Mayor Bloomberg has told New Yorkers he deserves four more years because crime rates in the city have fallen, the New York economy is back on track, and he is reforming the schools.

The mayor, who has an unshakable faith in figures, has told voters to look at the numbers. So The New York Sun has done just that, comparing New York City’s performance on crime, the economy, and education with the records of the nation’s three other largest cities over the same period. The Bloomberg report card is mixed.

Unquestionably, not all of a mayor’s successes and failures can be quantified, and, whoever runs City Hall, many other factors, from global energy prices to climate, influence the local economy, for example. Nevertheless, statistics will be a frequent weapon in the campaign battles of the next six plus months.

Consider crime. While New York has been dubbed the safest big city in America during the three years Mr. Bloomberg has been in office, other big cities have had a steeper decrease in their crime numbers than New York, according to national figures compiled by the Federal Bureau of Investigation.

But Mr. Bloomberg’s critics, including Steven Shaw, one of two men who hopes to beat Mr. Bloomberg in a Republican primary, see it differently. “Reduced crime is a national trend, not a remarkable accomplishment of the Bloomberg administration,” Mr. Shaw told the Sun. “If you look at the rate at which crime is falling in New York, it is falling slower than lots of other major cities.”

The FBI figures bear that out. In 2003, rape reports in New York declined 4% from the prior year but murders rose 1.7%. By contrast, Los Angeles – where the police chief is a former New York top cop, William Bratton – saw the steepest decrease in crime, with rapes declining 13% and murders 17%.

And in the first six months of last year, the latest figures available from the FBI show, the murder rate fell 9.7% in New York City but Chicago managed a 25.1% decrease. Forcible rape was up 2.1% in New York, but 13.8% in Los Angeles. Aggravated assault was down 2.6% in New York and 12.8% in Los Angeles.

Bloomberg administration officials have said they are working from a lower crime base – all the easy reductions in crime were achieved during Mayor Giuliani’s two terms – so it is harder to bring down crime when it is already at historic lows.

They point with pride to the drop of 3.6% in the city’s violent-crime rate in 2004, compared to a nationwide drop of 2%.

Another favorite statistic of the administration: Of the 217 cities reporting populations greater than 100,000, New York ranked 203rd in terms of crime, between Alexandria, Va., and Ann Arbor, Mich.

“If you had told New Yorkers when Bloomberg took office that murder and other index crime numbers would continue to decline, it would have been hard to believe,” a Baruch College political-science professor, Douglas Muzzio, said. “He is campaigning on crime with good reason. He has a good story to tell.”

On the economy, by contrast, Mr. Bloomberg came into office having nowhere to go but up. He was elected just eight weeks after the September 11 terror attacks, which hobbled the city’s economy. In 2002, the economy underwent a 3.8% contraction, according to figures from the city comptroller’s office. In 2003 it contracted a further 2.4%, and it saw a resurgence only in 2004, when it grew by 2.4%. The national economy growth rate in 2004 was recorded as 4.4%.

In 2002, Chicago, Los Angeles, and Houston all saw their economies grow by well over 3% in 2002.The next year, 2003, the Los Angeles economy grew at a 5% clip, while Houston’s grew by 3.2% and Chicago’s by 4.3%, according to figures from the U.S. Conference of Mayors.

New York under Mr. Bloomberg fared better than the other three cities, however, in terms of employment and job growth.

In 2002 New York’s jobless rate was 6.4%, in 2003 it was 6.5% but in 2004 it dropped to the national average of 5.5%, according to figures from the Bureau of Labor Statistics.

Houston’s unemployment rate, meanwhile, was higher in 2004 than in 2002. Chicago’s and Los Angeles’s were down last year but remained above the national rate.

In New York, an increase in 49,200 jobs created was recorded in 2004, while Chicago lost 52,000 jobs, Los Angeles lost nearly 120,000 jobs, and Houston’s total remained unchanged, according to numbers from the federal bureau.

The mayor’s record on education, too, appears to be mixed, when New York City students’ performance is compared to figures from other big cities and the nation as a whole. While Mr. Bloomberg managed to wrest control of the school system from the state early in his administration, his promises of better test scores for the city’s public schoolchildren did not immediately materialize. Experts said, though, that it would take more than a couple of years to see a marked difference in test scores in the 1.1 million student system.

The National Assessment of Educational Progress, or NAEP, provides a view of how schoolchildren in different states and big cities are faring. Comparing city scores with each other is difficult because there is no exam that is administered to, say, fourth graders all around the country, and the NAEP test is administered only to samples of students.

And the NAEP scores have their own shortcomings. The NAEP doesn’t provide scores for individual students or schools but instead looks at achievement in particular subjects – such as reading and mathematics – for states, regions, and urban centers. The NAEP crunches data from the U.S. Department of Education, the Institute of Education Sciences, and the National Center for Education Statistics to come out with its Nation’s Report Card.

The NAEP reading scale ranges from 0 to 500, and the NAEP exams used in the latest comparisons were administered before most of Mr. Bloomberg’s education changes, such as the new curricula, were in force. Students took them in February 2002 and February 2003.

“NAEP tests were administered with the students having very little time in the new program,” a former Reagan Department of Education official, Diane Ravitch, said. “So they don’t really show anything about Bloomberg’s reforms specifically. They haven’t had any time to work.”

All the same, education analysts said they provide a good frame of reference in comparing where New York stands in relative terms. At 210, New York City’s average score on the NAEP fourth grade reading exams was higher than the three other biggest cities, but it was 6 points below the national average.

Fourth-grade reading scores in 2003 were up 2% over the previous year in New York City, while Chicago saw a 2.6% increase in its reading scores for fourth-graders in 2003 compared to 2002. The scores there, however, are still significantly below New York’s, at 198. Houston saw a 0.5% increase in its scores, to 207, and Los Angeles’s inched up 1.6%, to 194.

In the 2003 mathematics exam for fourth-graders, New York City’s students scored 226, Houston’s averaged 227, and the national public-school average was 234. Chicago’s students scored a full 12 points below New York’s, at 214, and Los Angeles’s students scored 216.

There has been an uptick in math scores nationally in the past two years, according to the Council of the Great City Schools, which tracks student performance on state tests in the nation’s 65 largest cities.

“Well over half (70.8%) of the Great City School districts have improved math in all grades tested,” the group said in a recent report. “Some 41.5% of the city school districts improved their reading scores in all the grades tested.”

That trend underlines how it is hard to say definitively that Mr. Bloomberg’s takeover of the schools has made any difference at all in terms of student test scores. It is not for lack of trying, but experts said it is just too early to tell.

The mixed messages in the mayor’s numbers on crime, the economy, and education brought a mixed judgment from a professor at Cooper Union, Fred Siegel, who is the author of a forthcoming book on the Giuliani mayoralty.

“It is hard to see that there is any important trend he has initiated,” Mr. Siegel said of Mr. Bloomberg. “He can be praised for not screwing up what was already in place. That’s all.”