Rich Hill revived his career at just the right time. (Alex Brandon/Associated Press)

A year and a half ago, Rich Hill was the last player cut from the Washington Nationals’ roster coming out of spring training, a stopover on a steep career descent that bottomed out that summer when, devoid of better options, he signed on with the independent Long Island Ducks, the last resort of baseball’s most desperate.

When Hill, a 36-year-old left-hander, re-signed with the Los Angeles Dodgers for three years and $48 million Monday, the first inclination was to view the deal in baseball terms: The top starting pitcher in a historically weak free agent market landed with the team for which he excelled during last fall’s playoff run at Chavez Ravine.

But to grasp the full astonishment of the Hill signing, one is required to see it in human terms: A guy who was one small step from being out of the game a little more than a year ago – there being nowhere lower to go had he flamed out on Long Island – just signed a contract for life-changing money. It’s no wonder Hill choked up several times when addressing the media at the MLB Winter Meetings at the Gaylord National Resort and Convention Center in Oxon Hill, Md.

“I don’t think we were close to packing it in,” Hill said when asked whether, at his lowest point, he ever considered retirement. “I never thought I was done. But there’s a lot of emotion up here. It’s been an incredible journey to get to this point.”

Hill turned his career around with the 2015 Ducks, pitching well enough in two August starts to attract the attention of the Boston Red Sox, who signed him to a minor league deal and called him up in September. He turned that audition into a one-year, $6 million contract with the Oakland Athletics for 2016.

Hill was a revelation for the Dodgers at the end of 2016, going 3-2 with a 1.83 ERA in six starts after being acquired via trade in August, then beating the Chicago Cubs with six shutout innings in Game 3 of the National League Championship Series. Now, despite exceeding 100 innings pitched in the big leagues only twice in a 12-year career, he is the clear No. 3 starter – behind Clayton Kershaw and Kenta Maeda – in the rotation of the defending NL West champions.

“So much of our confidence [in Hill] comes from knowing him,” Dodgers General Manager Andrew Friedman said. “There aren’t 10 guys that I’ve been around in my career that ranked as highly as Rich does in terms of having that truly innate, burning desire to win.”

The 2016-17 free agent market will move on from Rich Hill, and at some point so will the Los Angeles Dodgers franchise. But for Hill himself, the deal he signed Monday will affect his life and that of his family forever, and sometimes that’s the most important takeaway.