Dusty Baker is no longer smiling about the endless questions he gets about his closer, still unannounced as of Tuesday. (Jonathan Newton/The Washington Post)

WEST PALM BEACH, Fla. — Dusty Baker is tired of answering questions about his closer. He is sick of people asking him what factors will go into the decision, why that decision has not been made and when he will make it.

“I hope we have it settled [soon] so you all can keep asking,” Baker said. “You hope we have it settled prior to going up north so everybody knows what their job is.”

So why haven’t the Nationals announced it yet? Baker acknowledged there is some internal debate about the question, and one can see why. Shawn Kelley is a veteran, an experienced choice with the strikeout stuff to close. But if he were needed three days in a row, he probably could not do that without risking injury to his twice-repaired elbow. Blake Treinen has the power sinker to close, but the Nationals need that sinker to get them ground balls and out of trouble. Limiting him to the ninth inning might mean limiting his impact. Koda Glover has the stuff and mentality to close, but he is 23 years old and has not pitched a full major league season. One could make the argument for any of them, and it seems the Nationals have not convinced themselves of the answer yet.

“There’s always debate. Healthy or unhealthy. But that’s what makes the world go round,” Baker said. “… I welcome differences of opinion because it’s hard sometimes for me to even agree with myself.”

Baker said Monday that he, General Manager Mike Rizzo, assistant GM Bob Miller, pitching coach Mike Maddux and others would be involved in the decision, whenever it was made. Baker has praised Glover all spring. Rizzo has said before that he thinks Treinen has the stuff to close, too. Multiple people within the clubhouse said they consider Kelley the natural choice. Consensus could be hard to achieve.

But Baker seems unwilling to compromise on his wish to have one man assigned to the job. Asked if a closer-by-committee might have value early in the season, he said “there’s no value at all.” Baker wants each pitcher to know his role.

“We just have to see who fits the best. Who can go three days in a row. Who’s good left-right. What we need — do we need ground balls from certain guys? How other guys slate,” Baker said. “… Right now, we’re trying to figure out how not to overwork somebody to get to the late innings. That’s the only thing about the closer — you have to get to the late innings.”

Who will close is not the only question surrounding Baker’s bullpen. If the Nationals carry the traditional seven relievers and want to keep both Glover and Enny Romero on the big league roster, they will not have room for a long man. They could, theoretically, carry eight pitchers to start the season, but that would limit Baker to a four-man bench.

“We may have to, but I’d rather not,” Baker said. “We’re trying to figure out off-days and things like that at the start of the season.”

As of Tuesday, four non-roster invitee pitchers remained in camp — Jeremy Guthrie, Neal Cotts, Vance Worley and Jacob Turner. Guthrie and Worley seem like natural choices for the long-man role, but Turner could also contend for innings. The Nationals have had their eye on the 25-year-old for years, thinking they might be able to help him put his natural stuff together if they could coach him. Turner threw four innings and allowed three runs on two hits Tuesday night, and his ERA this spring is 5.50.

Guthrie relieved Turner, and tossed four innings of one-run ball. The 37-year-old worked decisively and efficiently, exactly as one would hope a long man might. The right-hander’s spring ERA sits at 2.41 after Tuesday night, and of all the candidates for long man, he has made the most convincing case so far.

• Daniel Murphy, scheduled to get at-bats in minor league games Monday, did not take them because he was sick. Baker said the second baseman needed intravenous fluids to deal with the trouble, which will keep him out of action Tuesday, too. Murphy was already behind in at-bats because of his time at the World Baseball Classic, so Baker indicated the veteran will probably have to play his way into shape during the regular season, since he is running out of time before Opening Day.

• Anthony Rendon, who fouled a ball off his foot in Monday’s game, told Baker he was better Tuesday. Baker did not expect any lingering trouble for his third baseman.

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