The San Jose metropolitan area posted the nation’s steepest year-over-year plunge in the number of homes for sale in October — falling by a precipitous 51.6 percent.

With buyers competing for so few listings, San Jose also posted the nation’s sharpest year-over-year rise in the median cost of a home: up 19.2 percent to $1,049,000. That’s according to a new analysis by Redfin, which analyzed 74 U.S. housing markets with populations of 750,000 or more. Nationally, the home supply shrank for the 25th consecutive month, down 12.2 percent from a year earlier.

“Buyers are just flocking from one property to the next,” said Kevin Swartz, a Saratoga-based agent for the Sereno Group. “We’re at this point where they’re just making offers on whatever is available, because it’s so limited.”

The Redfin report also ranks the Bay Area’s three main metro areas as the most competitive markets in the U.S. Combining data for single-family homes, condominiums and townhouses, it ranks San Francisco as the nation’s most competitive market, with 78.6 percent of homes selling for above the list price in October. San Jose ranked second, with 76.3 percent of homes going for above list, and Oakland ranked third, with 63.7 percent of homes selling for more than the asking price.

Bay Area markets also figured among the five “fastest” metro areas in the U.S.

The speediest market was Seattle, where homes typically sold in 10 days, according to Redfin. Second speediest was San Jose (12 median days on market) and third was Boston (14 days). Oakland and San Francisco tied for fourth place; homes spent 15 median days on the market in both metros. Nationally, the typical home spent 44 days on the market, down from 49 in October 2016.

Underlying all these trends are the chronically low levels of homes for sale. Thursday in all of Santa Clara County, Swartz pointed out, only 620 single-family homes were on the market. Adding condominiums and townhouses to the mix, the total still only grew to 745 listings.

San Jose’s 51.6 percent year-over-year tumble in the number of homes for sale was unmatched, though San Francisco had the second steepest decline in the U.S., 28.5 percent. Oakland was close behind, with a 25.5 percent year-over-year drop. As the supply of available homes contracts, buyers keep putting pressure on prices. The median price of a home in the San Francisco metro area hit $1,282,200 in October, up 4.7 percent year-over-year. In the Oakland metro area, it climbed 13.1 percent year-over-year to $690,000, according to Redfin.

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Only eight of the 74 metros showed year-over-year increases in inventory. Those were mostly in the South and Midwest. Raleigh, N.C., had the largest jump in the number of available homes, up 16.1 percent, followed by Baton Rouge, LA (12.9 percent), Austin, Texas (8.8 percent), New Orleans (7.5 percent) and St. Louis (4.8 percent).

With home supplies chronically low in most U.S. metros, sales “are sputtering,” said Nela Richardson, Redfin’s chief economist. “The last time we saw a substantial increase in the number of homes for sale, Donald Trump was a candidate in a Republican field of 11.”

Also on Thursday, the California Association of Realtors (C.A.R.) issued its October report on the statewide housing market.

Looking at existing, single-family homes, C.A.R. reports that the median price in the nine-county Bay Area is $892,720, up 11.1 percent year-over-year.

County by county, again for single-family homes, here are a few more numbers.

The Contra Costa County median was $615,000, up 6.1 percent, while the Alameda County median was $862,450, up 11.3 percent. In Santa Clara County, the median was $1,242,500, up 18.6 percent. In San Mateo County, the median climbed 12.8 percent to $1,522,500, and in San Francisco County it rose 13.3 percent to $1,594,000.

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