The Chicago Tribune for years advertised itself, with enduring modesty, as The World's Greatest Newspaper. Last Week, the Trib may have qualified as the world's greatest something else, not necessarily flattering. For $20.5 million it bought 80 percent of the worst baseball team in the National League.

By its action, the Tribune was promising to save the Cubs for Chicago, against any threat the city would lose its failing NL franchise. In that sense, it was the Tribune to the rescue, and the newspaper will be instantly loved in Chicago.

But for how long? The number of club owners with a hold on the affections of a city's fans is not only fewer than few, but begs the challenge to name one. This is because all owners operate in a forbidding system that decrees that for every two teams that win pennants there must be 24 losers. In most cities, fans tend to become fretful after a look at the league's standings, and love for a team owner can grow faint.

It is a misalliance, anyway, ownership of a baseball team by a newspaper, an association more to be avoided than sought. The inherent dangers and embarrassments are many, and in another year, even the next one, a reflective Chicago Tribune could be asking itself: "Wherefore have we done such an ill-considered thing as to buy a ball club? Oh, Wisdom, why did you desert us? Why did we not know of the folly of a newspaper to meddle with the making of the news?"

The instant danger for a newspaper is that a city's fans will tend to view the paper in terms of an inept baseball team it owns: your ballclub is a bumbler and that goes for your newspaper, too.

Sure, the Tribune and the fans will have dreams of pennants of the Cubs. But there hasn't been one for 35 years and the present state of the Cubs, in last place and hopeless, indicates no early end of the famine. For every defeat, every bonehead play, every booted ground ball the Tribune will be guilty by association.

And if the Cubs don't improve quickly, there is a prospect that Chicago fans will direct toward the new ownership the loathing they felt for the last one, which, to cut their losses, sold off so many of the team's stars. t

It was Chicago Sun-Times columnist Mike Royko who, is one sentence, once described both the Cubs' ownership and the team, referring to "The nickel-biting Wrigley family which put a team of clowns on the field year after year."

A newspaper doesn't need this image. The Tribune is more in need of friends in Chicago than critics. It has been in a longtime circulation war with the aggressive Sun-Times anyway, and fans do tend to confuse an inept ball club with the ownership.

Granted, its purchase of the Cubs could be an immediate plus for the Tribune. But it is known that the long haul can beget fans who grow fretful and tend to measure their appreciation of the ownership by the standings of the clubs.

The St. Paul Pioneer Press Dispatch owned that city's baseball team many years ago, "and we were glad to get rid of it," said J. Russell Wiggins, then the editor of that newspaper. "It was too sticky."

The Washington Post once owned part of the Washington Senators' expansion franchise from 1961 to 1964. But its late publisher, Phillip Graham, bought 20 percent of the team only to keep the faith with a consortium of eight other investors he urged to help restore baseball to Washington. The team never was identified as a Washington Post undertaking.

Graham's purchase was a stopgap measure and he rejected permanent ownership. He did not want The Post in the direct line of fire. Three years later The Post gladly sold its shares. Meanwhile, Katharine Graham and her mother, the late Agnes Meyer, found themselves sitting on the board of directors of the Senators, leading Katharine Graham to remark at one point, "Why couldn't Phil have bought something we know something about, like an art gallery?

Another communications empire, the Columbia Broadcasting System, bought and operated the New York Yankees for nine years. It was a disaster. CBS took over a pennant-winning team and never won another pennant. In 1973 they sold to George Steinbrenner for $10 million the team they bought for $11.2 million in 1964. It was the only time in modern baseball history that a team was sold for less than it cost.

Even Merrill Lynch Pierce Fenner and Smith, those pragmatic folks excelled by none in giving the fish eye to a balance sheet, were once bullish on baseball. In the summer of 1980, the firm considered acquiring the White Sox as a possible investment plum for its customers seeking a tax shelter. One appeal of the White Sox for Merrill Lynch was the team's voluptuous $5.5 million carry-forward tax loss. But it was finally concluded that at $20 million the price was not right, although another bidder concluded it was.

The $20.5 million paid for the Cubs did not appear to be a glowing investment. It includes Wrigley Field, but not the land it is built on. Also, the Cub losses for the 1981 season already were projected at $3 million. And Wrigley Field is the NL's smallest park, with a mere 37,000 seating capacity. Yet the brave Chicago Tribune sallied in, even though all baseball was on strike and it would be all outgo with the case flow nil for an unspecified time.

However, the Tribune's purchase of a baseball team could go deeper than that. Perhaps in its thinking was the day when all of baseball would go on cable television, and the revenues would rocket, and the lucky team owners would be in clover. The Tribune happens to be a cable franchise owner.

The catch there is that a bad team would get even more exposure and its newspaper owner even more identified with a bad product. Fans know who owns a bad baseball club, and who to blame.Unless the Tribune can turn the Cubs' history around, it is a no-win situation.

The Tribune's editors have pledged that coverage of the team would be completely objective, and that is believable. But that would not divert responsibility if the city's fans did not like what they saw on the playing field. It says here that newspaper ownership of a baseball team is a bad mix.