When Ronald Reagan won the presidency, a former economics professor from Utah named Richard Wirthlin became America's new prince of polling, the victor who now collects the spoils. But Wirthlin is learning that the spoils include more than a lot of new business for his polling firm.

During his first year as the president's pollster, Wirthlin has discovered the pain of error and defeat, the sting of competitors' criticism, and the anxiety of a counselor at court whose advice is not always taken. His methods have been challenged by other pollsters, and his rosy view of President Reagan's popularity and the Republican Party's prospects has been questioned even inside the White House, where Wirthlin's most important clients spend their days.

Wirthlin is learning what his predecessor as crown prince, Patrick Caddell, found out in the Carter administration: that the president's pollster is torn between his role as adviser-promoter for his boss and his professional desire to preserve an image of honesty and objectivity. It is a tricky business to wear the robes of the Prince of Psephology.

Wirthlin's robes are grander than those of Caddell or any other predecessor. His firm, Decision Making Information, is doing nearly $1 million a year in polling for the White House and the Republican National Committee. By comparison, Caddell says he had a contract for "less than $250,000" from the Democratic National Committee in 1977, Carter's first year in the White House, and for considerably less in 1978.

Other pollsters say Wirthlin's is more money than is easy to spend. For many weeks last fall he was conducting daily samples of opinion for the White House. DMI conducted 25,000 separate interviews during 1981, building a huge base of data. During an interview in his elaborately decorated Washington office, Wirthlin produced a book five inches thick containing computer printouts exclusively devoted to the attitudes of blue collar workers during the last year.

But the president's pollster has to deal with a lot more than numbers. He has other problems. One is putting the boss in the best possible light.

"Keep in mind," Wirthlin said in the interview, "that between January of '77 and December of '77, according to Gallup, Jimmy Carter's job rating came down 19 points. Reagan's came down two points. Gerald Ford's came down 39 points for the first year..."

Wirthlin recited these numbers from memory. In fact, Carter didn't complete a fall of 19 points until the end of January, 1978, and Ford fell 25 points in his first year, not 39. Wirthlin liked those numbers because they showed a stronger trend for Reagan than his immediate predecessors.

Andrew Kohut, president of the Gallup organization, says that Wirthlin's analysis was all right as far as it went, "but you have to look at the whole pattern to see how the public has reacted to the Reagan presidency."

Reagan's disapproval went up during that first year, Kohut said, much higher than any recent president's. "And he started at a much lower level than any of those others," Kohut added. The month he took office Reagan's approval rating was just 51 percent; Ford's and Carter's first ratings were both 71 percent.

In fact, Reagan's popularity rating as measured by Gallup rose and fell like a Swiss Alp during 1981. Reagan's "trend" in the last half of the year was plummeting downward from a high of 68 percent in May, after the attempt on the president's life, to 49 last month. He ended his first year with a margin of just eight points, positive over negative.

Wirthlin acknowledged that his rating of the president from his own polls is consistently higher than the outside polls' findings. "Keep in mind," he said, "my reading of the president is not based upon job rating alone; it is based on a complex of about 15 attitudinal elements....We ask a lot of very open-ended questions--what do you like most about Ronald Reagan and what do you like least about him--and then we do content analysis, where you're measuring not only pluses and minuses..."

Reagan does not need poll results to help him set his agenda in the White House, Wirthlin said.

"He has some very definite goals clearly in mind and the surveys are not going to change those goals," Wirthlin said. On the other hand, he continued, the surveys can be valuable in understanding the order in which issues should be addressed. Based on polling, Wirthlin believes that the so-called "social issues" like abortion and school prayer are divisive and potentially damaging to the president.

Wirthlin is a regular visitor at the White House. In one two-week period early this month, he said, he had two private meetings with the president. Sometimes he meets with Mr. and Mrs. Reagan together. He also has private sessions with the senior presidential aides, and with the secretary of state, Alexander M. Haig Jr.

What policy or tactical decisions have been influenced by his advice? Wirthlin declines to say, though he acknowledged two instances in which his findings played a role, and another where his advice was rejected.

After Budget Director David A. Stockman's candid remarks to writer William Greider in the Atlantic Monthly magazine caused a political sensation, Wirthlin surveyed popular reaction. When told that some people close to Stockman credit his polls with helping save Stockman's job, Wirthlin nodded affirmatively.

But he added that he could never know "to what extent my surveys and results are being used" to make decisions. White House officials confirmed that it is difficult to separate survey results from other political intelligence.

And in some cases Wirthlin's own advice doesn't always jibe with the conclusions others draw from his polls. In the Stockman case, for example, Wirthlin is reliably said to have felt that the budget director's candor had damaged Reagan politically.

Wirthlin confirmed that he strongly opposed including a long section on Social Security in the televised speech Reagan gave last September in his "fall offensive" for more budget cuts. Wirthlin, sources said, argued that Reagan was very vulnerable on the issue and would be hurt by it. This advice was rejected in the White House.

After his man won in 1980, Wirthlin quickly became the pollster most Republican office-seekers wanted on their team. One of his first clients was Marshall Coleman, the Republican nominee for governor of Virginia.

"Everybody in the campaign was very, very pleased to have Dick," recalled Matt Wirgau, Coleman's political director. "He had a very good feel for Reagan-type coalitions, a good feel for where the electorate was going." He also had a successful record in previous Virginia campaigns.

But Wirthlin miscalled the Virginia gubernatorial election, both on election eve and, more significantly, four months earlier, when the Coleman camp was making key strategy decisions.

Wirthlin did a "benchmark" poll for Coleman last March, which found that he was at least 10 points behind Chuck Robb, the leading Democrat. In July Wirthlin made what pollsters call a "panel-back" survey in which his interviewers called the people who had participated in the March poll to measure any movement in their sentiment.

This showed Coleman ahead of Robb by seven percentage points, Wirgau recalls. There was some skepticism that this was too good to be true, Wirgau says, "But we really believed it because we all wanted to believe it."

This good news persuaded the Coleman camp to stick with the strategy that had apparently been working so well. "It was an incumbent, big lead, everything's-working strategy," charged a prominent Virginia Republican, "and it was all wet...because the poll was a fabrication."

A new Wirthlin poll in September showed Robb eight or nine points ahead, Wirgau says, and newspaper polls agreed.

One problem with Wirthlin's July panel-back poll might have been that he reached just half the original sample of 800, a smaller proportion than desirable for accuracy, according to other pollsters.

Wirthlin says the July poll might have reflected the volatility of the Virginia electorate and the impact of a concerted Coleman media campaign in the late spring.

At the end of the campaign Wirthlin told his candidate he was going to win handily because of a strong last-minute shift. But Robb won the election by seven percentage points. Wirthlin made no excuses for his miscall. "I did become more enthused about our possibilities than the data would indicate," he says.

Other sources who have worked with Wirthlin said the Virginia experience provided him a chastening reminder of the perils of polling.

Wirthlin has a good reputation with many other pollsters. Peter Hart, for example, calls him a talented professional and a friend. Others who have worked with him, however, say that Wirthlin has a tendency to bring his clients better news than a clear-eyed reading of the figures justifies.

Other pollsters, speaking "not for attribution," say they are dubious about some of Wirthlin's methods.

Warren Mitofsky, who administers polling operations for CBS News, has written an article implicitly accusing Wirthlin of using sloppy methodology. Mitofsky is one of several pollsters suspicious of Wirthlin 1980 findings which showed Reagan at least a five-point leader every day after Oct. 18. Nearly every public poll taken in late October showed the race even.

Others in the Reagan campaign, such as Lyn Nofziger, one of Reagan's most senior political aides, also thought their pollster was overoptimistic.

Wirthlin acknowledged that the last poll he took Monday before the voting showed Reagan with a 17 point lead, but he said this was part of a system of "rolling daily averages" which actually predicted a 10-point Reagan victory, which was the final result.

In some cases the differences between Wirthlin's poll results and others' are baffling.

For example, Wirthlin puts great stock in a question posed years ago by Elmo Roper, one of the deans of American polling: "Generally speaking, would you say that things in this country are going in the right direction, or have they pretty seriously gotten off on the wrong track?"

In early December, 1981, Wirthlin's poll showed that responses were evenly split between "right direction" and "wrong track." At exactly the same time, a consortium of Democratic pollsters was conducting a nationwide poll of 1,265 registered voters asking an almost identically worded question. Instead of the 50-50 response Wirthlin reported, the Democrats' poll said that 57 percent thought the country was on the wrong track, while 32 percent said it was going in the right direction, a 25-point difference.

Because of this wide gap, The Washington Post-ABC poll put the same question to a random sample of 750 Americans right after President Reagan's state of the union address last month. In it, 56 percent thought the country was on the wrong track, 39 percent said it was moving in the right direction.

Asked about these differences, Wirthlin said he thought his and the Democratic pollsters' results were "comparable" despite the wide gap between them. He added that it could make a substantial difference where in a poll the "right track, wrong direction" question is asked, because if the question followed others that reminded respondents of uncomfortable things, the negative answers could be higher. Wirthlin said he always asks the question near the beginning of his polls.

A check of the Democratic pollsters' questionnaire revealed that the question also was asked near the beginning of their survey, before any other subjects were mentioned.

Wirthlin also did a poll in January that showed the country's optimism restored--"right direction" responses again outnumbered "wrong track" ones. "It defies all logic," said Caddell, who helped do the Democrats' interview. "You don't need a poll to know that people didn't think things got a lot better between December and January."

Wirthlin has produced a recent poll for Lewis E. Lehrman, a wealthy businessman, on the Republican gubernatorial contest in New York that also differs with other pollsters' findings. Among 357 New York Republicans, Lehrman led state comptroller Edward V. Regan by 26 percent to 22 percent, with 42 percent undecided and 10 percent for other candidates. But a poll by Robert Teeter, retained by Regan, finds Regan ahead of Lehrman 50 to 22, with 8 percent favoring others and 20 percent undecided. Teeter's sample was virtually identical, and the poll was taken at the same time.

Polls by AP-NBC and the New York Post, taken at the same time, also give Regan big leads over Lehrman although they show higher undecideds.

Teeter said he had fewer undecideds because he pressed respondents to say whom they were leaning toward. "But there's no way that guy Lehrman is ahead," Teeter said.

Wirthlin said all the polls agreed that Lehrman had "come from nowhere to be an extremely strong contender." (In the three other polls, Lehrman was favored by 22, 13 and 13 percent of the Republicans polled.)

Wirthlin asserted that even in Teeter's poll, Lehrman had gained nearly 20 points and Regan had lost almost 25 since last fall, a shift of about 40 percent in Lehrman's favor. Teeter confirmed that Lerhman gained 19 points (from 3 to 22) but said Regan had only slipped 5 instead of 25.

Success and his new status as the president's pollster have transformed Wirthlin's life. He has moved from California to a big house overlooking the Potomac in McLean. His firm is growing, and now has 80 fulltime employes. Business is booming. (The firm has a distinctly Mormon cast; virtually all the employes belong to the Church of Jesus Christ of Latter-day Saints.)

Wirthlin was not always associated with conservative Republicans. In 1964 he joined a committee of Utah professors for Lyndon B. Johnson. In 1976, according to former associates, he did some work for Gerald Ford and appeared interested in working for Ford in the general election before signing up for Reagan's unsuccessful campaign.

During 1982, Wirthlin's firm will handle at least 100 campaigns around the country, besides working for the White House and the Republican National Committee. Wirthlin will have time for only four or five of them personally; his employes will do the others.

Wirthlin now seems totally devoted to the man he helped elect president. He recounted a recent luncheon with reporters where one accused him of losing his credibility because he was so upbeat about Reagan's popular standing.

That didn't bother him, Wirthlin said: "The story about where the president's weaknesses are and where the administration has failed is really a story that I don't feel I should tell."

A small man with bundles of nervous energy, Wirthlin is described by colleagues and acquaintances as edgy about his status at the White House. He is said to regard Teeter, a well-known Republican pollster, as a potential threat, partly because White House chief of staff James A. Baker III is known to hold Teeter in high esteem. When Reagan's top political aides retreated to Camp David to assess their boss's position, Teeter was invited as well as Wirthlin. (Teeter and Wirthlin describe each other as friends.)

The fun of his job, Wirthlin said at the end of a 90-minute conversation, is the knowledge that--although he cannot predict political outcomes with certainty--he has "some pretty good tools to look down the path two or three more yards than you could without them."

"If there weren't a Virginia once in a while, it would be a pretty boring kind of occupation," concluded the new prince of psephology.