Didi Gregorius has improved yet again. He is a better offensive player than ever and steadier on defense.

His acquisition stands as one of the best of Brian Cashman’s tenure because a) the cost was Shane Greene, who has turned into a good setup man for the Tigers, but you would turn a good setup man into a prime-aged shortstop 365 days a year; b) Gregorius has been cost-effective at a time when the Yankees are eyeballing payroll in a much more bottom-line way; and c) Gregorius has handled being the successor to Derek Jeter, who celebrated his 43rd birthday Monday.

Yet as good as Gregorius is — and he is probably the second-best overall Yankee after Aaron Judge — he pretty much has no chance of being an All-Star in 2017 and maybe ever unless there is a spate of injuries. That speaks to the quality at shortstop in the American League.

The AL voting totals were made public Monday for the last time before the team is announced over the weekend. Gregorius is in third, but he had half the votes of leader Carlos Correa and also trailed second-place Francisco Lindor by more than half a million votes.

Correa is 22 and Lindor is 23. Both have much higher profiles nationally than Gregorius has — Correa was a No. 1 overall pick in the draft, and Lindor was a breakout star during last year’s postseason.

But Gregorius’ chances of being an All-Star are hurt by more than that. This season, rather than 36 players per team, there will be 32, limiting the number of All-Star reserves. That also will curtail the number of Yankees who will be selected. Judge is a shoo-in, others such as Dellin Betances and Starlin Castro are likely, and Gary Sanchez, Brett Gardner and Luis Severino are possibilities.

And then there is just the overall quality of shortstops in the AL, now and into the future.

Boston’s Xander Bogaerts is 24, and was tied with Houston’s Correa for the lead among AL shortstops in Fangraphs’ version of Wins Above Replacement while hitting .319.

Andrelton Simmons, like Gregorius a 27-year-old shortstop from Curacao, is generally considered the best defensive shortstop in the game, and is having his best offensive season with seven homers, 13 steals and a .280 average.

Seattle’s Jean Segura, also 27, is hitting .330. Texas’ Elvis Andrus, 28, has seven homers, 18 steals and is hitting .293.

None of these players is close to free agency, so you can see how Gregorius could excel and never sniff an All-Star Game, though he is in the midst of a third straight season of raising his OPS by at least 50 points while convincing the Yankees to teach all of the talented shortstops in their system — such as Gleyber Torres, Tyler Wade and Jorge Mateo — how to play another position. In addition, Gregorius has demonstrated his marked improvement against lefties last year was no fluke by hitting .364 with an .871 OPS off southpaws this year.

Because he missed the first month with a shoulder injury, Gregorius was still about a week to 10 days of at-bats away from qualifying for the batting title. But going into Monday, Gregorius is hitting .312 – only Segura and Bogaerts were better among AL shortstops. He has an .810 OPS – topped by Correa, Bogaerts and Segura, who because of injury also was just shy of qualifying for the batting tittle.

Perhaps most interesting was that in Fangraphs’ formula for defense, which relies heavily on range, Gregorius was the 10th-best fielder in the majors. Detroit’s Jose Iglesias was the only shortstop ahead of him, while Simmons was an eyelash behind him.

It all speaks to Gregorius growing into a star — though perhaps never an All-Star.