The coyness that once made politicians play make-believe about maybe-running is over now. They are running, all of them, and -- with all the subtlety of John Philip Sousa on the Fourth of July -- they have lurched their pursuit of the presidency into its quadrennial phase: The Endorsements Game.

Anyone can play. And it seems, all of them are.

Greats and near-greats and ex-greats and ingrates are being courted and promised and signed up and trumpeted forth as "major endorsements" just as fast as the magnificent men and their press release machines can do the job.

Like fungi in belljars, the endorsement lists of 1980 are growing in ways that far exceed their importance.

Ronald Reagan, the Republican front-runner, has a lengthy list, stretching from a few conservatives in the U.S. Senate to such homestate stalwarts as Debby Boone and Frank Sinatra.

George Bush has a list of policians almost as long as Reagan's -- and yet his strategists are most proud of a fellow who is not in politics or show business: Texas attorney Leon Jaworski, who was Watergate special prosecutor, and who they hope will be remembered, every time he speaks out for Bush, as the man whose office prosecuted John Connally (unsuccessfully) in the milk fund case.

Connally has a weightly list of his own, heavy with people who served with him in the Nixon administration and heavier with the heads of America's largest corporations.

Then there is Sen. Howard Baker, whose list says he has the endorsments of a number of his Senate colleagues, plus Laurance Rockefeller. And there is John B. Anderson whose list says he has the endorsements of a number of his House colleagues, plus Laurance Rockefeller. (A spokesman for Laurance Rockefeller says his boss has not endorsed either candidate, but has contributed to "several" candidates.)

And there is Jimmy Carter, who has put out the largest endorsement list of all -- 561 -- and says the list is growing.

Sen. Edward Kennedy has no long endorsement list of his own as yet (he's only just begun, aides explain) but he has managed so far to chip a couple of names from the Carter list: Chicago's Mayor, Jane Byrne, and Carter's own State Department official in charge of refugee matters, former Iowa senator Dick Clark.

Just what do endorsements mean to a presidential candidate? One of Kennedy's closest advisers said, "You want to know what endorsements really mean? Just ask President Muskie."

In 1972, Sen. Edmund Muskie was far and away the frontrunner for the Democratic nomination and he won the early endorsements of most of the prominent Democratic officeholders -- only to learn, too late, that he could not convert his political endorsements into public votes in the primary elections.

Four years later, in 1976, one candidate more than all the rest made a public virtue out of the Muskie lesson of '72. He had no impressive endorsements and said he wasn't about to seek them.

Sure we said we didn't want endorsements in '76," recalls Hamilton Jordan, who ran that Carter campaign in 1976 and is setting a very different Carter strategy for 1980. "But that was because we didn't have any endorsements -- and we couldn't get any."

There can be no such thing as an imcombent ousider, the Carter strategists conceded long ago. So this time around they are gathering endorsements like pawpaws and putting them in their basket for all to see. "We had no choice," one of Carter's top campaign officials said of the strategy switch. "People have been saying that the trouble with Jimmy Carter is that no Democratic incumbents want to run with him. So we have to show that we do indeed have incumbents endorsing Jimmy Carter. Big names and big numbers."

All politicians know, in their strategic hearts, that although The Endorsements Game is played for big names and big numbers, that is not really how the game is won. For all endorsements are not equal. And many, in fact, are not even what they seem.

Compare, for example, the endorsements from two bright young U.S. senators who represent small East Coast states.

Sen. William Cohen of Maine is endorsing Howard Baker for president. Sen. Joseph Biden of Delaware is endorsing Jimmy Carter. On a scale of 1 to 10, Cohen's endorsement is at least an 8; Biden's is probably a 2.

The Cohen endorsements, by the assessment of Baker's 1980 competitors, means that Baker has locked up a victory in Saturday's straw vote at Maine's GOP convention. Cohen has been busily organizing the state for Baker, and he has taken political care to assure that Cohen/Baker people will dominate the convention -- a move that may well prove instrumental to carrying Maine's delegates in 1980.

The Biden endorsement, by Biden's own assessment, is something less. Joe Biden is a friend of Kennedy's. But he was out front early for Carter in 1976, and then Carter showed up at a fund-raiser for Biden, and then Biden's name showed up on the Carter list of endorsers.

"I don't plan on taking a very active role in this at all," Biden said in an interview. ". . . I don't plan to try to deliver votes. . . . I'm just saying I support the president."

Mayors, even big city mayors, can be even more unequal as players in The Endorsements Game.

and that is why the defection of Chicago's Jane Byrne particularly stung the Carter strategists. The president has an impressive list of local officials who have endorsed him -- 72 mayors and governors alone. lThe mayors range from Tom Bradley of Los Angleles to Coleman Young of Detroit to EdKoch of New York.

But Byrone's endorsement of Kennedy, because it is coupled with Cook County Democratic Chairman George Dunne's endorsement, means that Kennedy will most likely be starting the contest for Illinois' crucial 179 delegates with somewhere between onethird and one-half of them probably already won, with the battle now for the remainder of downstate votes.

Carter officials concede that no other big city mayor can deliver votes in that way.

The rules of The Endorsements Game include an inverse (some would say politically perverse) rule that says the lesser luminaries often prove to be the greater endorsement catches.

A congressman from Chicago explains why this is so. In his heart, he will not.

"Let's face it -- a county central committeeman has the power but I do not," says the congressman. "The county committemen have a lot to say. They name the choice for president. They also name the congressmen. . . . I have no voice at the convention. I have no voice in the county central committee. Once the county central committee meets, there is nothing I can do, anyway."

Throughout every candidate's endorsement list is the usual assortment of glitter litter. Actors and actresses, football coaches and jocks. Most mean little on election day. But politicians believe that football coaches are among the most trusted and respected of public figures. So no campaign bandwagon is complete without at least one coach.

" basically, the endorsements game always usually winds up as a wash," says James Brady, Connally's press secretary. "We all get the same types. And then we reach a point of endorsement parity."

Usually, this comes at about the same time that endorsements become a parity.

In 1976, for Carter, this point came on June 9.On that day, Carter won the first of his big-name endorsements -- the late mayor Richard Daley of Chicago and two onetime opponents, Sen. Henry Jackson of Washington, and Gov. George Wallace of Alabama. Populist candidate Carter had to break the news to the press that he had some endorsements after all (and that they assured him the nomination).

So he walk into his home in Plains, took off his business suit, and put on blue jeans and a denim jacket as a suitable costume for the cameras. Carter conceded later that he had wanted those endorsements all along. But he said he just didn't want to look like the sort of politician who wanted endorsements "so I took off my clothes and put my blue jeans on -- and then publicly made his first move in The Endorsements Game.