This week, school districts across New York State have been firming up their 2012-13 budget proposals — the first to be affected by the state’s new property tax cap. But in the run-up to the May 15 budget vote, some taxpayers may have trouble reconciling what they heard about the cap from Albany last year with what’s about to unfold in their school districts — and what they’ve already seen in their newly “capped” county and municipal tax bills

For example, while it is advertised at 2 percent, the tax cap will actually vary from district to district, although it typically won’t be much higher. What’s more, the change in individual property tax bills will not necessarily conform to the cap.

In other words, your mileage may vary.

To understand why, it’s important to understand that the cap applies to school tax levies and not tax rates. The levy is the total amount of property taxes needed to support the budget. The rate is computed by dividing the assessed value of all properties into the levy.

In a school district with a $2-million levy and a property tax base of $100 million in taxable assessed value, the rate will be $2 per $100, or $6,000 on a house assessed at $300,000. A levy limit of, say, 2.5 percent should hold the tax increase on that house to $150 — all else being equal.

But in the world of property taxes, all else seldom is equal from one year to the next. Some properties will decrease in value, while others will increase. So, in the end, even if the levy is raised by no more than 2.5 percent, some homeowners will end up paying more than that, others less.

From an individual taxpayer’s standpoint, directly capping tax rates might look like a better way to provide relief. But compared to a levy limit, a tax-rate cap would be more complicated and ultimately counterproductive to implement. A frozen rate would not stop taxes from increasing when assessed values increase — unless assessments, too, were capped.That comparatively draconian approach was taken by Proposition 13, California’s 1979 tax relief initiative, which capped property tax rates at 1 percent of full value and tightly limited assessment increases above the acquisition value of properties. As a result, California has some of the lowest property tax burdens in the nation — but, nonetheless, it also has a comparatively high combined state and local tax burden, and a local government sector heavily dependent on highly variable state aid and revenue sharing from Sacramento.

Gov. Andrew M. Cuomo wisely modeled New York’s tax cap law on Proposition 2½, the 1980 Massachusetts initiative limiting annual growth in local property tax levies to 2.5 percent. Like the Massachusetts law, New York’s cap formula includes exceptions and offsets that can make next year’s “allowable levy limit” lower or higher than the 2 percent starting point.

The biggest potential cap adjustments for school districts include changes in spending on voter-approved capital expenditures, the revenue yield from “payment of lieu of tax” deals with some property owners, and part (but only part) of any increase in pension contributions for district employees. The tax cap also excludes taxes generated by new property development in the past year.

In most cases, the impact of these exclusions on the school cap appears to be small. According to preliminary estimates compiled by the state comptroller’s office, the median cap on tax-levy growth in school districts next year is 2.7 percent.

Anything above the limit will require passage by 60 percent of the voters. This certainly raises the bar — but not necessarily to an insurmountable level for all districts. Last year, when proposed school tax increases averaged less than 3 percent, roughly seven in 10 budgets passed with more than 60 percent of the vote. Even in 2004, when proposed school budgets carried average hikes of 8 percent, more than half passed with more than 60 percent of the vote.

The real game-changing element of the tax cap law is a two-strikes-and-you’re-out provision for school boards: If any proposed budget, even one holding taxes under the cap, is rejected in two submissions to voters, or withdrawn after failing to pass on first submission, the allowable tax increase is zero — no exceptions.

Faced with that risk, how many school districts will propose tax increases above the cap? We’ll know more in a couple of weeks, when the state releases the next school Property Tax Report Cards.