Turnaround for red-hot Kings has four root causes

The Los Angeles Kings are off to the best start in their history (9-2-1) and are No. 3 in the NHL with 19 points. It's seven more than they had at this point last season (6-6-0), when they missed the Stanley Cup Playoffs by eight points.
The key to the Kings' early success is their strong defensive play. They lead the NHL with an average of 2.00 goals allowed per game and with a penalty kill of 93.0 percent.

There are four contributory stats to the Kings' defensive success: strong shot-based play, Jonathan Quick's goaltending, a new coaching staff headed by John Stevens, and sound two-way play by top veterans like forward Dustin Brown.

Strong shot-based metrics

The Kings have long been known in the analytical community for their outstanding shot-based metrics; they have led the NHL in 5-on-5 shot attempt differential (SAT) in each of the previous six seasons (2011-12 to 2016-17).
The Kings' SAT percentage of 50.83 in 2017-18 ranks No. 10, which doesn't seem outstanding. However, a team frequently holding a lead has a lower SAT percentage than expected because it tends to go into a defensive shell in the final period, which can skew the shot count. The Kings have often been ahead this season. When looking exclusively at situations when the score is tied, the Kings rank fourth with an SAT of 54.46 percent.
Strong shot-based metrics alone are not enough to win. During the previous six seasons of shot-based dominance, the Kings won the Stanley Cup in two of the first three but missed the Stanley Cup Playoffs in two of the past three. The difference between winning and losing with strong shot-based metrics often boils down to the effectiveness of the team's shooting and its goaltending.

Jonathan Quick

Save percentage has always been the best statistic to measure a goalie's performance. By this metric, Quick couldn't be playing much better. His .942 save percentage leads the NHL, among those who have played at least five games.
Quick played 17 games after missing most of last season with a lower-body injury. He made his return on Feb. 25, 2017. Since then, he has a .928 save percentage in 26 games, fifth in the NHL among those to play at least 20 games during that span, behind Sergei Bobrovsky of the Columbus Blue Jackets (.944), Jake Allen of the St. Louis Blues (.932), Pekka Rinne of the Nashville Predators (.930), and Andrei Vasilevskiy of the Tampa Bay Lightning (.928). In 26 games prior to the injury, Quick's save percentage was .907.
There is a metric that quantifies the value of a strong save percentage: Goals Saved Above Average (GSAA). It is calculated by multiplying the number of shots a goalie faced by the League-average save percentage, and then subtracting the number of goals allowed. This season, Quick leads NHL goalies with a GSAA of 10.78, according to the data compiled at Hockey Reference. To put that number into context, Quick's GSAA was 28.08 in 2011-12, the season when he was runner-up for the Vezina Trophy and the Kings won the Stanley Cup for the first time.

New coaching staff

On April 23, 2017, the Kings named John Stevens their coach, replacing Darryl Sutter, who was fired April 10. The new staff, which includes Dave Lowry, Don Nachbaur and Pierre Turgeon, has not required much transition time to get the most out of the lineup.
There is a metric that attempts to evaluate a coach's performance, based on how a coach's team has fared in the standings, relative to the prior season. To make it fair for those who coach particularly good or bad teams, results from the previous season are moved 35 percent toward the NHL average before the comparison is computed. With this metric, coaches have to keep good teams good and help bad teams improve by more than an average amount.
The Kings have already earned 5.9 more points than expected this season, according to this formula. Stevens was not expected to enjoy immediate success. Prior to this season, Stevens coached 267 NHL games and his teams finished 6.4 points below those expectations. In 480 games in the American Hockey League, his teams finished 9.5 points below expectations. Based on a weighted average of these results, Stevens ranked No. 26 among the NHL's 31 coaches, with minus-1.4 points per 82 games.

A Brown renaissance

One of the keys to success under Stevens has been getting the most out of Brown. Unlike many teams, the Kings' top players are not deployed primarily in offensive-minded situations and are expected to play sound two-way hockey while taking on top opponents in all three zones, at all scores, and in all manpower situations. Playing on the top line with captain Anze Kopitar and rookie Alexander Iafello, Brown has been doing exactly that.
Analytics aren't necessary to demonstrate Brown's turnaround performance this season. In traditional terms, Brown's average ice time dropped from 19:40 from 2007-08 to 2012-13 to 16:08 between 2013-14 and 2016-17, and his scoring dropped from an average of 0.69 points per game to 0.37. This season, Brown is back up to an average of 19:59 per game and has 12 points (six goals, six assists) in 12 games, an average of 1.0 points per game.