$239,958,219.15.

That’s how much Kenneth Griffin, the billionaire hedge fund manager and trophy home collector, paid last week, after taxes and fees, for a nearly 24,000-square-foot pied-à-terre on Central Park South — the most expensive home ever sold in the United States.

That’s enough money to cover a year of rent for 6,254 Manhattanites, who paid a median of $3,197 in the month of December; or enough to buy 946 homes, at the national median sale price of $253,600.

It is also enough to buy New York’s former record-holder — a $100.5 million penthouse that sold in 2014 — twice over, and still have change left for an eight-figure condo.

But in a city lousy with multimillion-dollar apartments, how did this sale eclipse them all? And what, exactly, is the difference between a $100 million concrete box in the sky and a $200 million one?

The answer is often more art than science, and it speaks to the torrent of luxury real estate built in recent years, which has been more brazenly priced than that of any previous cycle. But developers’ logic is not entirely untethered from reality: There is some method to the madness of $10,000 a square foot, the benchmark for the most ambitious new penthouses.

Imperfect though it may be, it remains the measure of choice for developers, in a city where new development sold for an average of $3,130 a square foot last quarter, according to a Douglas Elliman report.

The record-breaking sale, which went into contract in 2015, could be the last hurrah for a development boom that peaked the following year. There is now a surfeit of luxury apartments for sale in Manhattan, many of them shrinking in scale and price. Outliers may continue to emerge, but their sales will have increasingly little to do with the market at large.

“It’s about 24-karat ego, on steroids,” said Donna Olshan, the president of Olshan Realty, which tracks the market for $4 million-plus contracts. In her January report, which includes the last week of December, just 53 contracts above that price were signed, the lowest number since the same period in 2012. Never mind headwinds in the market, she said of the buyer, “he’s a billionaire going down the bucket list.”

This is not a short-term investment, but a home where Mr. Griffin will spend considerable time, said Zia Ahmed, his spokesman. He added that Mr. Griffin has given more than $700 million to charities, including a $150 million gift to Harvard, his alma mater, largely to support financial aid, and plans to give “billions more” to educational causes.

In late January, there were 497 active listings in New York seeking more than $10 million, according to the real estate website StreetEasy. That is off the peak of 579 apartments in June 2016, but still more than double the number at the end of 2011, when 223 were for sale. The latest figure is likely a low estimate, because developers have kept several pricey units off the market in response to a glut of new inventory, said Grant Long, the site’s senior economist.

Among the properties: 161 homes over $20 million, 61 over $30 million, 17 over $50 million, and just two units publicly listed for more than $75 million. There were no listings above $100 million.

The record sale, of a unit on four high floors of 220 Central Park South, a nearly 1,000-foot skyscraper still under construction, was not publicly listed. Many familiar with the project believe that mystique is what fueled the marketing campaign for Steven Roth of Vornado Realty Trust, the tight-lipped developer.

“He wanted to make sure there were very few people talking to the right people,” said Paul L. Whalen, a partner with Robert A.M. Stern Architects, the firm that designed the limestone-clad tower.

The unit starts on the 40th floor of a 65-story tower, according to city records. (Or the 50th floor, if you go by the developer’s marketing count.) In either case, it is not at the pinnacle of the building, where developers often seek the highest premiums.

What makes the apartment special is the sheer amount of space, combined with unobstructed views of Central Park, said Yair Tavivian, an agent with Douglas Elliman and a founder of Compit, an automated valuation platform. At almost 24,000 square feet, the apartment is one of the largest in the city to be sold as a single residence. The average Barnes & Noble bookstore is a tad larger, at around 26,000 square feet.

“In terms of price per square foot, it’s a pretty good deal,” said Mr. Tavivian, who noted that other units in the building are selling in the range of $8,000 to $9,000 a square foot. Moreover, a 24,000-square-foot apartment arguably has more in common with West Coast estates, like the 100,000-square-foot Bel Air mansion that was seeking $500 million, or a comparatively modest $5,000 a square foot.

“You’d be amazed at some of the product asking $5,000 or $6,000 a square foot,” Mr. Tavivian said, although they “still look out on somebody else’s building.”

The history of astronomic price jumps in the city is a recent one. Many credit the 2003 sale of a $43 million apartment at 25 Columbus Circle, a condo with Central Park views, with kicking off the wave of ambitious pricing. The unit sold for $2,630 a square foot, according to StreetEasy, when $1,000 a square foot was typical of the high-end. By 2007, 15 Central Park West, another tower designed by Robert A.M. Stern Architects, had established pricing of more than $3,000 a square foot, and a penthouse in the building sold for $9,230 a square foot last year, according to Compit data.

In 2012, Dmitry Rybolovlev, a Russian billionaire, set a record by buying a 6,744-square-foot penthouse in the building for $88 million, or $13,049 a square foot, which remains the square-foot price record, said Jonathan Miller, the president of the real estate appraisal firm Miller Samuel.

The last apartment to hold the record for total price, a duplex penthouse at One57, a glassy tower that set off the building boom along a stretch of 57th Street now known as Billionaires’ Row, sold for $100.5 million in 2014.

“It’s not just numbers out of a hat,” said Gary Barnett, the president and founder of Extell Development, which built One57, about how he arrives at prices. The penthouse there, on the 89th and 90th floors of the 90-story tower, was first listed for $98.5 million, then raised to $115 million, according to filings with the state attorney general. The apartment sold to a limited-liability company connected with the tech billionaire Michael Dell, according to people familiar with the sale.

At 10,923 square feet, the unit went for about $9,200 a square foot. “That’s not a crazy price,” Mr. Barnett said, as lower apartments in the building had sold for around $8,000 a square foot.

Maintaining those prices at resale, now that the luxury market is awash with unsold inventory, is another thing. While One57 set a high-water mark when sales began in 2011, recent resales have softened. An apartment on the 63rd floor that sold for $32.5 million in 2014 resold in 2018 for $23 million, a 29 percent price cut, according to StreetEasy data.

An unsold listing on the 87th floor, a 6,234-square-foot unit just a few floors below the penthouse, is now being listed for $67 million (or $10,748 a square foot). But Mr. Barnett, who has offered a number of sweeteners at his properties, including discounted common charges, has no illusions about the likely sales price. “My guess is it will trade somewhere in the 50s,” he said of the unit, predicting a considerable discount.

Falling prices and shrinking units are widespread. Nearby, at 432 Park Avenue, another Billionaires’ Row skyscraper with Central Park views, a 71st-floor unit that sold for $28.9 million in 2016 sold again last year for $25.25 million, a drop of almost 13 percent. And in a trend seen at other towers, a number of full-floor units near the top of the project were subdivided into smaller apartments in 2015, to appeal to a larger pool of buyers.

But each submarket of Manhattan has its own comparative set, with challenges that ultimately dictate the ceiling on prices. At Madison Square Park Tower, a new 777-foot tower in the Flatiron district in downtown Manhattan, the developer is listing a 13,060-square-foot triplex at the top of the building, with panoramic city views, for $77.7 million.

The unit, delivered as unfinished space, will include plans for three potential design layouts, as well as two studio apartments for staff or guests elsewhere in the building (valued at $1 million each) and two parking spaces ($500,000 each).

The developer, Ian Bruce Eichner, the founder and chairman of Continuum Company, said he set the price in part by comparing the space to a unit at 212 Fifth Avenue, a neo-Gothic condo conversion in nearby NoMad, where the more than 10,000-square-foot triplex with outdoor terraces is listed at $62.8 million, down from an earlier price of $73.8 million. If that unit could ask for $6,230 a square foot, surely his trophy apartment, in a new building at a taller height, though without outdoor space, should fetch close to $5,950 a square foot, he reasoned.

But why $77.7 million, specifically? Because it matches the height of the building, he said.

There is, of course, another reason some units command record prices while others don’t: The right buyer.

“There are times when the buyer is what we would call ‘atypically motivated,’” said Michael Vargas, the president of Vanderbilt Appraisal, referring to the practice of buyers, many from overseas, looking to park money in real estate.

Mr. Rybolovlev, the Russian billionaire who bought the record-setting $88 million penthouse, for instance, was accused by his ex-wife in divorce proceedings of buying the apartment, as well as a $95 million Palm Beach, Fla., mansion owned by Donald Trump, to shield his assets.

Could there be another record-breaking sale in the works? It’s unlikely, given the state of the luxury market, but developers are an optimistic lot.

Mr. Barnett, the developer behind One57, has big plans for a triplex apartment at Central Park Tower, an under-construction tower that he said will outmatch the views at other Billionaires’ Row skyscrapers, including that of the building where Mr. Griffin just spent nearly $240 million. The price has not been disclosed in state filings, but he said the space will have a 2,000-square-foot terrace, 30-foot ceilings and a ballroom-like entertaining space.

So far, there have been no takers, he said, “but I have an asking price in mind.”

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