In search of, ahem, better relations in the arts and good excuses to drink beer, some arts and humanities types played softball on a perfect Friday afternoon near the Lincoln Memorial.

The teams:

* National Endowment for the Arts, $119.3 million so far this season and losing fast.

* National Endowment for the Humanities, $113.7 million and ditto.

* The Presidential Task Force on the Arts and the Humanities -- they just keep score of the other teams. Yesterday, they decided to play for the fun of it -- after all, the game was their idea -- making it the first round-robin baseball game in recent history.

This caused some confusion. When the NEA's Don Moore made it to second base, NEH chairman Joseph Duffey was on the sidelines applauding. "Oh," he said, stopping abruptly, "who am I supposed to be rooting for?"

"This is our first, last and only game," said task force staff director David Morse. His team's game plan: "We were hoping to get Frank Hodsoll here to intimidate them," he said, soberly munching on a pretzel as he watched batting practice.

It's widely rumored -- and all but announced -- that Frank Hodsoll, who plays deputy to James Baker's White House chief of staff position and helped set up the task force, is being traded to the National Endowment for the Arts to play new chairman. For a good hour there, it was feared Hodsoll wouldn't show. He apparently hadn't been informed of the change of game location from Field 19 way out by the Tidal Basin to Field 11 near the Lincoln Memorial. Luckily, an hour and a half into the game, someone called Hodsoll and found him still in his office.

"I was trying to stay away as long as possible so by the time I got here I would have missed the game," Hodsoll confessed as he arrived with a business-suited friend. "I didn't want to show how bad I was." Still, he arrived in the uniform task force T-shirt: "Ars et Humanitas non sunt gratis." (The arts and humanities aren't free.) He was quickly given a beer.

"Hey, you can't drink that!" cried Russell Mead, liaison between NEH and the task force, and the man who came up with the idea of the game. "You're up!"

Hodsoll gallantly went to bat, hit the ball but was tagged out at first base. "I got it out there," Hodsoll commented later as he sipped on a beer, "but then I was so surprised I hit it that I didn't run until two minutes later."

The Endowment teams were driven to win, however. "If the Endowments score high," said Duffey, in a T-shirt that read "Elitism Lives!", "the Reagan-proposed cut goes down to 6 percent instead of 12 percent, so it's a pretty high stakes game."

"I think we get $1 million for each run scored," added NEH public relations official Barry Wanger.

"Oh, really?" asked Duffey.

NEA chairman Livingston Biddle went to bat and hit a fly ball to left field that was caught by fledgling baseball virtuoso Lynne Feingold, a staff member of the task force who just happens to be on loan from Biddle's office.

"TRAITOR!" yelled an NEA fan from the sidelines.

"I'll have to reconsider her job," said Biddle.

Still, after four innings, more or less, the NEA finished with a stunning victory of 12 over the NEH's meager 4 and the task force's dismal 3.

Afterwards, as the sun turned buttery gold over the Potomac River, they all shook hands and went off to spend the weekend fortifying themselves for next week's Washington games.