Despite a rough stretch in which some fans have questioned the team’s relative lack of transactions in the off-season, the Yankees have had a fairly good year. They are eight games above .500; through Monday, they were in line for a wild-card spot in the postseason. If a few injured players come back strong, the Yankees will be considered a serious playoff contender.

That said, the confluence of a down year for a few stars and the aforementioned injuries could lead to an occurrence that is almost impossible to imagine: The All-Star Game box score this season may not include a Yankees player.

There will be some Yankees at the game, of course. Every team is guaranteed at least one player on the All-Star roster, and the Yankees most likely will have at least two. Aaron Judge, the team’s otherworldly outfielder, will probably be elected as a starter despite being out indefinitely with a toe injury. And it is a safe bet that pitcher Gerrit Cole, the team’s ace, will be named to the team as well.

Cole, who is 8-1 with a 2.78 E.R.A., is the team’s best option to get into the game. The Yankees’ rotation currently lines up for him to enter the break with sufficient rest, and he should be among the top options to start for the American League. But rest is a tricky thing with starting pitchers. If Cole is not able to get enough rest days before the game, or if the A.L. manager, Dusty Baker of the Houston Astros, chooses to hold him in reserve, he may spend the entire game watching.

There is precedent for that. Cole has been selected to an All-Star team five times — once with the Pirates, twice with the Astros and twice with the Yankees — but he has appeared in the game only once, throwing a scoreless inning in 2015.

Beyond Cole, no other Yankee looks like a lock to make the roster. Clay Holmes’s numbers as the closer are good but not great. Michael King, a top reliever, has struggled recently. First baseman Anthony Rizzo has a lot of competition. So there is a possibility that the Yankees will not have a single player enter the game, which will be held on July 11 in Seattle.

A box score shutout would be quite a feat: It has not happened to the Yankees since 1991, when Scott Sanderson was the team’s lone representative at the game in Toronto and did not pitch. Overall, at least one Yankees player has appeared in 90 of the 92 All-Star Games.

Sanderson, who joined the Yankees before the 1991 season, was a bright spot in a horrible stretch in which the team finished with a losing record in four consecutive seasons. He was 9-3 at the 1991 All-Star break but with only a few days of rest after his last start of the first half, he did not get into the game as the A.L. manager, Tony La Russa of the A’s, used four starters (Jack Morris, Jimmy Key, Roger Clemens and Jack McDowell) and three relievers (Jeff Reardon, Rick Aguilera and Dennis Eckersley).

Sanderson’s inability to pitch in his only All-Star Game was a shame for a veteran pitcher having perhaps his most impressive season.

“He gave us a quality effort almost every time out,” Yankees Manager Stump Merrill said of Sanderson at the end of a season in which he won 16 games for a 91-loss team. “I hope the young guys on this team were paying attention when he was on the mound. They could have learned a lot.”

The only other time the Yankees were shut out of an All-Star Game box score was in 1943, and that time it was about proving a point.

Joe DiMaggio was away for military service, and the team, which went on to win the World Series that year, was represented at the game by catcher Bill Dickey; second baseman Joe Gordon; the outfielders Charlie Keller and Johnny Lindell; and the pitchers Tiny Bonham and Spud Chandler.

None of the six Yankees representatives got into the game, which was held at Shibe Park in Philadelphia. Their exclusion was especially notable since the roster decisions were made by Joe McCarthy — the manager of the Yankees.

“We didn’t need them,” McCarthy said boastfully after the game. “We got out there in front early enough. Besides, these other boys deserved a chance to shine. The Yankees have had enough of the limelight.”

In his account of the game, John Drebinger of The New York Times wrote about the A.L.’s dominance in the contest — it was the league’s eighth win in 11 All-Star Games — and said McCarthy’s choice not to use any of his own players only proved how superior his league’s roster was.

“It was, to say the least, a most astonishing demonstration of the junior circuit’s super supply of all-around talent and seemed to kill for all the ancient cry of National Leaguers that it was the Yankees and not the American League that was forever beating them,” Drebinger wrote.

The A.L. will go into this year’s All-Star Game riding a nine-game winning streak. Holding on to that streak without the use of any Yankees players might, once again, prove the might of the junior circuit.

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