When it comes to health-care math, sometimes the numbers don't add up for Florida Gov. Rick Scott.

As Scott's administration this week submits a request to the federal government to trim the amount of time people have to apply for Medicaid coverage, the state's estimate of $98 million in savings associated with the change has come under fire from health-care providers who contend the impact is much greater. Providers also allege that the number of people impacted will exceed the 39,000 projected by the state.

The providers' arguments are bolstered by a 2017 letter sent to the federal government by the secretary of Scott's Agency for Health Care Administration. The letter described savings associated with the change as high as $500 million.

That contradiction, however, is not the first time that a Medicaid cost analysis by the Scott administration has been called into question since he became Florida's chief executive officer in 2011.

"I would say that Governor Scott's Medicaid numbers should be carefully and independently analyzed," said Joan Alker, executive director of the Georgetown University Center for Children and Families who has extensively studied Florida's Medicaid program. "I certainly regard them with a healthy degree of skepticism."

Scott, who is running this year for U.S. Senate, made his fortune in health care and understands its many nuances. He led the Columbia/HCA hospital company before it forced him out amid an investigation into federal health care fraud. Scott was never charged in the case, but the company paid a then-record $1.7 billion fine.

John Tupps, a Scott spokesman, defended the governor's handling of the Medicaid program, which will total about $28.3 billion in the upcoming year.

"The bottom line is that Florida's Medicaid program is operating at the highest level of quality in its history," Tupps said. "These claims are unfounded and have zero impact on the services that Florida delivers to patients."

But the Scott administration's cost analyses sometimes have not made sense to Medicaid experts or health and social-service providers in the trenches.

Florida's disabled community cried foul just months after Scott's election after the governor ordered his chief inspector general to conduct a review of what is known as the home and community-based waiver program at the state Agency for Persons with Disabilities. The March 2011 report included budget information which, critics maintain, inflated a deficit at the agency by $75 million.

In 2012, Scott contended Florida's Medicaid costs would increase by $1.9 billion if the state were to expand Medicaid under the federal Affordable Care Act. The contention was disputed at the time by state economists and was later revised.

In 2017, Scott announced Florida had been approved for $1.5 billion in each of the next five years for the Low Income Pool program, which funnels additional money to hospitals that serve large numbers or poor and uninsured patients. Scott also praised President Donald Trump's administration for its willingness to work with the state.

So-called LIP funding is a supplemental Medicaid program and, like other programs, requires local matching dollars to draw down federal funds. In Florida, that match has come from counties and local hospital taxing districts whose interest in continuing to put up the funding waned after the Obama administration restricted how LIP dollars could be spent.

At a press conference following the announcement, Scott dismissed concerns that the local matching money would fall short and that the full $1.5 billion wouldn't be available, saying at the time Florida would "get more flexibility in a lot of things with regard to the Medicaid program."

But the final tally of LIP funding in fiscal year 2017-2018 is about $731 million, less than half of what is available, because of a lack of matching money.

Tupps dismissed the criticisms and placed blame on hospitals. He said Scott negotiated the $1.5 billion LIP program and "it's up to them to draw down the federal funding."

Moreover, Tupps said the announcement that Florida would have $1.5 billion isn't inaccurate because "this is year one of a five-year commitment."

The latest dispute centers on a proposal to trim a length of time people have to apply for the Medicaid program from the current 90 days to a maximum of 30 days.

Federal law requires states to cover the costs of medical bills incurred up to three months prior to the time people apply for Medicaid. So long as people qualify for Medicaid and the services are covered, the hospital, doctor and nursing-home bills that accrue during that period will be absorbed.

The longstanding policy, officially known as "retroactive eligibility," protects the poor from unpaid medical bills that they cannot afford and helps ensure that hospitals and nursing homes are paid for services they offer to Medicaid-eligible people.

Earlier this month, AHCA said 39,000 people would be impacted by a switch to a 30-day period and that it should save $98 million. That's a drastic reduction from the $500 million in savings that AHCA Secretary Justin Senior said could be saved in a March 2017 letter he sent to former U.S. Department of Health and Human Services Secretary Tom Price.

Senior said claims that accrue during the 90-day period are paid outside of the state's Medicaid managed-care system. That means Florida pays for "uncoordinated and potentially inappropriate utilization of medical services."

Months later, the Scott administration floated the proposal to the Legislature for consideration during the 2018 session. Ultimately, the $98 reduction was included in the new state budget that begins July 1.

At two public meetings this month, health-care providers testified that they believe the change in policy will lead to much larger reductions in spending than the $98 million the agency cited.

"It does appear low from what we're seeing anecdotally, but I don't have the numbers to back that," said Stephen Harris, vice-president of payor and government affairs for Tampa General Hospital.

What Harris does know is that Tampa General discharged 4,200 "straight Medicaid" patients last year, meaning they were not enrolled in Medicaid HMOs. And while he hasn't conducted an analysis of each of those patients to determine when they applied for Medicaid, Harris suspects many of them were enrolled retroactively.

Mallory McManus, a spokeswoman for the Agency for Health Care Administration, defended the $98 million figure and distributed backup details showing how the agency reached those conclusions.

But the agency provided no backup data on how it reached the $500 million estimate it touted as savings in 2017. Moreover, the agency now says the figure is irrelevant.

But when pressed for an answer, McManus attributed the huge difference to the Legislature's decision to exclude pregnant women and children from the policy change.

"As you know, the majority of the Florida Medicaid population is children," she added.

But the chances of McManus' explanation being accurate are nil because excluding pregnant women and children wouldn't lead to such a large reduction in the estimate, Alker said.

"While children account for about half of Florida's Medicaid enrollment, they constitute only 20 percent of total spending. And the good news is that most kids don't spend time in the hospital or in nursing homes — both of which are very expensive and likely the drivers of retroactive eligibility spending," Alker said. "Thus, the likelihood of a huge chunk of retroactive eligibility spending being due to children is close to zero."

The Agency for Health Care Administration used 2015 data in coming up with the $98 million projection. A News Service of Florida analysis of the 2015 data shows that bills for poor and elderly people who don't qualify for Social Security account for about half of that total. Another $31 million is attributed to bills for elderly patients who qualify for both Medicare and Medicaid.

That's not surprising to Tampa General's Harris, who also worries that, if the retroactivity change is approved by the Trump administration, it would become more difficult for hospitals to find skilled nursing facilities that are willing to accept patients that hospitals want to discharge.

"Knowing that the patient is Medicaid eligible is a big deal," he said. "If we can't tell them (nursing homes) that, it makes it more difficult for us to place them."