LAS VEGAS — The overtime coin flip came up tails, and San Francisco head coach Kyle Shanahan faced a decision never before made in Super Bowl history.

The NFL’s new playoff rule called for each team to get the ball at least once in overtime. That meant Shanhahan’s 49ers had the option to take the ball first or kick it off to Kansas City and bat second — either by KC kickoff after a score, a punt or a turnover.

He chose to take the ball.

He should have chosen to go second, not merely because Kansas City eventually turned a 19-19 tie into a 25-22 Super Bowl victory.

[For more on 49ers' Super Bowl heartbreak, check out Yahoo Sports NFL]

For San Francisco, the coin-flip decision was the culmination of a disastrous second half that led to its second consecutive crushing Super Bowl defeat to the Chiefs after leading by double digits.

To say there is a definitive answer — especially analytically — would be ridiculous. It’s a scenario that had never before occurred. Still, Shanahan's 49ers should've been prepared to make it, and multiple players admitted after the game that they didn't know the new overtime rules.

Shanahan’s decision will be picked apart like many others in this defeat: getting away from the run game that could have killed clock, the inability of the offense to do much of anything in the early third quarter and the fact that Shanahan now has three brutal Super Bowl defeats — two in San Francisco plus a blown 28-3 lead to New England when he was the offensive coordinator in Atlanta.

By choosing to receive rather than kick, Shanahan allowed the Chiefs and Patrick Mahomes to get the ball with more information to factor into their play-calling. It also meant less data for him.

When San Francisco drove down the field, it did not know that Kansas City would eventually score a touchdown. It’s why Shanahan said he “never thought about” going for it on fourth-and-4. Instead, the Niners kicked a field goal.

That meant Kansas City knew it needed to score and would never consider punting as an option.

As such, when the Chiefs faced fourth-and-1 from their own 34-yard line, they went for it. Had that same scenario played out on the first drive of overtime, Kansas City would've almost assuredly punted and allowed San Francisco to win it with a field goal.

Instead, Mahomes made a clever 8-yard run, and the drive rolled on until it found Lombardi Trophy paydirt.

Shanahan was left trying to explain his thinking.

“None of us have a ton of experience with it,” he said. “But we went through all the analytics and talked to those guys. We just thought it would be better. We wanted the ball third. If both teams matched and scored, we wanted to be the ones who had the chance to go win.”

His thinking was that if both teams were either forced to punt, kicked a field goal or scored a touchdown, then San Francisco would have the chance to score and win on the third possession. (Under the rules, Kansas City would not be assured another chance.) Shanahan said giving his defense a rest didn’t play into the decision.

“Our biggest thing is we knew both teams were going to get the ball at least once, so we wanted to make sure if we won the toss, we would be the team that got it the third time,” Shanahan said.

It’s not completely lacking in reasoning, but it is to defer an advantage three possessions into the future.

That means getting there … against Patrick Mahomes.

Allowing the Chiefs to go for it on fourth down was akin to a turnover. It was a second chance for the most dangerous late-game quarterback in the game, and he burned them for it. The decision also allowed Kansas City to make second- and third-down calls throughout the drive knowing it would have an extra play. It incalculably changed the decision-making.

And even under Shanahan’s scenario of getting the ball third if both teams scored, that would be the case only if the Chiefs were held to a field goal. If San Francisco had scored a touchdown and Kansas City responded, head coach Andy Reid would have had the option of winning the game with a 2-point conversion.

Shanahan essentially gave all the power and all the advantage of winning the coin flip to Kansas City for the first two possessions of the game and needed a specific result to get to the point of the game to regain it.

“[We] got that field goal, so [we] knew we had to hold them to at least a field goal, and if we did, we thought it was in our hands after that,” Shanahan said.

Not surprisingly, Mahomes and Co. never gave him the chance.

In truth, it probably should never have gotten to overtime. While Shanahan said afterward that he had no general regrets about the game (there are always regrets about certain plays), when he looks back, he will likely focus on the squandered opportunities early in the third quarter, when San Francisco held a 10-3 and then 10-6 lead.

One quality scoring drive would've tilted the game significantly in San Francisco’s favor. Instead, the 49ers' offense imploded on three consecutive drives, going three-and-out each time, actually losing 2 cumulative yards and burning just 3:26 off the clock.

Kansas City was struggling as well, the defending champs on the ropes and seemingly susceptible to a knockout blow. But Shanahan, known for his innovative play-calling, couldn’t deliver a single jab. The Chiefs kept getting lifelines and eventually found their footing.

Eight of those nine plays were Brock Purdy passes, with the Niners' offense essentially moving away from star running back Christian McCaffrey — he had one rush and one reception during that stretch.

“We didn’t get away from the run,” Shanahan said in his defense, stating that the drives just stalled. “... We couldn’t stay on the field.”

McCaffrey finished with 22 rushes. He probably needed 30.

There is no good way to lose the Super Bowl. Shanahan kept repeating that. He brushed off the fact that his teams keep losing double-digit leads, noting, fairly, that he has lost twice to Mahomes and once to Tom Brady.

Still, the losses at this stage linger, and he wasn’t downplaying the pain.

“We all hurt,” he said.

Maybe that coin-flip choice wouldn’t have changed that outcome. It didn’t help, though. And it isn’t likely to be repeated by coaches in the future.