NEW YORK – The Capitals did it again. Up three games to one, nursing a Game 5 lead, they were less than two minutes away from advancing to their first conference semifinals in 17 years. Implausibly, impossibly, miraculously, they let it slip away. They saw their two-game lead vaporize for the 10th time in franchise history, then saw a Game 7 outcome go wrong for the 10th time in 14 chances.

But also, the Capitals did it again. On the road, against a heavy favorite, the Caps traded uppercuts with the top-seeded Rangers. They mixed entertaining hockey — spurred by a posse of youngsters — with fabulous goaltending and a sturdy blueline, leaving them virtually indistinguishable from the NHL’s best team. All seven games of their second-round series were decided by one goal. And after the embarrassment of missing the playoffs last year, and the Game 7 castration of 2013, the Caps finally entered an offseason with a sheen of optimism.

All these things are true. And this mush of vastly different truths left observers scrambling into opposing camps in the emotional moments after Washington’s latest Game 7 disappointment.

If you wanted to find a broader meaning, you would argue that this result demonstrated some awful defect in the Caps’ DNA, apparent over three decades and visible again in the Ovechkin era.

This group — or at least portions of it — lost a three-games-to-one lead to Montreal in 2010. It lost a 3-2 lead to New York in 2013. It is now a horrifying 4-13 in potential clinching games, with the latest gaping wounds including that Game 5 lead lost with 101 seconds left, and a Game 6 deficit that appeared in the first 40 seconds. The franchise has seen five three-games-to-one leads transform into 4-3 losses – which has happened just 23 other times in the history of the NHL.

So you might fairly wonder why the Caps were unable to hang on in Game 5. Why they were so flat to start Game 6? Why they couldn’t make Wednesday’s 1-0 lead hold up? How did they give New York four power-play chances in the first 25 minutes, allowing the Rangers to climb back into the game?

Others, though, strode off in a completely different direction. The Caps — reimagined in their first year under new management and Coach Barry Trotz — went from out of the playoffs last season to its second round. In their final three losses, they launched the exact same number of shots as the Rangers. And in that final overtime session, they likely got the better of play, relentlessly cycling the puck behind Henrik Lundqvist and creating several luscious chances.

Which leaves a confusing slop of details rather than a clear explanation. Not just for us; for the players, too.

“Guys are a little bit shocked, don’t know what to think,” Matt Niskanen said after the loss. “We’re hurt, for sure. We were obviously in a great position. We believed that we could — we believed we had a good shot of moving on and doing something. And it didn’t happen.”

“I don’t know either,” Karl Alzner said, when asked for help interpreting the result. “Just don’t think about it for a day or two. I don’t really know how you can determine [who was the better team]. Well, I guess they are. They’re the team that’s moving on.”

Most team sports are capricious, but playoff hockey often seems especially so. New York’s Game 5 goals — both of which hit obstacles on their way past Braden Holtby — might easily have bounced in more favorable directions. A potential Washington goal was disallowed. Overtime is so often a coinflip, which Washington lost twice. Which helps explain why some Caps were left thinking they had played well enough to advance.

“We’re a great team, and I think we deserve a better result,” captain Alex Ovechkin said.

“I thought we deserved this series,” agreed Eric Fehr, who watched most of it as a spectator while he nursed an injury. “I thought we worked hard, and I thought that this was going to be the year we were going to break through.”

They didn’t. And because of that, the Caps must grapple with the same confusing questions the rest of us are facing. They might reject the franchise’s 30-year legacy of playoff heartbreak, but Washington’s core knows its own history, which has never extended beyond the second round. When will it be the year?

“I don’t know,” Alzner said. “That’s the crappy thing. Every year that goes by, you think that’s one less chance I have. That’s what a lot of guys think of. Especially the older guys that haven’t won, they think about that a lot. So hopefully next year.”

Of course, we’ve all heard (and thought) that before. Barry Trotz talked all season about not being shackled to the past —  “We’re learning from our history and we’re looking it right in the eye,” he said Wednesday night. But that’s tough to swallow for fans who have looked this history right in the eye for multiple decades. You can stare down a mud puddle all you want, but if you fall in it, you’ll still get dirty.

So how you do you move on as a player? How do you process these seven games of nearly 50-50 hockey, which yet again left Washington watching the playoff’s denouement from home?

“I don’t know — it’s our sport,” Niskanen said. “You talk to guys who have won it all before, and that experience is just so rewarding. Only players really realize just how hard it is, how many things have got to go right to win. Obviously you have to have a good team, but there’s a lot of things that’ve got to go right.”

Getting a final overtime goal would have been one of them. In this teeter-totter series, that one final fortunate bounce could have destroyed so many story lines. But without that, the Caps are instead staring at months of talk about their free agents, months of talk about whether optimism is justified, and months of talk about this latest bout of playoff agony.

Joel Ward was the last man to leave the silent, nearly empty locker room late Wednesday night. He stammered when asked to sum up the series, pointing to the seven one-goal games — “Doesn’t get any closer than that, I don’t think,” he said. “We went to seven games and overtime — that’s pretty close.”

As he walked toward the exit of the empty room, Ward was asked how players can deal with being so close to the top of this latest hill, before everything started rolling down again.

“We don’t have much of a choice, do we?” he said. “You just do it. That’s just sports, I think.”