But when I think about those series, why can’t I get Carl Hagelin out of my mind?

“Hated playing against him,” Capitals General Manager Brian MacLellan said.

“It’s a pain in the [rear] chasing him around the ice,” Caps defenseman Matt Niskanen said. “He’s a pest.”

Hagelin has just two goals this season, but that’s not why the Capitals brought him to Washington. (Jonathan Newton/The Washington Post)

“It’s one thing to play against a fast player,” Caps forward T.J. Oshie said. “And it’s another thing to play against a fast player who knows how to read the game. He’s always on you.”

Here’s the thing about the state of the Washington Capitals, even after Tuesday night’s 7-2 thrashing of the outmanned Ottawa Senators: Just because they won the Cup last year doesn’t mean they can’t try to win it again this spring, too. And that’s why Hagelin was here Tuesday, pulling on the red sweater he had, over the years, been trained to hate.

“They obviously acquired me for a reason,” Hagelin said.

Or, maybe, 100 reasons. We’ll get to them in a second.

Look, we don’t know what’s going to happen with these Capitals, who now have only 18 games left in a regular season that has been, on the whole, uneven. But in trading last week for Hagelin, long a Washington annoyance with both the New York Rangers and the Penguins, and defenseman Nick Jensen, already signed to a four-year extension to remain part of the core here, they’re making it clear: This group, with a couple of tweaks, was good enough to win it last year. So why wouldn’t some tweaks this year — better, more significant tweaks — put it in the same position again?

“You make some moves like this,” Oshie said, “and it kind of refocuses you that playoffs are coming here, and it’s time to get going.”

It says here Hagelin’s the kind of guy who could get them going.

Now, you’re not going to notice him much on the scoresheet. But watch him on the ice. He’s hard to miss.

No one knows that like the Caps. Hagelin’s rookie season was 2011-12, when he came up with the Rangers. Guess who ousted the Caps that spring? Yep, New York. That began a string of Hagelin’s personal playoff mastery of Washington. In 2012, ’13 and ’15 with the Rangers, then again in 2016 and ’17 with the Penguins, Hagelin was in the handshake line moving on as the Caps’ season ended. That finally ended last year, when the Capitals at last vanquished the Penguins (and Hagelin). So maybe Washington didn’t have a second-round problem or a Pittsburgh problem, after all. Maybe it had a Carl Hagelin problem.

That seems kind of crazy, given Hagelin, 30, arrives here — after a trade with the Los Angeles Kings, who had acquired him from the Penguins earlier this season — as a fourth-line left wing. But, man, Hagelin’s fingerprints were all over those Pittsburgh series victories, and the subsequent Pittsburgh Cups. His speed is what jumps out, but it’s not in a Jakub Vrana, offense-first kind of way. He’s the best kind of annoying — there when you don’t want him to be, killing penalties, anticipating plays before they happen.

“He doesn’t always get a breakaway out of everything or an odd-man rush out of everything,” Niskanen said. “But he drives defensemen back, and he creates room for teammates. There’s always the threat of him busting loose for a breakaway. You have to make plays a little sooner than you want to because he gets on you a little bit quicker because of his instincts and his speed.”

When MacLellan agreed to send a pair of draft picks to L.A. for Hagelin, MacLellan’s coach, Todd Reirden, about ran into the streets screaming, “Hallelujah!” Or some such.

“When we picked up this player,” Reirden said, “I thought about the amount of time that I’ve spent clipping video on this player.”

Uh, Todd: He arrived in Washington with all of two goals in 38 games this season with the Penguins and Kings. This is a guy you lose sleep over?

“You can walk right down the ice and I can talk to you about how he can have an effect,” Reirden said.

So let’s do it. In the Caps’ end, Hagelin can help not only defend — which he does well whether he’s on the puck or off it — but can improve Washington’s breakouts. Pittsburgh used him by playing pucks to space, then allowing Hagelin to track them down. Reirden envisions the same here.

In the neutral zone, Hagelin can sneak behind defensemen, so a regrouping situation can turn into instant offense. And on the forecheck, he’s liable to get to the puck a step sooner than an opponent, helping maintain possession. Plus, once Hagelin establishes possession, the Caps have seen him win the race to the front of the net, which leads to backdoor or rebound goals.

At Tuesday’s morning skate, Reirden couldn’t stop gushing.

“I’m pretty excited!” he said. “Can we get him out there?”

Pile on here: All of those skills Hagelin has — using his speed to take away time and space, forcing a mistake, turning a 50-50 puck into a high-quality scoring chance — they’re elements that are particularly helpful in the playoffs.

“The things he does, we don’t have a lot of,” MacLellan said. “He brings tenacity.”

I’ll reiterate: I’m not awarding the Cup to the Caps again because they traded for Carl Hagelin. Tampa Bay is running away with the best record in the East. (Ask the Caps how valuable that status is come May.) Tuesday’s blowout of decimated Ottawa only pulled Washington even with the New York Islanders atop the Metropolitan Division — with the Isles, who have two games in hand, up next Friday night on Long Island. Jensen, 28, with his youth and his new contract, will have more of a long-term impact on this club. And whomever the Caps face in the first round will be a tough out.