In the financial-aid showdown between the world’s richest universities, Harvard may have beaten Yale to the punch when it announced a sweeping new initiative last month. But unlike The Game last November, Yale may have been able to mount a comeback to tie the score.

On the surface, Yale’s new financial-aid plan, announced Monday, seemed to match Harvard’s blow for blow. But because Yale still lags behind Harvard in enrolling low- and middle-income students, the University will still budget over 10 percent less in financial-aid funding per student next year than will Harvard, according to an analysis conducted by the News.

And therein lies the difficulty in determining a winner between the two new initiatives. Five weeks after Harvard dared the world of higher education to match its sweeping initiative, Yale appears to have done just that, an early examination of both plans indicates. But even when accounting for Yale’s smaller size, the University has significantly fewer students eligible to receive the additional money, meaning Yale students will benefit less from the new aid package than will their Cantab counterparts.

On Dec. 10, Harvard announced it would increase its financial-aid budget from $98 million to $120 million next year, an increase of more than 20 percent. Per undergraduate, that equaled just over $18,000 in aid, on average.

But in an interview only hours after Harvard made its announcement, University President Richard Levin vowed that Yale would soon unveil its own “major financial-aid initiative,” and one that would be “commensurate with Harvard’s changes.”

The suspense built. Few details about Yale’s forthcoming initiative emerged, but a magic number did: $33 million, the amount by which the University would have to boost its financial-aid budget in order to equal Harvard, adjusted for the two schools’ differing enrollments.

Then Monday came, and the University unveiled its own plan. Under the new initiative, the University will increase its financial-aid budget next year from $62 million to $86 million, a stunning increase of nearly 40 percent, or $24 million.

A stunning increase, some students said. But by the numbers, the initiative did not measure up. Under the new aid plan, Yale will budget $16,300 per student in aid dollars — 10 percent less than what Harvard said it would budget under its new policy.

The reason: Yale students are wealthier than their Cantab peers, meaning fewer students actually will receive the enhanced aid packages. Forty-three percent of Yale students are on financial aid this year, compared to two-thirds of Harvard students. And when the financial-aid plans are compared not on the basis of aid per student but on the basis of aid per student receiving financial assistance, under the new policies, Yale actually comes out on top.

Still, because fewer students will benefit, some observers said that could make Yale’s move less meaningful than Harvard’s.

“It’s a calculation,” said Steven Roy Goodman, an educational consultant and admissions expert in Washington, D.C. “If a university gives full financial aid to every student who comes from the wrong side of the tracks, but then there are [few] of those students in the applicant pool, then it’s a hollow announcement.”

But if all goes well, Yale’s aid spending will increase in future years. Levin said he hopes the Yale’s new aid plan gets more expensive to sustain over the coming years, because that would signify an increase in socioeconomic diversity among Yale College students.

“If we achieve our objective, our cost will rise,” he said.

But Goodman was not the only one to doubt the depth of Yale’s changes.

Reecy Aresty, a financial advisor and college aid expert in Boca Raton, Fla., said Yale’s announcement, like Harvard’s before it, was more about showmanship than substance. Committing its resources to lowering tuition would be a better use of the University’s time than devising grandiloquent marketing pitches to counteract Harvard, he said.

“Yale is playing the game, no question about it,” Aresty said. “What’s Harvard going to do, raise [their limit to receive aid] to $250,000 next year to outdo Yale? And then what are you going to do, raise it to $300,000?”

Still, while Harvard may have pulled away with its announcement five weeks ago, after Monday, Yale appears to have drawn even. In the realm of financial aid, an arms race seems to have begun, said Robert Shireman, the executive director of The Project on Student Debt, a nonprofit group.

“We expect more institutions — and not just Ivy League schools — to announce plans to eliminate loans and reduce costs for low- and middle-income families in the coming weeks and months,” he said in a statement.

-Samantha Broussard-Wilson contributed reporting.