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Toronto Maple Leafs' right wing William Nylander, left, celebrates his goal with teammates Connor Brown and P.A. Parenteau during on March 19, 2016.Nathan Denette/The Canadian Press

The Toronto Maple Leafs are streaking.

After beating up the bewildered Buffalo Sabres 4-1 on Saturday, the last-place Leafs are doing their best impression of a team still pushing to make the playoffs.

They are on a 4-2-1 run despite (a) facing five good teams in that stretch and (b) dressing as many as 10 players who are 22 or younger. That includes big centre Frédérik Gauthier, who played 11 minutes in his NHL debut against Buffalo.

"We were sort of on our heels most of the game," Sabres netminder Chad Johnson lamented afterward, noting how impressed he was with Toronto's speed.

"Our kids were good," Leafs coach Mike Babcock said. "I thought Gauthier's line was real good. I thought – everybody – we were fine. We played well."

The Leafs were beaming in the dressing room after this latest win, even though they became the first NHL team mathematically eliminated from making the playoffs on Saturday night. But this is no longer the team that lost all those games earlier in the year: Only seven of the 21 players who dressed Saturday were on the Leafs roster before the Dion Phaneuf trade.

That was less than six weeks ago.

The group that has emerged from that upheaval has been fun to watch. They're quick, tenacious and largely undaunted despite playing in their first stretch of NHL games.

They won Saturday because William Nylander and defenceman Connor Carrick were able to unleash big-league shots with perfect timing, continuing a trend of the Leafs youngest players producing most of the offence since the trade deadline.

Other aspects of their play are helping earn points, too. Goaltender Jonathan Bernier – whose technique has been in the wilderness much of the year – has a .940 save percentage since the deadline and will start Monday against the Calgary Flames.

The Leafs are also the NHL's fifth-best possession team in that time frame (53.4 per cent).

The issue with all this winning is what it might do to their draft pick. Two weeks ago, the Leafs appeared destined to finish 30th, which comes with a guarantee of a 20-per-cent shot at the No. 1 pick (which is expected to be Auston Matthews) and a 100-per-cent shot at a player in the top four.

Before Sunday's games, however, the Leafs had gained five points on fellow bottom feeders Winnipeg, Vancouver and Columbus in their past seven games. With 11 to go, Toronto sat between two and five points back of the five teams ahead of it in the standings (Calgary and Edmonton being the others).

The Jets and Canucks, in particular, have been in free fall, with the NHL's worst record over the past 15 games.

If the Leafs keep grabbing points at even a modest rate, in other words, they'll start to pass some of these flailing teams.

Statisticians like the odds of that happening. Micah Blake McCurdy, who runs hockeyviz.com, gives the Leafs only a one-in-three shot at finishing 30th, in part because of their strong possession play.

Another site, sportsclubstats.com, has the Leafs with a better than 50-per-cent chance of finishing higher than 30th. They believe Toronto has a 15-per-cent chance of passing at least two other teams, with Winnipeg and Edmonton the most likely candidates.

The NHL's new draft lottery format, which was introduced this year to further dissuade teams from tanking, could be a big problem for Leafs fans hoping for a very high pick. According to McCurdy, the Leafs have a 19-per-cent chance of not even selecting in the top five in the draft.

One reason this is happening is the Leafs had an elite minor-league team to draw on. The Marlies have had the best record in the AHL almost all season and became the first team to clinch a playoff spot on Saturday.

The other top AHL teams are almost all affiliated with playoff-bound NHL teams, and their best young players have been kept in the minors. In Toronto, meanwhile, there's an argument to be made that the powerhouse Marlies – who were 42-10-4 before most of their top players were called up – would have fared better in the NHL than the roster the Leafs iced much of the year.

Which explains some of their recent success.

But Babcock cautioned against projecting this Marlies-fuelled run to carry over into next season, noting that the Leafs were beating teams that were underestimating his 30th-place team.

"One of the things you have to be real careful of this time of the year when you're a non-playoff team is overevaluating what you have," Babcock said. "Because the team playing against you some nights isn't prepared to play. When you're a really good team, teams prepare to play against you every night.

"We don't want to overevaluate anybody."