the Chiefs leading 28-24, he acknowledged the ruling that offset Charvarius Ward’s interception was “legitimate.”

For that matter, it was just one of myriad reasons the franchise’s best season in 25 years ended in torment, just short of its first Super Bowl berth in nearly half a century.

Yet again, the Chiefs couldn’t stop the run enough (176 yards) in a playoff game. In response to New England’s 15-play drive to open the game, the Chiefs in the first half amassed all of 32 yards and were shut out for the first time all season.

During that span, an off-kilter Patrick Mahomes overthrew an abandoned Damien Williams for a would-be touchdown. Tyreek Hill, draped in two defenders most of the game, had one catch for 42 yards … in the game. Travis Kelce had three for 23.

They were dissected on third downs (13 of 19), and they couldn’t get within an area code of Patriots quarterback Tom Brady. Unless, that is, you count the phantom roughing-the-passer call on Chris Jones —who swatted Brady’s shoulder when Brady still had the ball in his hand —that Reid publicly disputed and helped enable a fourth-quarter touchdown.

All distressing, all stuff that will linger.

But at least all of that, even the blown call, is part of the fabric of the game.

All of that, you just have to learn to live with, if not grudgingly accept.

What shouldn’t be accepted going forward, though, is the illogical, unfair, unsatisfying and arbitrary premise this incredible game ultimately game down to: the flawed structure of overtime.

After a mesmerizing 60 minutes, which included the Chiefs coming back from a 14-0 deficit and four lead changes in the fourth quarter before Harrison Butker tied it with a field goal from 39 yards out with 8 seconds left, it’s absurd and downright brutal that a whimsical coin toss was so fundamental in the final result.

“I saw ‘heads’ … and I know what happens at the end of this one,” Patriot safety Devin McCourty told reporters after the game. “Any time we go to overtime and we get the ball, I’m not really worried about anything. I’m going to get comfy.”

To be clear, the Patriots won this game fair and square under the established setup everyone understood: If the team that gets the ball first scores a touchdown, game over.

The Chiefs in overtime were free to stop what proved to be a 13-play, 75-yard drive for a touchdown that instantly ended it when Rex Burkhead barged in from 2 yards out. They were allowed to break up any of Brady’s three masterful third and 10 passes that put the Pats in position to create sudden death for the Chiefs.

And this isn’t the first time a coin toss has been so pivotal; the Patriots, after all, won Super Bowl LI against Atlanta with the same indulgence of fate.

But what seems vaguely odd and just not quite right at a distance is amplified when it arrives at a theater near you, doesn’t it? What might have struck you as mildly head-scratching if the Chiefs had won that way, and instead been jarring to Patriots fans, resonates differently since they lost that way.

Now, who knows if the Chiefs would have been able to respond in kind if overtime didn’t reduce the game of inches to a game of chance? And for their part, the Chiefs weren’t exactly griping over this.

“I think the overtime rule’s perfect,” safety Jordan Lucas said Monday. “You shouldn’t be rewarded if the other team scores. You gotta stop them on defense. If you stop them to a field goal, OK, that’s more points that they left out there on the board. I think that’s fair. I think the overtime rule is pretty fair, if you ask me.”

Meanwhile, confident as the Chiefs might have been that they would have scored a touchdown with the toss (or in return if the rule provided for that and more), guard Cam Erving said, “I feel like we would’ve won, but that’s one for the imagination right now.” Or as Mahomes put it, “No doubt at all (that the Chiefs would have scored a TD), but that’s just ifs and buts. You can’t look at that.”

The NFL, though, should take a hard look at this again.

Because a league built on a revenue-sharing model to enhance parity, a league that touts its equity rule for game operations, a league made up of control-freak coaches and administrators who scrutinize every possible variable has to be capable of coming up with something more sophisticated than this.

And there are simple alternatives that would yield a more egalitarian result.

Consider just two:

The collegiate model, where each team is guaranteed a shot from the 25-yard line in to start it off. Better yet, modify it to start at midfield, like my wise friend and colleague Blair Kerkhoff says, so that scoring isn’t so rampant and more strategy is required.

Or just guarantee each team gets one chance, a notion my friend, author and Chiefs fan Michael MacCambridge reminded me of. If, say, the team that gets the ball first scores a touchdown and the other team follows suit, it can go for two to win or take its chances in sudden overtime from there.

Especially when it comes to playoff games.

At least in any of those scenarios, each side of the ball gets a legitimate opportunity in a game that otherwise is predicated on that yin and yang dynamic.

Except for, somehow, in the most decisive and consequential circumstances, in games that define seasons and careers, after two teams have battled and bled and exhausted themselves to a thrilling standstill.

“It’s just how the coin tosses, I guess you would say,” Mahomes said.

Good on him that that’s how he said it. To put it otherwise might come off as sour grapes. Reid basically avoided that path, too.

“I’ve sat in on a few of those (rules) meetings, and, you know, they go back and forth,” he said. “It’s what the league came up with, and I support it. I’d sort of like to have had another crack, though.”

Asked if it seemed unfair, no matter which team benefits from it, Reid smiled and said, “You’ve got to be a good coin-flipper, and then you’ve got to get off the field if you don’t have the ball.”

Entirely true as it stands now, and, again, it’s on the Chiefs that they couldn’t stop the Patriots when the game depended on it.

But it’s still no way to settle such a momentous game. It can be hard enough to live with the unpredictability inherent in this game of inches. Chiefs fans know. It’s time to rethink this senseless emphasis on a haphazard concept.