Los Angeles right wing Marian Gaborik, center, celebrates tying the game in the third period against Washington and goalie Jaroslav Halak on Tuesday. The Kings went on to win in a shootout. (John McDonnell/The Washington Post)

A shootout that shouldn’t have been necessary had already begun, and Washington Capitals Coach Adam Oates looked to the corners of the upper deck Tuesday night at Verizon Center, home to the out-of-town scoreboards. So much that mattered: Columbus and Detroit, Toronto and St. Louis, the standings reshuffling in his head.

“You take in a lot of information,” Oates said.

The information that matters for the Capitals at the moment: Their season is teetering on the edge, perhaps with the direction of the franchise at stake. On Tuesday, while needing help in other games, they turned a likely win into a likely loss and then forced overtime anyway, a perfect fit for a season that has careened in all directions. It ended with a clunk, a 5-4, what-do-we-make-of-this shootout defeat to Los Angeles.

The other information that matters: Top center Nicklas Backstrom took a thunderous hit from Kings defenseman Drew Doughty in the second period, and he was finished for the night. We don’t yet know his status for Saturday’s crucial game — they’re all crucial at this point — against Boston. Defenseman Jack Hillen took a thunderous hit from — get this — his own Alex Ovechkin in overtime and lay prone on the ice for an eerie few moments. We don’t yet know his status, either, for the Boston game.

So here we are with these Caps, where we’ve always been with them, really — right on the edge. They are in some ways a mess — injured, with lines and lineups in flux, rookies and call-ups entrusted with critical roles both by necessity and design. But they are also, in some ways, so enticing. Evgeny Kuznetsov pushed through a shorthanded, game-tying goal in the final minute — the first of a promising career — proving again what Caps fans know too well: Hope is among the most dangerous commodities.

After a successful West Coast trip, the Capitals are on the verge of yet another postseason appearance. The Post Sports Live crew debates whether their recent hot streak portends a run to the playoffs. (Post Sports Live/The Washington Post)

Get ready to dismiss them — and you did, right, after Dmitry Orlov took an egregious five-minute major March 2, leading to a gut-churning overtime loss to Philadelphia and sparking five losses in six games? — and they reel you back in. Last week, in the dead of night, games that only Washington’s hardiest hockey insomniacs witnessed, they came up with three season-sustaining performances against three stout playoff shoo-ins on the West Coast.

They came back east with five out of six points secured against Anaheim, Los Angeles and San Jose. On Tuesday, for the first time in two months, they could have stamped themselves as favorites to secure a playoff berth, leading the wild-card race in the Eastern Conference.

They lost, gaining a point. So here they sit, with three days off, still on the outside looking in.

“We shut our brains off for a second,” defenseman Karl Alzner said. “. . . It’s so frustrating we went back to old habits for a game.”

Old habits? They are season-long habits. The reason this team keeps yo-yoing with its fan base is because it cannot seem to handle good fortune, either on a micro or macro level. Two-goal leads are supposed to be good, right? They’re perilous for the Caps, who have coughed them up 13 times. Which is why, in the narrow view of Tuesday night, the 3-1 lead they took after two periods felt unusually perilous.

Forty-five seconds into the third, it was 3-2.

“Here they come,” Oates said. “Couldn’t hold ’em.”

They can’t, either, hold their own hot streaks. Six times this season, the Caps have won at least three games in a row. Four of those times, they have followed with at least two consecutive losses.

There are nine games remaining. The optimistic view is that they have now gained points in six straight games, and with just four outings left against likely playoff teams, there is an opportunity. The pessimistic view would be: Why should we believe in these guys? They’re injured (Brooks Laich, Mikhail Grabovski, Aaron Volpatti and now maybe Backstrom and Hillen) and inconsistent. Aren’t the Nats home soon?

That is the nightly frustration for the fans of a team that has built its own expectations — both through previous seasons and its own internal hype — yet seems to undo what good it does. But for those who don’t pay attention to each point gained and point lost, there would be the overarching question around this franchise: What next?

“Stay calm” was the advice of Dustin Penner, the veteran forward acquired at the trade deadline with two Stanley Cups to his credit.

But does the calm extend to the owner’s box? Ted Leonsis chimed in on his blog Wednesday, lamenting some of the injuries, the dozen overtime or shootout losses and all the two-goal leads lost.

“That will be the stat that haunts us most however this season plays out I believe,” Leonsis wrote.

While the Caps handed over their latest two-goal lead, the scoreboards in the upper reaches of Verizon Center showed St. Louis beating Toronto and Columbus beating Detroit. Both results helped Washington, and at the end of the night, four teams had 80 points. A mess.

But what can be expected next — against Boston and beyond? These Caps never give a predictable answer, and it is Leonsis who must ultimately take in the most information from a season that has been all over the map. At this point, there’s no way of telling whether the next nine games will sway him one way or another: Bring a version of the same group back to try yet again, or go with a more fundamental change.