Each spring in recent years, at least one blockbuster work of art has come up for sale at the major auction houses. In 2005, Constantin Brancusi’s marble Oiseau dans l’espace generated massive buzz at Christie’s; last year it was Picasso’s Dora Maar au chat at Sotheby’s. This spring, Sotheby’s is triumphantly showcasing a color-field painting by Mark Rothko. An early example of his characteristic style, White Center (Yellow, Pink, and Lavender on Rose) was painted in 1950, a turning point in Rothko’s career. The work has an impeccable pedigree, having been owned by David Rockefeller, who has a redoubtable family name and is a major benefactor of the Museum of Modern Art in New York.

As striking as the painting itself was the auction house’s estimate that it would sell for “in excess of $40 million”—nearly double Rothko’s auction record, set in November 2005 when Homage to Matisse sold for $22.4 million at Christie’s. The prediction turned out to be right; when the lot came up at Sotheby’s on the evening of May 15, auctioneer Tobias Meyer brought his gavel down at $65 million—$72.8 million with the buyer’s premium.

The Rockefeller Rothko estimate and record-setting price—it is the most ever paid for a work of contemporary art at auction—pose a question: How, exactly, do Sotheby’s, Christie’s, and their colleagues pair a work of art and a dollar amount?

An auction house’s main business is, of course, to make money. But the purpose of an estimate—well, that’s far more difficult to comprehend. Some seem absurdly low: In 1996, a faux-pearl necklace that belonged to Jacqueline Kennedy Onassis sold for $211,500 after its presale estimate was just $500 to $700. Others, such as the Rothko estimate, appear to be plucked from the stratosphere to test billionaire bidders.

The reality is that estimates are tools to entice buyers and encourage sellers. And in this hot art market, auction houses have been changing the way they set estimates to better compete with their rivals—not the other auction houses but art dealers who can broker far quieter sales at much higher prices.

According to the Sotheby’s website, presale estimates are based on an “examination of the item” and “knowledge of the prices achieved by similar objects.” Sounds simple enough. But as the market for postwar and contemporary art has risen dramatically in the past five years, auction houses have begun to take into account private sales, as long as the prices obtained in them can be verified.

Sotheby’s wouldn’t comment on its presale estimates, but Christie’s spokeswoman Bendetta Roux says in an email, “What we have seen in recent seasons is that the level of prices achieved in the private market has also influenced the setting of auction estimates.”

That can make estimates more aggressive for the most desirable pieces at the top end of the market, where competition is fiercest, says Todd Levin, who worked for Sotheby’s before curating hedge fund manager Adam Sender’s collection.

A number of consultants and dealers confirm that they have heard of huge sums changing hands in recent Rothko sales. Abigail Asher of Guggenheim, Asher Associates, an art advisory firm with offices in New York and Los Angeles, says that a number of lesser-quality paintings by the artist have sold privately for $20 million and up, indicating a strong market interest that helps account for the size of Sotheby’s estimate.

Past prices, condition, and provenance aren’t the only things that factor into an estimate, however. Behind-the-scenes strategizing often affects the number as well.

“The conventional wisdom has always been that a more conservative estimate induces more competitive bidding,” says Mary Hoeveler, a former senior vice president at Christie’s who is now managing director of the Citigroup Art Advisory Service.

A lower estimate gives buyers the sense that the work is attainable and may end up being a bargain. This provokes more bidders to go after the piece, which in turn can spark a bidding war that drives the selling price to a level that might have seemed too high were it actually set as the estimate. (Obviously, Sotheby’s did not choose this approach in pricing the Rothko.) This tactic has plenty of potential upside, but there’s also a risk that the work will sell at its reserve—the secret minimum price agreed upon by the auction house and the owner.

Take, for example, an Alexander Calder wire sculpture that came up for sale at Sotheby’s in 1998. Asher calls the $100,000 to $150,000 presale estimate a “joke estimate,” because the work was really worth far more. Bidders ended up driving the price  up to nearly $800,000.

It’s harder to get people to start bidding, Hoeveler says, than to get them to stop.

On the other hand, a higher estimate can be the result of a higher guarantee, the amount that the auction house promises to pay the consignor regardless of the piece’s final sale price. Guarantees are an increasingly common way to lure sellers, especially as price records are smashed, sellers become more savvy, and competition between auction houses grows fiercer.

“Going through the Sotheby’s catalog, I couldn’t believe how many works were guaranteed,” says Manhattan art adviser Kim Heirston. “It was staggering.”

Last year, Sotheby’s and Christie’s were jockeying for the right to sell 1947-R-No.1, a painting by Clyfford Still. At the time, the auction record for a Still work was slightly more than $3 million, according to Neal Meltzer, who runs an eponymous art dealership and advisory service in New York. Christie’s won the consignment, gave the seller a guarantee, and put the estimate at $5 million to $7 million. It proved to be a worthy risk: The red-and-black painting sold for more than $21 million.

“It’s a fine line between respecting the value of an object and keeping the price enticing,” Hoeveler says. “That’s the art of proper estimation.”