On-Chart Success Dynamics of Popular Songs Seungkyu Shin and Juyong Park Graduate School of Culture Technology and BK21 Plus Postgraduate Programme for Content Science, Korea Advanced Institute of Science & Technology, Daejeon, Republic of Korea 34141 In the modern era where highly-commodified cultural products compete heavily for mass consump- tion, finding the principles behind the complex process of how successful, “hit” products emerge remains a vital scientific goal that requires an interdisciplinary approach. Here we present a frame- work for tracing the cycle of prosperity-and-decline of a product to find insights into influential and potent factors that determine its success. As a rapid, high-throughput indicator of the preference of the public, popularity charts have emerged as a useful information source for finding the market performance patterns of products over time, which we call the on-chart life trajectories that show how the products enter the chart, fare inside it, and eventually exit from it. We propose quantitative parameters to characterise a life trajectory, and analyse a large-scale data set of nearly 7 000 songs from Gaon Chart, a major weekly Korean Pop (K-Pop) chart that cover a span of six years. We find that a significant role is played by non-musical extrinsic factors such as the established fan base of the artist and the might of production companies in the on-chart success of songs, strongly indicative of the commodified nature of modern cultural products. We also review a possible mathematical model of this phenomenon, and discuss several nontrivial yet intriguing trajectories that we call the “Late Bloomers” and the “Re-entrants” that appears to be strongly driven by serendipitous exposure on mass media and the changes of seasons. I. INTRODUCTION using high-quality contemporary data and scientific me- thodology, we study the chart dynamics of K-Pop (Ko- Competition for survival and success is a crucial me- rean pop) songs, i.e. how the songs fare on popularity chanism underlying the evolution of species or actors in charts and what factors are behind it. K-Pop, a relati- a complex system, be it biological, social, or technologi- vely recent international cultural sensation from South cal [1–3]. The increasing availability of large-scale data Korea, is characterised by catchy tunes and a heavy use along with a remarkable progress in the theory and mo- of audiovisual elements. One of the early pinnacles of deling of complex systems has led to the emergence of the its global success happened in July of 2012 with PSY’s “science of success” that aims to reveal common patterns Gangnam Style that reached number two on the U.S. in the success of people or products in such diverse sub- Billboard Hot 100. Its online success can be said to be jects as viral spreading of content, performance of ath- even more phenomenal, scoring nearly three billion views letes in sports, popularity of emergent technologies, and on YouTube as of this writing (April 2017) to become the impact of scientific works [4–7]. most-watched online video. Another prominent characte- The scientific study of success is also deeply related ristic of K-Pop is the prominence of “idols”, young, highly- to the tradition of developing robust and effective ran- trained dancer-singers who are designed to be the hub king methods for identifying the most successful and su- around which an entire industry of production and mer- perior actors in a competition system [8–12]. Rankings chandise/service providers are organised [17]. This type of products and commodities serve a useful purpose for of intensive commercialisation places K-Pop at the fore- customers looking to purchase, or firms planning to ad- front of the contemporary music industry where the in- vertise and market products. Cultural products such as trinsic, musical properties of a song such as its melody or popular songs are no exception, especially in this day and lyrics are relegated to being merely one factor that affects age where digital communication technology has enabled its success [18–21]. Prompted by this sweeping trend, in massive and efficient dissemination and consumption. Po- this paper we study a prominent K-Pop chart data to pularity charts have accordingly become more instanta- characterise the chart dynamics of successful songs, and neously updated, emerging as an essential reference for then determine the extent to which such extrinsic factors correlated with their successes. arXiv:1704.08437v2 [physics.soc-ph] 15 May 2018 customers trying to make decisions in the face of a flood of new content and information, therefore becoming a co- veted platform that affords products more exposure and prolonged success [13–16]. This brings up the hope that II. POPULARITY CHARTS AND THE LIFE we may now be able to search for answers to many inter- TRAJECTORY OF A PRODUCT esting questions into the underlying mechanisms of suc- cessful products, including “What are the features of ‘hit’ A. Data, methodology, and life trajectory patterns products that can be learnt from their chart dynamics ?”, “What are the factors–intrinsic or extrinsic–behind the We analyze the data from Gaon Music success of products ?”, and so forth. Charts (www.gaonchart.co.kr), a collection of weekly In this paper, as an attempt to answer these questions music charts serviced by the association of Korea’s 2 Four parameters of a song’s life trajectory 2000 (a) 1000 Young Girls Peak (Bruno Mars, 10 weeks) 1 2 Let It Go 20 (Idina Menzel, 16 weeks) 100 40 init max r 60 r Neoui Uimi (Meaning of You, 80 IU,2 73 weeks) 10 Gangnam Style Rank (Popularity) 100 Number of Songs (PSY, 24 weeks) 0 5 10 15 20 25 30 35 (Weeks) Time Party Rock Anthem t pre t post (LMFAO, 33 weeks) ( N=4810 ) 1 median=2 mean=3.95 (b) 1 week 4 weeks 16 weeks 64 weeks r init r max Bandwidth = 4.816 Bandwidth = 3.794 0.015 Number of Weeks on top 100 0.020 0.010 0.010 0.005 Figure 1. Histogram of the number of weeks spent by the 0.000 0.000 songs on the Gaon Digital Chart that exhibits a highly skewed Kernel Density 100 80 60 40 20 1 (Rank) 100 80 60 40 20 1 (Rank) behavior. The mean is 3:95 and the median is 2 for the songs t pre t post Bandwidth = 0.6161 that spend at least one week on the chart. The longest is for 2.0 Bandwidth = 0.1232 0.20 1.5 IU’s Neoui Uimi (The Meaning of You) at 73 weeks. 0.15 1.0 0.10 0.5 0.05 0.0 0.00 Kernel Density 0 5 10 15 20 (Weeks) 0 20 40 60 (Weeks) music industry. We focus on the Gaon Digital Chart, the signature one similar in spirit to the U.S. Billboard Hot Figure 2. (a) Four parameters that describe a song’s life tra- 100. It ranks the top-100 songs (both domestic K-Pop jectory on a chart : inaugural rank (rinit), peak rank (rmax), and foreign songs in a single chart) according to their di- time spent on the chart before peak rank (tpre), and time gital sales figures including downloads, online streaming spent on the chart after its peak (tpost). (b) The distribution density of the four parameters estimated using Kernel Density counts, and their offline album sales, etc. (The exact Estimation (KDE) method. The r and r are weighted weights given to each factor has not been made public, init max towards high values, whereas tpre and tpost are weighted to- although the rankings themselves are open for anyone.) wards low values. Songs that appeared on the chart for two Our data covers all weeks between the second week of weeks or more (4 810 songs in total, see definition of rinit in 2010 (the actual beginning of Gaon) and the 53rd week Table.) were anlayzed to generate these figures. of 2015, for a total of 313 weeks. During this period there have been in total 7 560 songs that appeared at least once on the chart. The actual numbers of weeks spent on the chart, however, vary widely as shown in An example is shown in Fig. 2(a) for girlband EXI- Fig. 1 : 36:4% of the songs (2 750) appeared for one week D’s Wiarae (Up and Down). It first entered the chart at only, whereas 9:1% of the songs (689) stayed on the rinit = 7, reaching its peak (rmax = 1) tpre = 6 weeks chart more than ten weeks. The longest life on the chart later, then fell gradually (save for some brief rallies) for was enjoyed by IU’s Neoui Uimi (The Meaning of You) tpost = 30 weeks until it left the chart. In Fig. 2(b) we for a record of the 73 weeks. The same artist’s Joeun show the probability density function of the four para- Nal (Good Day) and PSY’s Gangnam Style topped the meters using Kernel Density Estimation (KDE) method chart at number one for the most weeks (5). in the R statistical package [23, 24]. rinit and rmax are For most songs, the weekly rankings follow roughly a slightly skewed towards high values whereas tpre and tpost similar pattern (notable exceptions are discussed later) : are more heavily skewed towards lower values, meaning It appears in the chart, reaches its peak rank at some that an overwhelming majority of songs enjoy only brief point, declines, and eventually leaves the chart. Upon ins- stints on the chart. We can also define the overall success pection of numerous curves made by the songs’ rankings, of a song to be the area under its trajectory curve so that we find it useful to characterise such life trajectory of the longer-surviving, higher-ranking songs can naturally a song via the following parameters : be called more successful.