Art Market

Using AI to Predict Rothko Paintings’ Auction Prices

Christie’s staff member looks at Mark Rothko’s No 11 (Untitled), London, 2013. Photo by Peter Macdiarmid/Getty Images

Christie’s staff member looks at Mark Rothko’s No 11 (Untitled), London, 2013. Photo by Peter Macdiarmid/Getty Images

’s hovering rectangles of color suspended within monochromatic fields are among the most recognizable paintings produced in the 20th century. Working within a highly constricted format, he produced a surprisingly varied body of work coveted by collectors and museums around the world. His widespread popularity and secure position in the canon of art history, combined with rapid growth in the number of people with the means and desire to own his paintings, have transformed them into extraordinarily expensive trophy art. Since 2010, buyers at auction have spent about $1.1 billion on Rothko paintings.
The relative uniformity of Rothko’s paintings, especially when compared to other art world icons like and , makes them ideal candidates for using artificial intelligence tools to develop a predictive model for estimating sale prices at auction. We explain below how we developed one such model, using variables like the number of billionaires in the world and the wealth they control. We then used our model to predict the sale price of three Rothko works that will appear in Sotheby’s Contemporary Art evening sale on May 16th. But first, a brief overview of the Rothko marketplace.

The Yale dropout

Mark Rothko, 1961. Photo by Kate Rothko/Apic/Getty Images.

Mark Rothko, 1961. Photo by Kate Rothko/Apic/Getty Images.

An immigrant from a part of Russia that is now Latvia, Rothko arrived at New York’s Ellis Island in late 1913, when he was 10 years old. His family settled in Portland, Oregon, where he attended high school, after which he attended Yale University for two years before dropping out. He moved to New York in 1923 and remained there until his death by suicide in 1970, at age 66.
Scholars tend to break his career into three periods. During the “Early Years” (1924–39), he frequently painted mythological subjects or works inspired by , few of which are especially distinguished or interesting. During the “Years of Transition” period (1940–50), he moved from representation to exploring how juxtapositions of color and form can be used to create interesting spatial relationships. Most of the paintings for which he became world famous were made during the later years of his life, what scholars call the “Classic Years” (1951–70). A catalogue raisonné (the list of works recognized as authentic by scholars) of all Rothko’s works on canvas and rigid board, published in 1998 by the National Gallery in Washington, includes 386 works from this third and most important period.
Rothko also made numerous works on paper, which he considered to be full-fledged paintings, rather than drawings. Christopher Rothko, the artist’s son, has written that Rothko insisted that all his works on paper “be mounted on a support, and presented matteless, frameless, unglazed. In other words, they should be treated like paintings, with nothing to impede our view or our approach. To the best of my knowledge, all classic Rothko works on paper that were exhibited or sold during my father’s lifetime were mounted, not framed, some more successfully than others, but the consistency makes my father’s wishes clear.”
A catalogue raisonné solely of the artist’s works on paper is currently being assembled by the National Gallery and is estimated to be available by 2020. Because paper was cheaper and easier to work with, the artist probably created more Classic Years paintings on paper than on canvas, although the exact count will not become clear until the catalogue’s publication.
Both his works on paper and his canvases regularly appear at auction. Rothko’s works are also sold privately, largely through Pace Gallery, which has represented the artist’s estate since 1978.

A Rothko price forecasting model

Mark Rothko, Untitled (Red and Burgundy Over Blue), 1969. Courtesy of Sotheby’s.

Mark Rothko, Untitled (Red and Burgundy Over Blue), 1969. Courtesy of Sotheby’s.

Imagine standing in front of a Rothko and really looking at it. You will quickly notice the number of rectangles, their colors, and how they compare with the monochromatic field on which they are painted. These are easily measured aspects of the painting. But there are so many other qualities to a Rothko that are hard to verbalize, let alone quantify, that contribute to its emotive beauty, such as how the edges of the rectangles dissolve into the base color, the luminosity of the paint, and the unusual spatial relationships created by the juxtapositions of color and form. Our eyes see this information and transmit it to our brains, provoking an emotional response.
Artificial intelligence now enables machines to view the world, in some respects, as humans do and allows them to use that knowledge for a variety of tasks, including driving autonomous cars and monitoring people in Times Square using video surveillance systems. The revolution in computer vision is due in large part to a pattern-recognition algorithm called a Convolutional Neural Network (CNN). A CNN looks at pixels in digital images and finds patterns in them, without the machine first being told what to look for. Put another way, this technique involves the machine extracting underlying characteristics of an image on its own, including characteristics that are difficult to pre-specify. We used this method to analyze digital images of Rothko paintings, generating information that could be used to predict sale prices.
To build our model, we created a database of all Classic Years and late Years of Transition works by the artist that have sold at auction since 2000, a total of 118 objects. The database includes not only all-in sale prices (hammer price plus buyer’s premium) and object descriptors (size, date painting was made, date it was sold, painting on canvas or paper, etc.) gathered from the artnet price database, but also digital images of each work that we pulled from the web. As a potential replacement for the digital images, we also hand scored the formal properties of each painting: the number of color blocks, number of horizontal stripes the artist may have used to separate these color blocks, the dominant color in the painting, and the background color. These four variables would typically be assembled by an appraiser to compare such paintings. In addition to these “supply” variables, we also gathered various measures of the “demand” for art, such as growth in worldwide wealth, growth in various stock indexes, and the aggregate wealth and total count of billionaires in the Forbes Billionaires Index. We then used these data to develop a model that would predict auction sale prices.
The model we created is surprisingly accurate, with just a 5.5% margin of error for past sales. This means that the difference between the actual sale price and the forecasted sale price was on average just 5.5% across all the paintings in our database. What makes this best-performing model so interesting is that its predictions are based simply on the digital image plus five variables: painting height and width, whether it’s a work on paper or canvas, the number of billionaires in the world, and the wealth they control. None of the other variables in our database appeared relevant to the price, including the date the painting was made. We also compared our computer-generated model with our own assessments, replacing the digital image with the four hand-scored variables mentioned above. With those hand-scored variables, the prediction error soared to 20%, making it woefully inadequate as a model. That difference is a vivid reminder a machine can often “look” at a painting more incisively than the human eye.
A few general observations about the model before putting it to work. First, the number of billionaires and the wealth they control were by far the most important demand-side variables in explaining sale prices. Second, size matters: The larger the work, the more valuable it is, all else being held constant. Third, paintings on paper trade at a significant discount compared to paintings on canvas, all else held constant. Lastly, brightly colored orange and purple paintings that pop off the wall tend to open buyers’ wallets more than darkly colored browns and grays.

Predicting May auction sales prices

Mark Rothko, Untitled (Red on Red), 1969. Courtesy of Sotheby’s.

Mark Rothko, Untitled (Red on Red), 1969. Courtesy of Sotheby’s.

Mark Rothko, Untitled, 1960. Courtesy Sotheby’s.

Mark Rothko, Untitled, 1960. Courtesy Sotheby’s.

This leads us to the three works by Mark Rothko up for auction in the Sotheby’s Contemporary Art Evening Sale on May 16th.
The San Francisco Museum of Modern Art (SFMOMA), which has seven works by Rothko in its collection, is deaccessioning an untitled Classic Years painting from 1960. In the press release announcing the sale, the museum said it intends to use sale proceeds to acquire works to help diversify its collection. Like many museums today, SFMOMA wants to buy more works by women, people of color, and other overlooked or marginalized communities.
Sotheby’s estimates the painting will sell for a hammer price between $35 million and $50 million. But the successful bidder will also be required to pay Sotheby’s buyer’s premium, which equals 25% of the hammer price up to and including $400,000, 20% of amounts in excess of $400,000 up to and including $4,000,000, and 13.9% of any amounts in excess of $4,000,000. After adding buyer’s premium, Sotheby’s is forecasting the painting will sell for between $40.1-$57.2 million.
After running this painting through our algorithm, the model predicts it will sell for $42.3 million (including buyer’s premium), toward the lower end of Sotheby’s auction estimates. This is still a staggering sum of money that will bring joy to the hearts of acquisitive SFMOMA curators. Sotheby’s specialists may believe this work will sell for more because artworks deaccessioned by museums often sell for high prices at auction. But this possibility is not something we can account for in our model.
For fun, we also played with the model to see how changing aspects of the SFMOMA painting would impact its value. If the colors tilted more orange than the current brownish burgundy, the projected sale price would jump to $66.5 million, almost 60% higher than the existing work. If it were a work on paper, its value would drop to $20.3 million, reflecting a long-held preference among collectors for paintings on canvas over paintings on paper.
Two Classic Years paintings on paper from 1969 are also for sale this May at Sotheby’s. The larger of the two works, Untitled (Red and Burgundy Over Blue), has a pre-sale estimate of $9 million to $12 million, or $10.5 million to $13.9 with buyer’s premium. Our artificial intelligence model predicts the painting will sell for $16.6 million, above the top end of the auction estimates, which would make it the second most expensive work on paper by the artist to sell at auction. If everything about the painting was the same, except it was on canvas, the model predicts it would sell for $33.4 million, almost twice the price of its paper-based twin.
The second work on paper, Untitled (Red on Red), is smaller but notable for its bright red palette. Sotheby’s estimates it will sell for a hammer price between $7 million to $10 million, or $8.2 million to $11.7 million with buyer’s premium. Given its appealing color scheme, our model predicts it will sell for $13.7 million, also above the top end of the auction estimates. The prospect of both works on paper selling for above the auction estimates reflects not only the inherent quality of the works, but also a longstanding auction house practice of trying to keep estimates as low as possible in the hopes of attracting more bidders.
Rothko is one of the most beloved artists of the 20th century. Because his mature works fall within a restricted visual vocabulary, digital images of his paintings can be used to create reliable price forecasting models. We eagerly await the results of the upcoming Sotheby’s sale to see how this model performed.
Devin Liu is a software engineer specializing in applying artificial intelligence to the future of work. He is currently automating repetitive job functions for large enterprise companies at Cresta.
Doug Woodham is Managing Partner of Art Fiduciary Advisors, former President of Christie’s for the Americas, and author of Art Collecting Today: Market Insights for Everyone Passionate About Art.