State and local government officials, stung by costly legal defeats in recent years before the U.S. Supreme Court, are about to open a legal defense center in Washington to help improve their performance.

The new center will help state attorneys general and city attorneys prepare briefs for the court, prepare for oral argument and, occasionally, coordinate "friend-of-the-court briefs" in support of positions favorable to state and local governments, according to Stewart A. Baker, a former law clerk to Supreme Court Justice John Paul Stevens and organizer of the center.

The State and Local Legal Center, expected to open within the next month with two full-time lawyers, was inspired in part by organizations like the NAACP Legal Defense Fund and the American Civil Liberties Union, which traditionally have had a good record of success before the court, frequently in opposition to the governments now following their examples.

Often, the lawyers representing states and cities have never argued a case before the Supreme Court and are outgunned and outclassed by specialists from such organizations. In addition, the local governments have often failed to alert the court through friend-of-the-court briefs to the potential impact of pending cases, an opportunity never missed by their well-organized opponents.

Baker estimated that one-third of the Supreme Court's caseload involves basic questions over the authority of state and local governments, such as their liability in civil rights and antitrust suits, and their power to control police departments, penal institutions and hospitals, and to legislate in the fields of pornography, land use and health.

Baker said a series of decisions since 1978 that dramatically increased the vulnerability of municipalities and state officials to civil rights damage suits has caused special concern.

Last term, the court opened the door to antitrust suits against cities over their handling of cable television franchises.

Baker and James R. Asperger recently published in the Catholic University Law Review an analysis of success rates at the Supreme Court between the 1976 and 1979 terms, during which they said that the state and local governments went up against the ACLU directly or indirectly in 35 cases. The ACLU position prevailed in more than two-thirds of the cases, while the position of the state and local governments prevailed in less than one-fourth of the cases.

Baker said court observers, as well as some justices, have commented "on the fact that the advocacy of state and local governments is among the most uneven of the advocates who appear before the court regularly."

In a 1974 speech, Justice Lewis F. Powell Jr. noted that "some of the weakest briefs and arguments come from these representatives of the public interest" and suggested that "the imbalance in representation" was in part responsible for the "marked trend of the law toward expanded rights of defendants."

Baker said the problem is not that the lawyers are any less capable. They are simply unfamiliar with Supreme Court litigation. An office is lucky if one lawyer has ever argued a Supreme Court case, he said, and rarely has an assistant attorney general or city attorney argued more than one.

In contrast, lawyers for the ACLU and NAACP Legal Defense Fund make frequent Supreme Court appearances and like lawyers in the office of U.S. Solicitor General, are considered among the best.

Baker, now with the Washington law firm of Steptoe & Johnson, has been working to set up the new center, which will be financed with grants from the Pew Memorial Trust of Philadelphia and the Academy for State and Local Government and operated by seven associations of state and local officials, including the National Governors Association and the U.S. Conference of Mayors.