Deciding on a law school is a numbers game: cost versus reward.

The stick is $150,000+ for studies, but the carrot is a great-paying job. But maybe not, according to recent graduates from the city’s elite law schools, who relied on job placement after getting their sheepskins.

Critics of local law schools say Columbia, NYU and Fordham overpromise the economic benefit of a degree, inflating the number of students who find employment after graduation — and how much those jobs pay.

“My life will be fairly uncomfortable for the next several decades,” said a third-year Columbia Law School student who borrowed $170,000 to attend and ended up with a job in which he will earn between $50,000 and $60,000.

“But when you look at how big a bite $170,000 takes out of you, even over 25 years, it’s really going to sting. . . . Was it worth it? The answer is no,” he said.

The student estimated that roughly 35 percent of his class are in a similar position in terms of the salaries they are expecting — a disappointment compared to the glowing portrait of employment opportunity and affluence with which the school had presented them.

After an inquiry by The Post, Columbia Law School last week published a spate of new data detailing its employment rate, which dropped from a previously reported National Association for Law Placement’s 98.6 percent level to 96.5 percent.

The new data include information such as the number of jobs that require bar admission, the percentage of students reporting salary information, and the fact that all the jobs reported are full time, specifications that schools are now required to report to the American Bar Association, and which have become standard to share online.

But the new numbers quickly raised questions among legal scholars. Paul Campos, a professor at the University of Colorado Law School, pointed to discrepancies between the number of students reported by Columbia to have gotten big-law jobs — employment at a large firm with a salary of $150,000 a year on average — and those counted in a corresponding report by the National Law Journal (NLJ).

“According to Columbia, somewhere between 285 and 298 of its 2010 graduates were working for the top NLJ 250 firms. NLJ 250 firms reported only 239 2010 Columbia grads working for such firms. This is not, needless to say, a trivial discrepancy,” he posted on his blog. Campos approximated a similar difference in the case of NYU.

Noticeably missing from Columbia’s numbers is a breakdown of school-funded jobs — a red flag, as other schools have been called out for creating short-term jobs to temporarily boost the percentage of students employed for the ABA survey, which counts the employment figure nine months after graduation.

NYU Law School — which also revised its numbers after The Post contacted it — revealed that 38 students in the class of 2010 counted as employed held temporary positions paid by the school. Students earned $2,000 a month, and the positions lasted between three and six months.

Fordham Law School includes a footnote, in fine print, that 14.7 percent of its employment was comprised of school-funded jobs. While Columbia acknowledged that it offers fellowships to students seeking employment, the school could not say how many jobs it had funded for the class of 2010, or whether they were comparable to the prestigious one- and two-year opportunities advertised on its website.

One student claimed the school offers six-month fellowships to unemployed students at the end of their third year and called the jobs “a last- resort option.”

On campus, the goal, and expectation, for most students, is to get a big-law job earning $150,000 out of the gate. “To want a big-law job and not get one is a pretty big deal,” said a first-year Columbia Law student, who noted that many students turn down scholarships from lower-ranked schools in order to attend.

Some students reported having jobs paying $160,000 lined up. But legal-staffing firms reported placing recent grads of both NYU and Columbia in paralegal and support staff positions for as little as $35,000.

“I’ve never seen more attorneys applying for non-attorney jobs,” said Tony Filson, president of Filcro Personnel, a staffing firm in New York.

“They’re all from top schools,” said Maritza Murphy, a legal account manager at DeltaForce legal staffing. “Columbia, NYU, Fordham. A lot of small law firms are hiring them in paralegal jobs because they can get them at a lower cost.”

Brian Leiter, a professor at the University of Chicago Law School, noted that the number of big-law jobs available has decreased significantly. “The [focus on the] highest paid [law school graduates] make it seem like you’ll earn $160,000. There are about 30 to 40 percent fewer of those jobs than there were a few years ago,” he said.

Columbia’s current listing of second-year summer associate positions, which remain at a low 76.7 percent for the class of 2012, after falling from 91.3 percent for the class of 2010, suggests that those jobs are not making a strong comeback.

With average student debts of $127,000 and $125,000, Columbia and NYU fall into the top 22 schools in student indebtedness, according to Brian Tamanaha, author of the new book “Failing Law Schools.”

“I feel ashamed for my family because they expected big things for me, and now I might end up living with them after graduation, which is very disheartening,” said a Columbia third-year student struggling with no job offers.