Bay Area home sales sagged last month — the slowest September in three years. But as sales dwindled, in a reflection of the region’s shrinking home supply, buyers continued to bid up the region’s notoriously high prices.

The median sales price of a single-family home in the Bay Area jumped 15.5 percent on a year-over-year basis, the sharpest gain since May 2014.

First-time buyers face a “daunting challenge here,” said Andrew LePage, research analyst for the CoreLogic real estate information service, which on Friday issued its latest report on the housing market for the nine-county region. “Can you imagine being out there looking for anything under $500,000?”

To illustrate just how dire the affordability crisis has become, he offered these numbers: In Santa Clara County, where the median price of a single-family home now stands at $1,075,000, homes selling for $500,000 or less accounted for just 8.7 percent of all sales last month – down from 12.8 percent of the single-family homes sold in September 2016. Meanwhile, houses selling for $800,000 or higher, accounted for 75.8 percent of all sales – up from 62.4 percent a year earlier.

Across the bay in Contra Costa County, a relative bastion of affordability, the share of homes selling in the lower-price ranges is also shrinking. Homes selling for $500,000 or less accounted for 37.5 percent of September sales in Contra Costa County – down from 50.2 percent a year ago. During the same time period, the share of homes selling for $300,000 or less was halved, dropping from 14.1 percent of all sales to 7 percent.

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For the nine-county region as a whole, the median price last month was $768,000, up from $665,000 in September 2016.

It’s a sellers’ market, yet many potential sellers are choosing to sit tight.

They don’t want to pay capital gains penalties, or they prefer to sit on their equity, or they can’t imagine where else they would move in the region to find something remotely affordable, agents have observed. These tendencies play out in city after city: The number of active listings plunged year-over-year in September by 38 percent in Concord and 23 percent in Walnut Creek, according to the Bay East Association of Realtors.

Consequently, when a home hits the market, said Kevin Kieffer, a Keller Williams agent in Walnut Creek, “There’s no lingering. None. Stuff that goes for sale, goes.”

In Silicon Valley, agents lately have adopted the strategy of listing homes below their market value to attract buyers who then bid up the price, almost like an auction. Looking at transactions between Sept. 12 and Oct. 15, Alain Pinel agent Mark Wong counted nearly 70 sales for $200,000 or more above the asking price in Sunnyvale, Cupertino, West San Jose and Saratoga. Of those, he said, seven sold for at least $500,000 above asking price.

He and other agents said they have noticed a growing number of off-market sales, where agents quietly hear about soon-to-be-available properties and notify clients who make offers – avoiding the competitive bidding of the marketplace.

“There’s a ton of that,” said agent Joban Brown, of Fisher and Brown Real Estate in San Jose. “It kind of makes it unfair if you’re in the market, looking.” On the other hand, he said, if a buyer is lucky enough to plug into an off-market sale, he or she “may find something that’s more of a fair value.”

Alfred Au Yeung did.

He and his wife Candice, who are Kieffer’s clients in the East Bay, plan to buy between one and three houses a year over the next five to seven years, converting them into rentals to generate income for retirement. So far this year, they have bought three, including one they found off-market in Pacheco, in Contra Costa County, where they paid $545,000 and closed the deal about a month ago.

“We came in, made an offer and they accepted right away,” said Au Yeung, who works in sales for a telecommunications company. Already, the house — three bedrooms, two baths, 1,200 square feet – is rented: “We’re getting $3,000 a month. There will never be a short list of renters in the Bay Area right now, especially with the way prices are going up for houses.”

Still it can take months for many buyers “to wrap their head around the market and be as aggressive as they need to be,” said Sereno agent Roxy Laufer, based in Saratoga. “The prevailing psychology is, ‘Oh my God, it’s going to go for hundreds of thousands over asking.’”

Her client, Hitesh Patwari, who works in tech in Redwood City, can attest to that.

When he and his wife, longtime renters, began looking for a house last year, they discovered that “the market was crazy,” he said. They quit looking, then got up their nerve and re-entered the hunt early this year.

Setting their budget at around $850,000, they began looking in areas they hadn’t previously considered: San Jose’s Evergreen and Blossom Valley areas, as well as Milpitas and Fremont. Everywhere, he said, “Prices were going up so quickly. They were coming on in the high $700,000s and selling for $925,000 or $930,000. We lost two or three offers where we just didn’t feel sure enough to go that high.”

They reconsidered their budget, figuring out a way to stretch their offers – and then a house in Fremont caught their eye. With three bedrooms and two baths, it was a modest place, only 1,300 square feet. But “it was quite cozy and in top-class condition.” It even had a sizable backyard – important because the couple hopes to have children.

“We said, `That’s the place,’” Patwari recalled.

The house listed for around $825,000. They bid $960,000 – one of 15 offers, though not the highest.

“To win the house, when you don’t have the highest offer — nowadays this rarely happens, especially in the Bay Area,” Patwari said.

He wonders if the personal letter he sent to the seller may have proven persuasive.

“I think that was it,” he said. “But still, I am shocked.”