On June 21, the Dodgers lost 5-2 to the San Diego Padres to fall to 30-42, last in the National League West and 9.5 games out of first place.

Clayton Kershaw had been roughed up a little, and the Dodgers hitters didn’t get much going against the parade of relievers the Padres used that day … and ESPN’s Dodgers blogger filed an item with this title:

“This looks a lot like hopeless”.

And he went on to count the ways the Dodgers were not playing well. Pretty much any way you cared to evaluate. He opened his piece with a suggestion that the Dodgers were “getting awfully close to the point of no return” — and who would have argued that?

He added: “Of course, stranger things have happened than this team turning it around, but betting on that doesn’t exactly seem like the smart play right now.”

They looked like a very expensive team, put together with little rhyme or reason other than ownership’s appetite for enormous contracts … and it seemed as if it might take years to straighten out the mess.

Yet here we are, 44 games from 32-40, and the Dodgers are an astonishing 36-8 since touching that nadir, and now are 66-50.

And if anyone saw that coming … well, they aren’t being honest.

This is a turnaround that came from out of the blue.

What happened?

In part, it is Yasiel Puig. He gave the club reason to hope when he got to Dodger Stadium on June 3. People who were in Chavez Ravine the first two months of the year talked about how dead it was — before Puig.

But his arrival didn’t lead directly to results. The Dodgers went 7-10 in his first 17 games.

No, it’s been more than that. Much more.

The offense has picked up significantly. The key guy there has been Hanley Ramirez, who for stretches of the season — he has played in only 55 games — has looked like the Best Player In Ball he arguably was from 2007 through 2009.

(The Dodgers are 33-12 since June 14, when he got into the lineup for the first long stretch of the season, playing nearly every day for 52 days, before his latest injury.)

Adrian Gonzalez has been steady, leading the team in nearly every meaningful offensive stat. Though not overwhelming in any of them.

Kenley Jansen took over as the closer on June 11 and finished off 14 of the 16 games entrusted to him — a big improvement on Brandon League.

The starting pitching has been very solid. Kershaw is as good as he has ever been, which is very good, indeed, but he no longer is a one-man rotation. Zack Greinke has come on strong, and Hyun-Jin Ryu wins a lot, and the addition of Ricky Nolasco helped settle the back of the rotation.

But, still, what is striking about this club is how modest the stats are of so many hitters. Only Adrian Gonzalez has more than 11 homers (16). He also is the only Dodger to score more than 45 runs (with 54).

It has been a largely unsettled team — 43 guys have appeared in boxscores so far, and that’s even before the September call-ups.

Ramirez has missed 61 of 116 games; Matt Kemp has missed 54. And there are two of your three best hitters — though Kemp has struggled, even when he has played.

Andre Ethier has come on, a bit (a .353 OBP), but the Dodgers still have very average players at catcher (A.J. Ellis) and second base (Mark Ellis). Shortstop is a problem when Ramirez doesn’t play, and third base is always a problem.

Two guys who define “journeyman” — Skip Schumaker and Nick Punto — have been in starting lineups far too often; Schumaker is on pace to get 334 at-bats, Punto 317.

A factor in the surge is this: The Dodgers have played lots and lots of bad or slumping teams since June 22 — San Diego, San Francisco, Philadelphia, Colorado, Arizona, Washington, Toronto, Cincinnati, the Yankees, the Cubs. Most of those teams have been bad all year; a few of them (Cincy and Toronto) were struggling when the Dodgers got them.

But now, they have taken three of four from St. Louis and two from Tampa Bay, teams with reasonably good chances of playing in the World Series.

At the end of this, what the Dodgers have done does not make much sense. And it seems as if it is not sustainable, given their sketchy offense and the shaky health of two of their stars, and a bullpen untrustworthy, aside from Jansen … but they have been very, very good for almost two months now.

If they can play .500 ball from here on out, they will finish 89-73, and that ought to be enough to win the West. And put them in the playoffs.

Mind-boggling. Almost beyond belief. Seeing how this turns out will be very interesting.