Sheriffs who would lose money under the recommended formula say there is no way to craft a formula that reflects the unique circumstances and programs provided by each sheriff.

"Each sheriff answers to its constituents and its demographics," said Bill Christofori, assistant superintendent at the Hampden County Sheriff's Department. Christofori said some departments, for example, provide regional lockups for municipal police forces or offer educational programming in schools.

Middlesex County Sheriff Peter Koutoujian said his jail transports people to 13 courts and numerous hospitals. He runs re-entry programs for inmates.

"It's because those are the needs of the community that the community asks of them," Koutoujian said. "If you try to bring everyone in line, counties will lose services they rely on heavily."

However, Evangelidis argues there is a vicious cycle: Sheriffs cannot provide services because they do not have money. Worcester has fewer educators and substance abuse counselors, for example, than comparable jails.

"I'm not able to provide people in my community with the same public safety measures that other sheriffs can because of their budgets, and it's frustrating for me," Evangelidis said.

If PCG's recommended formula were applied to each county's 2015 budget, Suffolk and Middlesex counties would lose $22 million and $11 million, respectively. Essex County would get a $32 million boost, while most other counties would get relatively small funding increases or decreases.

The study recommends several variations of the formula for upcoming years, based on different levels of growth in state spending on the sheriffs. In all the scenarios, Franklin, Hampshire, Worcester and Essex counties would receive the biggest funding boosts. Other counties would see their budgets remain flat, decline or receive small increases.

The study also recommends changes in staffing to give each similarly sized jail similar numbers of staff. Currently, the report finds that Massachusetts — which has 4,170 correctional officers and 10,350 inmates — has more staff per inmate than the national average. The numbers of staff are relatively similar among comparably sized systems, except for the largest facilities.

Suffolk County has just over 1,000 staff for 1,600 daily inmates, while Essex County has 570 staff for 1,700 inmates.

There are, however, questions about the accuracy of the data, since not every sheriff's office follows the same standards for keeping data. For example, a jail that hires an outside company to provide food and medical services will be listed as having fewer staff than a jail that employs its own food and medical workers — but really, the jail is paying for the same number of positions.

The report also bases its recommendations solely on inmate and staff counts, but ignores quality measures, such as recidivism rates. It does not consider external factors, such as a county's geographic size, which would impact transportation costs. It does not reflect that some sheriffs get funding to run programs outside jails, such as after-incarceration support.

Koutoujian said no sheriff disputes that certain departments are underfunded, but he disagrees with the contention that any are overfunded. Middlesex County, for example, receives $1.5 million less today than it did in 2009. It has cut temporary employees, hired more full-time staff to reduce overtime costs, limited take-home cars and implemented telemedicine and videoconferencing.

"I don't know that any are overfunded," Koutoujian said. "It is about which shops are underfunded, and all the sheriffs wholeheartedly agree that those who are structurally underfunded should be brought to a budget level under which they can manage their operations."

Reasons for unequal funding

Several factors contribute to the disparity.

The county jails used to be run by county governments, but were gradually brought under control of state government. To some extent, Koutoujian said, funding levels depend on the state's fiscal condition at the time each jail first received state funding.

Hampshire County Sheriff Robert Garvey said his jail is the oldest facility in Western Massachusetts — so while the other counties got funding increases to pay for operational expenses at new facilities, Hampshire County lagged behind. Budget appropriations have not increased in proportion to new programs the county has added.

Evangelidis said when it became popular in the 1980s and 1990s to run more programs out of correctional facilities, Worcester did not do so, so it never received funding to create those programs.

Guy Glodis, a former Worcester sheriff who is now a lobbyist representing corrections officers, said some of it comes down to political clout and who spends time lobbying.

"I'd definitely advocate for a more fair and balanced funding formula," Glodis said.

Whatever the cause, Garvey said funding disparities have a major impact. Hampshire County, for example, has delayed maintenance. And, it may not be able to continue operating a less restrictive "bridge" house — for inmates nearing their release date — without more money. Compared to other Western Massachusetts jails, Garvey said, "Our staff's smaller, our budget's smaller, and we're falling further behind all the time."

PCG's findings are not reflected in state budget proposals for fiscal 2017, which starts this July.

As to whether the report will be considered in future budgets, Dominick Ianno, chief of staff for the Executive Office of Administration and Finance, said, "The administration is currently reviewing the consultant's findings and analysis and will work with the Legislature and the sheriffs to determine any potential changes to the formula."

State Rep. Stephen Kulik, D-Worthington, vice chair of the budget-writing Committee on Ways and Means, said lawmakers "will take a serious look" at the report before writing next year's budget.

"Our desire is to get to a place where every sheriff is getting a fair amount of budget resources to address their needs," Kulik said. "I can't predict when we will be able to devote some time and attention to this, but I'm sure that at some point in the future we will."

Another quirk in the sheriffs' budgets is that every year the sheriffs are underfunded. Throughout the year, lawmakers pass supplemental budgets to give them enough money to keep their facilities open.

"That's frustrating for us in Ways and Means because we want to be able to more accurately and predictably gauge what their spending needs are going to be for an entire fiscal year," Kulik said. "We'd like to make it a more stable and predictable budget item in the future, and now that we have this report, we have an opportunity to really work on it with some serious data and analysis and recommendations before us."