When the Ottawa Senators square off against the Pittsburgh Penguins in Game 1 of the Eastern Conference finals Saturday night, they’ll be carrying the banner as Canada’s last hope this season to end its Stanley Cup drought. And make no mistake, the Sens earned their place here with a couple of hard-fought series wins over the Rangers and Bruins. But nothing about Ottawa’s play during the regular season suggested the team would make it this far. In fact, very little suggested the Senators should be in the playoffs at all.

For starters, the Senators gave up more goals than they scored this season. In particular, they struggled to light the lamp, scoring fewer goals per game than six teams that missed the playoffs, with a shooting percentage that ranked 22nd in the league and a power play that ranked 24th.

The Sens weren’t terrible on defense during the regular season (they let in the NHL’s 11th-fewest goals), but they weren’t exactly great, either — they ranked 15th in shots allowed per game, and their penalty kill was second-worst among playoff teams. Overall, Hockey Reference.com’s Simple Rating System listed Ottawa as the 18th-best team in the league — easily the worst of any team to qualify for the playoffs.

Those are not the kind of numbers you’d expect from a team preparing for the conference finals, and yet here the Sens are, just four wins away from the Stanley Cup Final. So what has Ottawa done so differently in the playoffs that’s enabled this deep run?

Well, not much, actually. They’re shooting the puck better, but only slightly so; they’ve scored on 9 percent of shots in the playoffs versus 8.4 percent during the regular season. Their power play has also continued to struggle: they rank 13th out of 16 playoff teams. At the other end of the ice, goalie Craig Anderson’s save percentage and goals against average are both significantly worse during the postseason than they were in the regular season, and he’s only recorded six quality starts in 12 chances (well below his career rate of 62 percent).

And although Ottawa is scoring more goals than they’re giving up in these playoffs (again, a novel development compared with the regular season), they’re only barely doing so, scraping past opponents by a measly 0.08 goals per game.

Because they’re basically conceding goals at the same rate they’re scoring them, the Sens have been involved in a lot of close games: Nine of their 12 games this postseason have been decided by one goal, and six of those nine games have gone into overtime.

To their credit, the Sens have won seven of those nine one-goal games, including five of the six games that required extra time. But it’s a dangerous way for a team to go about its business. A big save here or a post there, and it might have meant a different fate for Ottawa.

Still, the Sens are in the NHL’s final four, close wins and shaky resume be damned. This is the third conference finals bid in franchise history, and they’ll be looking to make a second-ever Stanley Cup finals berth with a win over Pittsburgh. Of course, in Ottawa’s previous two runs beyond the second round of the playoffs, they had much stronger teams — on paper, at least.

In 2002-03, the Sens won their first and only Presidents’ Trophy on the strength of great seasons from Marian Hossa, Daniel Alfredsson, Radek Bonk (remember Radek Bonk?), Martin Havlat and a young, 6-foot-nine-inch defenseman named Zdeno Chara. They entered the playoffs as the top seed in the Eastern Conference, but despite holding opponents to the league’s second-fewest goals per game in the postseason, the Sens were unable to top Martin Brodeur’s mighty New Jersey Devils.

The Sens made another deep springtime push when they got to the Stanley Cup Final just three seasons later. That 2006-07 Senators squad was custom-built to make a run to the finals; they scored the second-most goals and gave up the second-fewest in the East during the regular season. In the playoffs, they scored on a scorching 10.3 percent of the shots they took and received strong goaltending from Ray Emery (up until the Cup finals). But they ultimately fell short again, losing the championship to the Anaheim Ducks.

In both of those years, it at least felt as if Ottawa belonged deep in the playoffs. This year, the numbers say that’s less the case. And now the Sens face the unenviable task of taking on the defending champs, a Penguins team that’s doing just about everything right so far during these playoffs despite being banged up. All signs point to Pittsburgh’s winning this series.

But nothing necessarily suggested Ottawa would make it this far, either. In order to advance, recent history tells us the Sens might want this series to be tight; they’ve been exceptional in 50/50 games after all. And if their track record this postseason tells us anything, it’s that Ottawa might still have some surprises left up their sleeves. They may not look as good on paper as their conference-final forerunners, but those teams also lost before they could sip from Lord Stanley’s mug. Perhaps these Senators will be the ones who finally get to take a swig.