This is the season for video games and home computers, and Office of Management and Budget Director David Stockman had something of the kind on his private Christmas list, it turns out.

At Stockman's request, the Office of Management and Budget is preparing a computerized "OMB Scorekeeping Unit" to enable it to keep up with budget changes that tend to come in a blur when Congress reaches budget deadlines, as it did in November.

The plan is still confidential because of "sensitive" personnel aspects, but copies of the plan were left in a Northern Virginia taxicab accidentally last week by one of the OMB's top officials. After waiting several days for the OMB to retrieve the documents, some of the drivers got curious and began passing them around. Copies reached The Washington Post yesterday.

"We notified them OMB four days ago," Warren Anderson, manager of Red Top Cab Co. of Arlington, said yesterday. He said he hadn't looked at the papers. "It's confidential stuff. I know that," Anderson said.

The need for a fast budget scorekeeping system became painfully apparent during the budget crunch just before Thanksgiving when billion-dollar differences in estimates between the OMB and congressional analysts added to the bad feelings and sense of disorder.

"The absence of up-to-date scorekeeping and rapid output-response capability is a serious problem," OMB Executive Associate Director Glenn R. Schleede observed in one memo.

There is no way now to keep overall budget numbers up to date as Congress makes hour-to-hour changes in specific programs and policies, the OMB aides complained. The software of existing OMB computer systems isn't designed for the task.

OMB's Fiscal Analysis Branch provided four persons for such tasks last year, said OMB aide David Mathiasen in another memo, but that proved "totally inadequate."

Stockman--who was obliged to do some of the totaling with a hand calculator under the gaze of Senate leaders--apparently is determined to avoid a repeat of that spectacle.

OMB spokesman Edwin L. Dale Jr. confirmed that the scorekeeping system is in the final stages of preparation. "We hope to have it ready in early February, by the time the budget is presented," he said.

There was no word on whether the system will come equipped with joy sticks.