The next out that Nationals reliever Trevor Rosenthal records will be his first since Aug. 12, 2017, when he earned a save with the St. Louis Cardinals. Should Rosenthal, who missed the entire 2018 season after undergoing Tommy John surgery, retire a batter before allowing another earned run, it will lower his season ERA to 189.00. That’s a heck of a lot better than infinity, which is where Rosenthal’s ERA stands after a historically rough start to the season.

Rosenthal made his Nationals debut against the Mets on Saturday and allowed consecutive singles before issuing a walk to load the bases. Manager Dave Martinez pulled Rosenthal after he allowed a two-run single to J.D. Davis, who later came around to score in New York’s 11-8 win.

Martinez called Rosenthal’s number again in the eighth inning Sunday with runners on first and third and one out. After Mets shortstop Amed Rosario slapped Rosenthal’s first pitch into center field to score Robinson Cano, Martinez emerged from the dugout and summoned closer Sean Doolittle from the bullpen.

“I’m going to get the ball authenticated when I get my first out,” Rosenthal said with a grin after the Nationals came back to win the game on Trea Turner’s walk-off home run.

Rosenthal’s third appearance came Wednesday against the Phillies. He entered the game with one out, a runner on first base and the Nationals protecting a 6-4 lead in the eighth inning and promptly walked the first two batters he faced before Martinez decided he had seen enough. Both batters Rosenthal walked scored.

To recap, that’s four walks, three hits and seven earned runs allowed in three appearances this season, without recording an out. (For any mathematicians whose blood-pressure is rising faster than the Nationals’ bullpen ERA, Rosenthal’s ERA — [7 Earned Runs * 9] / [0.0 Innings Pitched] — might more accurately be described as “undefined” as a result of dividing by zero, but it’s conventional to refer to infinite ERAs when they occur in baseball. Besides, it just sounds cooler.)

According to the Elias Sports Bureau, Rosenthal is the first pitcher in major league history to allow at least one run without recording an out in four consecutive appearances. The streak dates from Aug. 16, 2017, when Rosenthal allowed a home run and a walk in his final appearance before being diagnosed with a partially torn ulnar collateral ligament in his right elbow. What’s more, all nine batters Rosenthal faced in that span, including the seven this season, went on to score.

“I’ve looked at everything and talked to people,” Rosenthal told the Athletic’s Brittany Ghiroli on Wednesday. “Mechanically, my stuff is fine. It’s just, I think building some confidence and continuing to get game reps. That’s going to continue to help me get in the groove. Once I get there, I’ll be in a good spot.”

According to FanGraphs, taking into account the number of outs and runners on base in his three appearances this season, Rosenthal has allowed five more runs than expected.

Rosenthal joined Dodgers starter Rich Hill as the only pitchers who failed to record an out in their first three appearances of a season since 1920, according to ESPN Stats and Information. In 2014, while serving as a reliever for the Angels, Hill walked two batters and allowed a hit before being removed in the first game of a doubleheader. Hill walked the only batter he faced in the second game and was released 10 days later. Hill signed with the Yankees and was pulled after hitting the first batter he faced in his New York debut. He lowered his infinity ERA to a respectable 3.38 by the end of the season.

Rosenthal would need to pitch 21 consecutive scoreless innings to lower his ERA from infinity to 3.00. A more modest goal is two consecutive outs and a 94.50 ERA, which still would be unsightly but no longer the worst single-season ERA in Nationals history. That title belongs to Jeremy Guthrie, who was designated for assignment with a 135.00 ERA in 2017 after allowing 10 runs in two-thirds of an inning against the Phillies. It was Guthrie’s only appearance in a Nationals uniform and the final start of the 13-year veteran’s career.

Neil Greenberg contributed to this report.

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