Art Metrics

Jul 19, 2019 · 6 min read

Success for an artist is difficult to quantify objectively, as it depends on endogenous factors such as the quality of the created artworks, but also on exogenous variables like endorsements received by the artist from art collectors and experts as well as the position and centrality of the artist in social networks.

Performance drives success, but when performance can’t be measured, networks drive success. Albert-László Barabasi (The Formula)

We focus on the general problem of developing art metrics, that is rating and ranking systems tailored for art markets. We suggest that art metrics should consider a set of requirements:

  1. Firstly, different roles must be taken into account, including artists, collectors, investors and experts. The reputation of these roles is typically mutually dependent, for instance the works of prominent artists belong to renowned collections or is reviewed by famous experts. We argue distinct yet coupled ratings should be developed for each role.
  2. Secondly, the metrics should be time-aware and computationally efficient to account for the dynamic nature of art markets.
  3. Lastly, metrics should be predictive of future success, so they can be used both to rank actors according to their past performance as well as to foresee the most promising players of the system in the near future.

A characteristic of the art market, one that allows to draw a parallelism with the scientific publication system or with the Web, is the mechanism of endorsement of artists and collectors:

  • Both works of art and science can be endorsed by the respective communities, thus gaining in popularity and, for artworks, in commercial value. A scientific paper (author) is endorsed when a peer references it in another article. An artwork (artist) is endorsed when a collector makes a bid or a direct purchase.
  • The number of bids made for the artwork, or the number of times the artwork is traded among collectors, are indicators of the popularity of the piece of art in the artistic setting, as much as the number of citations from other scholars accrued by a paper is an indicator of its popularity within the scientific community.
  • Besides popularity, one can also investigate the prestige of the works of art and of scholarly publications and, indirectly, of artists and authors. We might argue that a bid to an artwork made by a prestigious collector, or a citation to an article given by an authoritative scientist, are more important than endorsements given by unknown individuals.
  • Alternative metrics (so called altmetrics, for instance views and likes), might also be part of the endorsement system in both science and art.

We begin our work on art metrics by considering a simplified view of the art market (and resulting sales network) as bipartite between the roles of the artist and the collector.

Artists create and sell artworks, they are the sources of art. Collectors purchase and pull together artworks, they have some sense of where good art is.

We posit that there exists a mutual reinforcement mechanism in the definition of the dominating figures of artists and collectors, that can be summarized as follows:

Important collectors purchase works of important artists; important artists sell their works to important collectors.

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SuperRare gallery’s first year of activity. Each point is a user with the number of sales on the x-axis and the number of purchases on the y-axis, while 95% percentiles are plotted as lines. Kendall’s correlation between sales and purchases is weakly negative (-0.19), confirming that sellers (artists) typically do not buy and buyers (collectors) typically do not sell.

We thus propose a rating method to understand current market positions of artists and collectors, fulfilling the following facets of the art system:

  • Mutual reinforcement: the metric computes the reward for an artist selling an artwork in terms of the rating of the collector buying the artwork. Similarly, it computes the reward for a collector purchasing an artwork in terms of the rating of the artist selling the artwork.
  • Time-awareness: the metric adapts to the rapid stream of sale events that increasingly characterizes the art market by updating the rating for the actors participating in a sale event immediately after the event has happened.
  • Efficiency: each update operation has low computational cost and hence can be performed efficiently. This allows the rating system to be always synchronized with respect to the flow of sales.

It is worth highlighting that Kleinberg’s Hyperlink-Induced Topic Search (HITS) method, developed in 1998 for the Web, proceeds from a similar definition and will be used as our starting point. HITS’s assumption is that in certain networks there are two types of important nodes: authorities, that contain reliable information on the topic of interest, and hubs, that tell us where to find authoritative information. For instance, on the Web hubs are pages that compile lists of resources relevant to a given topic of interest, while authorities are pages that contain explicit information on the topic. In an article citation network, hubs are for example review papers that mainly reference other papers containing relevant information on a given topic, while authorities are articles that contain the explicit information. This calls for two distinct but interrelated notions of centrality: authority and hub centrality.

Our first proposal is therefore to define the artist centrality as the authority centrality and the collector centrality as the hub centrality over a weighted sales network where links go from buyer to seller and are weighted with the sale price.

The proposal, however, misses a fundamental ingredient of art markets: the importance of timing. For example, suppose that a collector bought (for the same price) two artworks A and B from the same artist but at different times: artwork A when the artist was unknown and artwork B after the artist became famous. Reasonably, the collector expects a larger increase in centrality from the second purchase, since they acquired a piece from a more renowned artist. Unfortunately, HITS does not distinguish between the two purchases. A timed-aware metric, on the other hand, would distinguish between the two scenarios, assigning to the collector different centrality gains, proportional to the artist’s centrality at the time of each sale.

We hence develop a time-aware extension of HITS. Initially, at time 0, all actors of the gallery have null rating. Then, at each sale, we update the rating of the selling artist using the sale price and the rating that the buying collector had before the sale. Similarly, we update the rating of the buying collector using the sale price and the rating that the selling artist had before the sale.

Our proposal is meaningful for the traditional art market as well as for the emerging market of crypto art.

Crypto art, also known as blockchain art, is a recent artistic movement in which the artist produces works of art, typically still or animated images and distributes them via a crypto art gallery using blockchain and IPFS peer-to-peer networks. In particular, we stress the importance of time-aware and efficient art metrics for crypto art market. Indeed, the most distinctive facet of crypto art that sets it apart from the traditional art system is its higher velocity. In crypto art something can happen at every instant: an artist forges a new piece or accepts a bid made from a collector, a collector makes a bid for an artwork or directly purchases it, two artists or collectors exchange artworks. The work flow of crypto art is potentially very fast: having the right idea and using a generative computer-aided process, an author can quickly produce an artwork, almost instantaneously tokenize it on the blockchain and hence exhibit it in an online gallery. Bids and sales can arrive in a matter of minutes and after its sale, the artwork can be traded in the secondary market (even outside the gallery) with the same speed. We might say that the working time granularity in traditional art is months or even years, while the time granularity in crypto art is already practically of hours or even minutes, and could go down to any granularity supported by the underlying blockchain.

This defines crypto art as a real-time stream of events, more similar to financial trading than traditional art.

To test our proposed method, we make use, for the very first time in academic research, of crypto art transaction data from the SuperRare digital art gallery. The dataset explored contains all sale events of the first year in the life of the SuperRare crypto art gallery, from April 2018 to April 2019.

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The SuperRare sale network during the first year of activity laid out using Sugiyama algorithm for layered directed acyclic graphs (the algorithm minimized edge crossings).

We find that our proposed method works well at capturing the complementary and mutually reinforcing roles of artists and collectors, by implementing the intuition that leading artists sell to leading collectors, and leading collectors buy from leading artists. The method is also predictive of future success, and better so than a the original HITS, as well as of simple metrics like number of sold artworks and overall amount of sales.

The full version of the paper contains all the details. It is freely available on arXiv preprint repository and is currently submitted for journal publication.

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