Making sense of state aid for schools is like touching air.

You can’t see it, but you know it’s there. And if there isn’t enough of it, you’re in trouble.

“It’s complicated, but it isn’t,” is how one superintendent described the varying amounts of state aid to local districts.

Gov. Andrew Cuomo released his third state budget last week, and it recommends $21.08 billion in money for education in the 2013-14 school year.

That’s 4.4 percent more than schools got for this year.

But that doesn’t mean every school district is in line for a 4.4 percent increase in aid.

One local district would get nearly 9 percent more in aid, while three others combined would receive nearly $1 million less than this year.

There are different reasons why some districts seem to be getting large increases, while others would remain stable or get less.

Some types of state aid are distributed by formulas, often depending on the need of the district and its students.

Other state aid is a reimbursement that depends on how much districts spent the previous year.

And sometimes the numbers are wrong.

Some examples of the varying amounts of aid in the governor’s budget:

• Sloan goes up 8.72 percent. Sloan would receive $520,911 extra from a pot of money for districts with low wealth and high property taxes.

• East Aurora goes down 4.37 percent. East Aurora would not receive the $369,000 it got this year for instituting full-day kindergarten.

• Cleveland Hill goes up just 0.43 percent. Cleveland Hill’s BOCES reimbursement is down nearly $700,000, and that’s about how much the district was reimbursed this year for a large investment in technology.

The governor divides the $889 million in increased state aid to schools into three categories.

Overall aid would go up 3 percent.

The rest of the increase comes in the form of a $203 million fiscal stabilization fund and $75 million for education reform initiatives, some of which would be competitive grants.

Money in the financial stabilization fund has not been allocated, said Robert N. Lowry Jr., deputy director of the New York State Council of School Superintendents. And it appears the State Legislature will debate how to allocate that fund, he said.

“Legislators don’t want to go back to their voters and say ‘you got less than what the governor proposed,’ ” he said. “Most districts will take [the governor’s proposal] as the absolute minimum they’re likely to get.”

School aid “runs,” – the list of aid broken down for each school district for this year compared with what is proposed for next year – have 42 lines for each district. It is those figures that business managers, treasurers and superintendents pore over to interpret for school boards and the public. The description of the recommended aid is 64 pages long.

After the runs came out late Tuesday afternoon, Iroquois Superintendent Douglas Scofield went home happy, when he saw his district would be getting 6 percent more in aid.

“I was all excited. I was happy. Yes, the governor did something,” he recalled.

But the next morning he examined each line and realized this year’s BOCES reimbursement was listed at $409,000 lower than it should have been, making next year’s BOCES allotment seem like a huge increase.

“As I analyzed it, I said, ‘oh my,’ ” he said. “I pulled it up and started to cry.”

The 6 percent increase would actually translate to about a 1.8 percent increase.

Scofield said the district submitted its estimate of what it would spend in BOCES this year the day it was due, but it must have been several hours after the numbers were run through the formula. He’s confident it will be caught by the state on the next run in February.

The aid numbers are fluid, since much is based on reimbursements. Districts give the state an estimation of what they will spend, but it’s not known until the end of the school year how much a district actually spends.

Sloan Acting Superintendent Andrea Galenski, putting together her first district budget, has extra money under Cuomo’s plan. State aid is projected to increase by 8.72 percent.

This is the first time the district has received money on the “High Tax Aid” line, which is designed to help lower-wealth districts that have high taxes. But because districts have been burned before, she is skeptical.

“When you go from zero to half a million, you want to check and make sure it’s accurate,” she said. “If this is accurate, it certainly is a nice increase.”

But she said it’s not enough to erase a budget gap.

After the governor decides how much money to allot to education, it’s up to the formulas to distribute the money.

Aid in some categories, like BOCES, transportation and special education, depends on what was spent the previous year. Districts get a percentage back the following year, based on what they spent and the wealth in the district.

Wealthier districts would get a smaller reimbursement.

Most formulas have remained stable.

“If a district goes up or down, it’s because of change in the data,” said Lowry of the council of school superintendents.

Then there is the “less is more” line for the gap elimination adjustment, or GEA. That is money the state deducted from districts to fill its budget gap. Things are looking a little better, and the governor has added a line, GEA Restoration, which ends up reducing the gap elimination adjustment. The lower the gap elimination adjustment, the better.

If it’s confusing to the general public, it can be confusing to school district officials, too.

Lewiston-Porter Superintendent Chris Roser said it “stands to reason” that the district would get less aid on the High Tax Aid line, but the district also appears to be losing more than $150,000 on the BOCES and transportation lines.

“We’re befuddled at that as well. Aid is expense-driven. Our expenses have not differed in those areas,” he said.

He said Lewiston-Porter has held the line on its budget, with the tax levy going up a total of 2 percent over five years, and expenses are up only $45,000 over the same period. It has an eight-year contract with teachers.

“We’ve done everything that the governor said we should be doing,” Roser said. “We’ve done our part. The only revenue a school district gets is, quite frankly, through taxes. There is no other pot of money out there.”