Crooked politicians and bureaucrats should note the arrival in Washington of the Better Government Association, a benign name for a team of investigators whose first love is the search for scandal. Several former Illinois public officials who now receive their mail in prison can attest to that.

"The organization's famous formula," says Tom Moore, head of BGA's Washington Office, "is uncovering waste, inefficiency, corruption and fraud in government."

Which, Moore figures, means he'll be working overtime in the nation's capital.

Begun in Chicago about 55 years ago, the BGA was a nonpartisan group charged with finding and endorsing honest political candidates, no small task in the Windy City. The endorsing function was later dropped as the BGA evolved into an investigative organization after sparking a post-World War II scandal; BGA secured and produced for the public a tape recording of some state legislators chortling in a hotel room as they divided a pile of ill-gotten cash.

More recently, the BGA gained national attention by collaborating with newspapers or television in its investigations, sometimes with dramatic results:

In 1976 a BGA-initiated investigation of Medicaid fraud was aired on "60 Minutes." The result: a Senate investigation that found nationwide abuse of the health care system, with waste totaling as much as $3 billion.

Last year, working in partnership with the Chicago Sun-Times, BGA opened a tavern in Chicago appropriately named the Mirage. Hidden cameras and microphones captured city inspectors shaking down the bar "owners" for payoffs, and several indictments resulted from the stories about the operation.

ABC's "20/20" recently exposed the plight of patients released from Chicago mental hospitals with BGA help.

When the founder of Bankers Life in Chicago, John D. MacArthur, died last year, he left instructions that a foundation set up with his $750 million fortune would finance the expansion of the BGA into a nationwide organization. With a $2.5 million, five year grant, BGA opened its Washington office.

Moore left a job as investigative reporter with the Chicago Sun-Times in 1975 to work as a muckraker for Sen. Gary Hart on Capitol Hill. He later spent two years as an investigator on Frank Church's Senate intelligence subcommittee-- "I had the Kennedy account for a little while," says Moore, before he quit.

"Two years in the intelligence business is enough for the watchdog role," he says. "After two years either you love it too much to be effective or you hate it too much to be ofjective. Or both."

He found writing a novel hard-going, and happily accepted the $37,500-a-year job of opening BGA's first office outside of Illinois. His task: to convince Washington newspapers wary of working with outsiders that collaboration can be beneficial even if BGA's means of obtaining information have been historically unorthodox.

"We do whatever is necessary to get information, and we're willing to invest a great deal of imagination and whatever is necessary to get the information," says Moore. "We've never had any reverence for political sacred cows. But we don't expect to use much, if any, undercover work."

For Moore, whose demeanor is more reminiscent of a friendly grocer's than a hard nosed investigator's, digging about in Washington's closet is tough work whose time has come.

"For all the political statements, posturing, press releases and awards, we think hundreds of millions of dollars are being wasted here because no one has either the time, courage or staff to cut it out," he says. "For hiring people I have a kind of tedium test. I give them four copies of the Congressional Record and ask them to call through and come up with four suggestions for BGA investigations. In most issues of the Record there is substantial evidence of waste. Any person who can go through 700 pages of that and come up with something lively and interesting is my kind of guy."