Why AI Can’t Yet Predict Mark Rothko Paintings’ Auction Prices

A popular art-world parlor game is predicting sale prices for masterworks in upcoming evening auctions. Just how much will someone pay for a dazzling painting by , an iconic sculpture by , or a classic work by ? Earlier this year, the consignment of three Rothko paintings to Sotheby’s prompted us to build a model for predicting sale prices using artificial intelligence (AI) tools applied to historical Rothko sales data. While the analytic techniques we used were complicated, our approach to modeling was straightforward: combine information on the nature of the paintings sold (“supply”) with gauges for how many people may have the means and desire to acquire something so expensive (“demand”).

We explained in an earlier article that the best way to measure supply is by using digital images of paintings, their dimensions, and whether it is a work on paper or canvas. We also found that the best measures of demand are the number of billionaires in the world and the amount of wealth they control. When we put these supply-and-demand metrics together in May, they explained close to 95% of movements in prices paid at auction for Rothko paintings. While that was a tantalizingly high percentage, how did the model perform when predicting the future? And what do these results tell us about the market for Rothko’s paintings?

At the evening auction at Sotheby’s on May 16th, the San Francisco Museum of Modern Art (SFMOMA) was selling a Rothko painting from 1960, one of seven Rothko works in its collection. Like many museums today, SFMOMA wants to buy works by women, people of color, and other overlooked or marginalized communities, but it lacks the funds to do so. Selling the Rothko would hopefully provide the museum with the fuel it needs to achieve its ambitions.

Lot 12 was hanging where it could not be missed: at the front of the room near the auctioneer, a suitable spot for what could have been the most expensive artwork sold that night. Sotheby’s estimated that it would sell for a hammer price between $35 million and $50 million. But the successful bidder would also have to pay the auction house’s buyer’s premium on top of that, which equals 25% of the hammer price up to and including $400,000; 20% of the amount between $400,000 and $4 million; and then 13.9% on the amount in excess of $4 million. With the buyer’s premium, Sotheby’s was forecasting that the painting would go for a figure between $40.1 million and $57.2 million. After running the painting through our AI algorithm, the model predicted it would sell for $42.3 million (hammer price plus buyer’s premium), toward the lower end of what Sotheby’s estimated.

In the months leading up to the sale, Sotheby’s specialists no doubt spent countless hours trying to develop interest in the painting—perhaps from Silicon Valley tech investors soon to be flush with cash from the Uber IPO, or SFMOMA trustees with emotional connections to the work, or Chinese billionaires looking to put offshore cash to work in something that would look splendid in new apartments overlooking Central Park. But as the sale began, these specialists knew their hopes and dreams could easily be dashed if bidders elected to sit on their hands or refused to engage in a bidding war. To hedge against this, SFMOMA chose to sell the work with a guarantee, meaning the museum would receive at least the (confidential) minimum guarantee amount it negotiated with Sotheby’s when consigning the work to the auction house.

Bidding for the painting was slow, with what appeared to be fewer than five bidders. Contrary to popular belief, there are just not that many people in the world with the means and desire to buy an artwork at this price point. Bidding soon stalled around $37 million (or $42.7 million with buyer’s premium), teasingly close to our AI model’s prediction. But the auctioneer did not take the lull as a sign that the sale was over. His patience was ultimately rewarded when bidders pushed the final hammer price to $43.8 million (or $50.1 million with the buyer’s premium). Respectful applause filled the auction room with the tap of the auctioneer’s gavel.

How did the model do? The AI forecast was off by 15.6%, a much larger margin than the deviations we found when training the model on historical data. A possible explanation for the higher price may be the painting’s special provenance: Many auction specialists believe collectors are willing to pay a premium for museum property relative to what they would otherwise pay for a similar object. In any event, the bidding gods that night were certainly smiling on the SFMOMA painting, but they capriciously withheld their affections when the other two Rothkos went up for sale.

Canadian businessman Arnold Steinberg and his wife, Blema, a professor at McGill University, were passionate collectors of post-war and contemporary art. Their heirs elected to sell over 100 valuable works from their collection—assembled from the mid-1960s through 2014—at Sotheby’s. Two Rothko paintings on paper from 1969 were up just three lots after the SFMOMA painting; perhaps an underbidder would elect to buy one as a consolation prize.

The larger of the two works, Untitled (Red and Burgundy Over Blue), had a pre-sale estimate between $9 million and $12 million, or $10.5 million and $13.9 million with buyer’s premium. Our artificial intelligence model predicted that lot 15 would sell for $16.6 million, above the top end of the auction estimates, which would make it the second–most expensive Rothko work on paper to sell at auction. The second work, Untitled (Red on Red), was smaller, but notable for its bright-red palette. Sotheby’s estimated it would go for a hammer price between $7 million and $10 million, or $8.2 million and $11.6 million with the buyer’s premium. Given its appealing color scheme, our model predicted that lot 16 would sell for $13.7 million. Unlike the SFMOMA painting, neither of these works were being sold with a guarantee. But given the strong showing on lot 12, the auctioneer and the heirs were probably anticipating great interest in the works, perhaps even a bidding war.

Auctioneers try to hide their machinations, but it soon became clear that most of the bidders interested in lot 15 were of the imaginary type. The auctioneer took chandelier bids up to one bidding increment below the reserve price, which is where he must stop so that legitimate bidders can buy the work at the reserve. After a very pregnant pause, a lone phone bidder emerged with a $9 million bid (or $10.5 million including buyer’s premium). The auctioneer’s job was now clear: Don’t panic, but wait for it to sink into the minds of other potential bidders that the painting could sell very shortly for that amount unless they jumped in.

The auctioneer soon turned his attention to someone sitting in the very front of the room: Marc Glimcher, president and CEO of Pace, the gallery that represents the Rothko estate. The auctioneer tried repeatedly to cajole him to bid, but Glimcher declined. Perhaps he had other works on paper by the artist back at his gallery that he preferred to sell instead of investing capital in another. When it became clear the auctioneer’s gambit was not working, and that no one else was interested in bidding, he brought the sale to a close.

Lot 16 followed the same dance with chandelier bids into a quiet auction room. The awkward space was finally pierced when a phone bidder came in at $7 million ($8.2 million with buyer’s premium), the low end of the auction estimate. Knowing it was the end of the game, the auctioneer quickly pronounced the lot “sold.”

How did the model do? Very poorly. The AI estimates were about 60% higher than what the works sold for. The model was expecting much stronger demand, which did not materialize that night. Having the works appear after the SFMOMA painting as a consolation prize was smart positioning by Sotheby’s. But with the sale occurring at the end of a packed week of auctions, plus after the successful Frieze and TEFAF art fairs earlier in the month, maybe collectors considering the Steinberg Rothkos had already bought other things. Being late in the sales calendar can disadvantage consignors.

Did the buyer(s) of the works on paper get a deal? Two measures of value say yes. First, Sotheby’s sold a similar Rothko work on paper last year in its May evening auction. It was from 1969, the same year as the Steinberg Rothkos. Smaller than Untitled (Red and Burgundy Over Blue) but about the same size as Untitled (Red on Red), you might expect some sort of pricing parity between works sold within such a short period, but the painting offered in May 2018 went for $18.9 million—completely out of whack with the much lower May 2019 results.

A second measure of value is found by comparing the all-in sale price to the low end of the auction estimates. Both Steinberg Rothkos sold for almost 1.2 times their low estimates, well below the 1.8 average for the other 23 Rothko works on paper from what are considered his classic years (1951–70) that sold at auction since 2010.

While these measures suggest the buyer(s) got “a deal,” what’s causing such fragility in the demand for Rothko works on paper? Statistical models—no matter how sophisticated—are generally poor predictors of turning points because they are trained using historical data. But when models fail, it can sometimes be a signal that changes are afoot. While Rothko’s position in the history of is secure, pricing for his work is subject to the whims of today’s collectors.

Over the past few years, there’s been a noticeable shift among institutional and private collectors to focus more of their time and resources on buying artworks by women, people of color, and other overlooked or marginalized communities. This trend is likely to continue for some time, impacting people’s willingness to pay big prices for works by important male artists in the historical canon. For the price of a single Rothko work on paper, collectors could buy iconic works by , , and —and still have some money left over in their pockets. The lower prices paid this season for the Steinberg Rothkos may be the new normal.