They call it "the formula": an arcane scheme as unknowable as the recipe for Coca-Cola that is supposed to determine with mathematical objectivity how the state divides education aid among 677 school districts.
But as every legislator knows, politics, not formulas, actually govern the allocation of school aid, more than $17 billion this year. And guiding that process, which riles Albany every budget season, are a couple of unwritten rules.
No. 1: Every school district will receive more aid every year, even if it loses students or has a tax windfall.
No. 2: New York City's share of an increase in basic state education aid will be capped at 38.86 percent even if its student population grows faster than that. With this comes a corollary: Long Island's portion of the increase will never decrease, even if its student population does.
Gov. George E. Pataki once called the school aid system an incomprehensible "dinosaur" that should be discarded "on the ash heap of history."
And education activists have long complained that the formulas there are actually dozens of them are a stew of political calculations with rules so ingrained that legislators recite them with ironclad certainty, even when they cannot be found in law.
But now, the system is facing its toughest challenge in many years: a lawsuit filed by the Campaign for Fiscal Equity, a group of parent and community groups, resulted in a ruling in 2003 by the state's highest court that students in New York City have been denied a sound, basic education because of the inequities in state aid.
And last week, an intermediate appellate court ruling in the same case found that children in New York City schools are being shortchanged by $4.7 billion to $5.6 billion a year, and directed the Legislature to develop a plan to fix the problem. The plaintiffs in the suit say that without overhauling the formulas, Albany is only taking a "half-step" toward compliance.
Yet despite those rulings, the budget that lawmakers are expected to approve today does little to break from Albany's decades-old rules. Under intense pressure from Mayor Michael R. Bloomberg, the Legislature's budget includes a plan to issue $1.8 billion in bonds to help New York City rebuild aging schools. But it largely keeps intact the system of allocating money for classroom programs.
The Assembly, dominated by Democrats from New York City, has advocated overhauling the formulas to allocate more money to urban and poor areas. But they have met resistance from the Republican-controlled Senate, whose base is in upstate and suburban counties.
On Thursday, the Senate majority leader, Joseph L. Bruno, questioned whether the formulas need to be changed, asserting that "there are high needs throughout the entire state."
"When dollars go out the door, they're going to go and be distributed where the sound, basic education requirement applies, whether it's New York City, upstate or on the Island," Mr. Bruno said. "And we think that we did a pretty good job in that distribution."
There are actually as many as 40 school-aid formulas on the books. The dizzying system is so complex that a long-running joke in Albany keeps tally on how many people understand it: six, says one estimate.
Even the office in charge of sending state checks to local schools finds it difficult to nail down the total number; more than a dozen apparently haven't been used for years.
Lawmakers often view those dormant formulas as standbys, ready for use in case they need a mechanism to justify funneling money to a particular district, education experts say.
In theory, the formulas are supposed to send more money to districts that have less ability to pay for schools through local property taxes, using a number known as the combined-wealth ratio that measures relative affluence.
In reality, those experts say, the process works backward, with leaders determining how much money certain regions will receive and then manipulating the formulas to conform.
Burt Porter, director of education finance for the State Education Department, says that trying to explain the system is like trying to diagram a sentence from "Finnegans Wake."
"We've gotten to the point where we have so many layers, that it's impossible to see how it works without precise technicalities," Mr. Porter said. "The more technical it is, the more easily it can be manipulated. And nobody in the public can get it or debate it."
Even the lawmakers who vote on the state aid for public schools year after year as part of the state budget acknowledge the problems understanding the system. Comparing similar districts across the state proves just how inscrutable that system can be.
Johnstown and Crown Point are both small, rural districts in northern New York, each with a chunk of poor students. Last year, the state sent Johnstown about $6,000 a student. Crown Point received close to $11,000 for each of its students.
One reason? A rule known as "hold harmless" that prevents districts from losing state aid, even if they lose students.
Thus, even though Crown Point has slowly hemorrhaged students over the last few years, the amount of money it receives keeps inching up.
In another example, Miller Place, a well-performing and wealthy district in Suffolk County, receives about 75 percent more in state education aid a student than its counterpart in Bethlehem, a suburban Albany district with similar demographics.
That is partly because costs are higher on Long Island. But it is also because of another rule, known as "shares," ensuring that a certain portion of any increase in state aid will always go to Long Island districts.
"The Senate and Assembly both jealously and tenaciously guard their education share from the state," said Steven Sanders, formerly chairman of the Assembly's education committee and now a lobbyist. "Who benefits the most? I wish I could say the school districts and children, but clearly that has not been the case, and that has not changed."
Even the political calculus that dictates how money is sent to schools is murky. Sometimes, the more power legislators have, the more money their districts receive. Other times, the aid is doled out to protect vulnerable members.
"Once the budget is passed, it is the first thing the legislators are judged on," said Thomas Rogers, executive director of the New York State Council of School Superintendents. "Everyone wants to know: how much money is my school getting?"
To meet those political demands, legislative staff members isolate a formula and then funnel more money into it, thereby ensuring that targeted districts get additional aid, experts and legislators say. A school district with a large number of gifted students, for example, would collect more aid if that formula were weighed more heavily one year.
The result is that while certain politically potent districts may get additional aid, less powerful ones may lose out. Many experts say that kind of trade-off has hurt struggling urban districts like Syracuse. Though its student poverty rate is climbing and its property values declining, Syracuse receives less aid than some more affluent districts.
"Formulas don't reflect the changes in wealth or enrollment," said Robert N. Lowry, of the state council of superintendents. "Instead, you have political reasons that carry more money to particular districts. It's not serving anyone certainly not anyone in the schools."