Kings’ Ilya Kovalchuk has improved his play when they have needed it most

This movie has played out before for Ilya Kovalchuk.

He was with the Atlanta Thrashers when they began the 2007-08 season 0-6 and fired coach Bob Hartley. They were a sub-.500 team the rest of the way. Kovalchuk, in his inimitable way, remembers the feeling.

“Those days are not what you’re looking for,” Kovalchuk said.

The same could be said 11 years later, at least to start. The 4-8-1 record the Kings compiled in their first 13 games was enough to cost John Stevens his job. It’s not what Kovalchuk predicted when he signed a three-year, $18.75-million contract, but the aforementioned experience conditioned him to the harsh realities of the game.

“It should be the wake-up call for all of us, because nobody’s safe here,” Kovalchuk said.

A 4-1 win over the Ducks on Tuesday is more of what Kovalchuk is looking for after five years away from the NHL. He scored his team-leading fifth goal and recorded his fourth multi-point game this season.

Kovalchuk has been more noticeable on a line with Jeff Carter and Tyler Toffoli the last two games, both wins. His hands and flashes of elite skill have been apparent, such as his one-time swat of the puck past Ducks goalie John Gibson on a break-in on net.

Kovalchuk is able to produce at 35 partly because of his much talked-about conditioning regimen, which is what drew Kings coach Willie Desjardins to Kovalchuk on a trip to Russia with the Canadian national team in the summer of 2017.

“We played them in Russia, and he was training,” Desjardins said. “I had my camera out and I was video [taping him], and I didn’t know if I was supposed to [film], so I had the camera down low.”

The trip was a run-up to the 2018 Olympics, when Desjardins coached Canada. His team didn’t play Kovalchuk and the Olympic Athletes from Russia in the tournament but Desjardins remembers seeing Kovalchuk play.

Desjardins has coached players from all walks of life, from Japan to North America, but he admits this is new territory to coach a world-class player who stepped away from the league for years.

But it’s an experience that he welcomes, judging by what he’s seen.

“Usually elite guys don’t leave the league,” Desjardins said. “He made some really high-end plays [Tuesday]. The key for me is just to get him to work hard. If I can get him to work hard, everything else will fall in place.”

One avenue toward that might be the less-is-more approach. Kovalchuk’s sub-16-minutes of playing time in each the last two games are among his fewest of the season. But he has four points in that span and the Kings’ power play has clicked at a five-for-14 rate the last four games.

Kovalchuk’s five goals put him on pace for more than 25 on the season, which falls into the 25-30 goal projection of the organization upon signing him. He remains, neatly, a point-per-game player with 830 points in 830 games. He has said he’s adapted to the new NHL but on Wednesday he offered up a 14-game critique.

“I think I can be much better,” he said. “I think we all can be more consistent, but me personally, I know I can do better. It’s still an adjustment process for me, but I feel much better.”

UP NEXT VS. MINNESOTA

When: Thursday, 7:30 p.m.

On the air: TV: FS West; Radio: iHeartRadio (LA Kings Audio Network).

Update: Minnesota center Eric Staal is sick and questionable to play, according to the Minneapolis Star Tribune. The Wild have won seven of nine games, which included a 4-1 win against the Kings on Oct.25.

curtis.zupke@latimes.com

Twitter: @curtiszupke