The Bay Area housing market perked up in March as usual, but the median price paid for a home posted its lowest year-over-year gain in four years.

The median price paid for new and existing homes and condos in the nine-county Bay Area was $643,250 in March, up 4.6 percent from February, according to CoreLogic. Prices typically rise between February and March, by 4.5 percent on average since 1988.

On a year-over-year basis, the median price rose for a 48th consecutive month in March, but only by 1.4 percent. That’s the smallest increase over that four-year period.

The median is the price at which half of homes that closed in March sold for more and half sold for less. The median can go up or down based on changes in the location and type of homes being sold. In March there was “a meaningful shift in sales” to more affordable areas, CoreLogic research analyst Andrew LePage said. “That is going to tug down the median.”

Indeed, the only Bay Area counties where sales increased on a year-over-year basis were Contra Costa, Napa, Solano and Sonoma. “People are getting priced out in the coastal markets and heading further inland,” LePage said.

In all nine counties combined, 6,754 homes and condos were sold in March, 37 percent more than in February — close to the long-term average between those two months. And yet, that number represented a 2.9 percent drop from March of last year, the first year-over-year decrease since October and only the second in the past year.

This reflects inventory and affordability constraints. And even though mortgage rates are ultra low, some would-be buyers are still having trouble getting loans.

“One question in the Bay Area and beyond is, will we see a more significant buildup of inventory this spring and summer than we have the last couple years,” LePage said. In March, “there was a seasonal upswing but nothing extraordinary.”

In San Francisco, however, there’s a heated debate over whether the luxury-condo market is slowing.

In early April, Patrick Carlisle of Paragon Real Estate Group issued a report that said while the non-luxury market “remains white hot,” the luxury condo market shows signs of cooling as “thousands of new-construction condos have hit the market in recent years or are arriving shortly, with many thousands more in the five-year pipeline.”

His data came from the Multiple Listing Service, which excludes most newly constructed condos because they typically are not sold on the MLS.

In the first quarter of 2016, the San Francisco market began to diverge, Carlisle wrote. “As of early April, the number of condo listings actively for sale in MLS is up over 40% year over year. … This does not mean that condos are not selling, because many are at top prices. But the demand-per-listing ratio is declining, multiple offers are less common, and more listings are expiring without being sold.” The luxury-condo segment “appears to be most affected.”

For example, 84 percent of single-family homes priced under $2 million sold for more than the asking price in the first quarter, up from 83 percent in the fourth quarter. But only 55 percent of condos priced over $1.5 million sold over asking price, down from 59 percent in the fourth quarter.

The median percentage of sales price over asking price was 12 percent for homes under $2 million, compared to essentially zero for condos priced over $1.5 million.

Carlisle also noted “big jumps in expired/withdrawn condo listings” in the first quarter of 2016 compared with the same period last year. The number of expired/withdrawn home listings was unchanged or down slightly over the same period.

He emphasized that some statistics that “appear to illustrate a cooling of certain market segments in San Francisco, would in most other areas of the country often be considered signs of crazy-hot markets.”

Nevertheless, blogger Wolf Richter seized on the report as evidence that the market is crashing. In a post titled “San Francisco’s Epic Condo Bubble Bursts,” he wrote, “a phenomenal building boom is causing a condo glut that will reach dizzying proportions as new condo towers are completed.” The post also ran on Business Insider.

That prompted a rebuttal from Polaris Pacific, the selling agent for several large condo projects in San Francisco, including the Lumina, Summit 800, 6 Mint and Rockwell. In a post on its web site, Polaris noted that “From 2010 through 2015, approximately 100,000 new jobs were created in San Francisco. During that same time frame, only 10,000 housing units were produced.”

In an interview, Garrett Frakes, managing partner of Polaris Pacific, said that “the overall market slowed as we got into the second half of 2015. It has been pretty healthy since then. If you are traveling at 95, then slow down to 60 or 65, you are still going fast, not as fast as you were before. I think we have probably slowed to 60 or 65.”

He said the Paragon report “didn’t comprehend the nature of the pipeline” in San Francisco. The Paragon report said that as of December, there were about 62,000 housing units of all kinds — luxury condos, rental apartments, market rate and affordable units, and social project housing - in the relatively near-term pipeline,” the next one to six years.

Frakes said 62,000 units “is about a 20-year supply. Many of those projects will never come to market,” he said.

At the Rockwell, which has 229 market-rate homes, about 90 percent are sold. And at the Lumina, “we are about two-thirds sold,” Frakes said. Out of 656 units in four buildings, only 220 are left to sell. “The market feels relatively healthy,” he said.

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Blog: http://blog.sfgate.com/pender Twitter: @kathpender