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Home , Busker Busker, Davichi, Gangnam Style, Gaon Digital Chart, Huh Gak, MC The Max

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 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. 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 ’s “science of success” that aims to reveal common patterns 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 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 (, 10 weeks) 1 2 Let It Go 20 (Idina Menzel, 16 weeks) 100 40 init 60 max r Neoui Uimi r (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 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 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 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. The relationships between the parameters reveal more rinit Song’s inaugural rank on the interesting patterns about the trajectories of the songs, chart [22] presented in Fig. 3 and 4. In Fig. 3(a), the inaugural rmax Peak rank ranks {rinit} are plotted along the x-axis, and the maxi- tpre Time taken to reach the peak mum ranks {rmax} are plotted along the y-axis. The data since inaugural appearance on points appear to be roughly evenly spread out here with chart the exception of a high density of points along the diago- tpost Time taken to exit from chart nal rinit = rmax, meaning that for many songs the inaugu- since peak rank ral rank was indeed the peak. In Fig. 3(b), the time until 3

within groups and the variance between groups, then if (a) ( > 1 week on chart) All the latter is significantly larger than the former, ANOVA

1 lets us conclude that does exist a difference between the

0.25 groups [25]. The original ANOVA requires the popula-

20 tion to be close to a normal distribution and population 0.20 variances to be equal. For our kind of data that do not

40 satisfy those conditions we use the Kruskal-Wallis test, 0.15 max x=y non-parametric version of ANOVA [26]. If the p-value 60 r 0.10 from the test is less than or equal to the significance level (0.05), we reject the null hypothesis and conclude 80 0.05 that not all populations are equal. In Table I, we specify

0.00 the average trajectory parameters of all groups based on 100 the metadata and show the p-values from the Kruskal- 100 80 60 40 20 1 Wallis test. The p-values shown in Table I tell us that in r init most cases there exist statistically significant differences (b) All ( > 1 week on chart) (p < 0.05) depending on the properties of the songs. It is noteworthy that songs exhibit differences based on their 20 80 extrinsic properties. However, the significances are gene- 15 rally weaker for the Gender classes, and particularly rmax 10 0.4

60 in regards to Gender (p = 0.31) and tpost in regards to

05 0.3 Nationality (p = 0.12) show insignificant differences. This 0510 15 20 means that the artist’s Gender is not a strong factor in 40 post 0.2

t a song’s peak rank, and domestic (Korean) and foreign songs do not differ in the time they take to exit the chart. 20 0.1 To further characterize the differences between groups using ANOVA, we conducted follow-up tests to see whe-

0 0.0 ther certain extrinsic properties led to different chart 0 20 40 60 80 dynamics. We see that “Male” and “Solo” artists show t pre significantly lower values on all parameters in Table I. Therefore their songs enter the chart lower, reach lower Figure 3. The life trajectory parameters of the songs on the peak ranks, and exit the chart quickly. Amongst different chart. (a) The inaugural rank is plotted along the x-axis, and genres, Ballad, R&B and soul, and Rock do not show the peak rank is plotted along the y-axis. (b) The amount significant differences, while Dance and Hiphop genres of time taken to reach the peak is plotted along the x-axis, are similar. Ballads are less successful than Dance and and the amount of time taken to first go off the chart after Hiphop music, reflecting the current state of the dance- reaching the peak is plotted along the y-axis. heavy K-Pop. When we study the more successful, “hit” songs, dis- tinct patterns emerge. In Fig. 4(a) and (b) we show ana- logous plots for the 689 songs that stayed on the chart the peak {t } are plotted along the x-axis, and the time pre for longer than ten weeks, accounting for 9.1% of the until exiting the chart since the peak {t } are plotted post songs in the full data set. In Fig. 4(a) we see that now along the y-axis. Since most songs stay on the chart for the songs occupy the top right side, meaning that suc- only a short period of time as shown in Fig. 1, they are cessful songs are likely to be already ranked high in its largely concentrated in the bottom left area. But overall early phase, implying that a song’s potential for on-chart tpost > tpre, meaning that for most songs the decay is success is realised at the very beginning, and appearing longer than ascension. on the chart does not necessarily translate to opportu- In order to understand how these parameters are re- nity for attaining a higher rank. The message is similar lated to the extrinsic properties of the songs, we uti- in Fig. 4(b) where tpre (x-axis) ranges merely between lize additional metadata of the artists and the genres. one and ten weeks (with the exception of Rock Party The artist metadata consists of three properties : Gen- Anthem by LMFAO which is not a K-Pop but a foreign der (Male, Female, or Mixed), Type (Solo, Group, or song, which we will discuss later in more detail) while Collaboration), and Nationality (Domestic or Foreign). tpost on the y-axis assume much wider values with the The genre metadata consists of five major classes–Ballad, maximum of 71 weeks. Consider PSY’s Gangnam Style Dance, Rap and Hiphop, R&B and Soul, and Rock– and IU’s Neoui Uimi in Fig. 4(c) A and B that do show that each accounts for at least five percent of the songs typical behaviors of K-Pop : Both take no to a very short in the entire data set. We use the analysis of variance time on the chart to reach their peaks. (ANOVA) method to determine whether there exist sta- We also find that foreign songs tend to show a tistically significant differences between groups of songs noticeably different general behavior from that of K- with those extrinsic properties. We compare the variance 4

Table I. Average trajectory parameters, and results of Kruskal test for 4810 songs (>1 week on chart).

Variable Subgroup N rinit rmax tpre tpost Success p-value Malea 2738 58.09 71.42 0.43 4.02 288.54 All < 0.01** Gender Femaleb 1684 60.74 72.41 0.48 4.38 320.90 but rmax : 0.31 Mixedb 388 61.52 72.60 0.51 4.55 327.91 Soloa 2509 57.13 70.17 0.43 3.78 273.08 All : 0.000*** Type Groupb 1897 61.70 74.12 0.46 4.69 339.11 but tpre : 0.0025** Collabob 404 61.49 71.76 0.55 4.38 319.80 Domestic 4654 60.05 72.70 0.43 4.19 305.79 All : 0.000*** Nationality Foreign 156 36.88 46.74 0.96 4.03 221.19 but tpost : 0.12 Ballada 1637 58.51 72.08 0.38 3.74 274.76 R&Ba 325 56.14 70.45 0.38 3.92 277.36 Genre Rocka 311 55.05 72.43 0.30 3.91 276.42 All : 0.000*** Danceb 1039 65.39 76.62 0.47 5.19 380.97 Hiphopb 653 61.05 70.95 0.48 4.31 308.15

Table II. Average trajectory parameters, and results of Kruskal test for 689 songs (>10 weeks on chart).

Variable Subgroup N rinit rmax tpre tpost Success p-value Male 361 91.63 94.43 0.88 13.93 934.56 All > 0.05 Gender Female 259 93.32 95.35 0.88 13.41 953.95 but r : 0.045* Mixed 69 93.48 96.57 0.86 14.41 972.33 max Solo 274 91.72 94.38 0.85 13.94 940.89 Type Group 346 92.95 95.44 0.86 13.50 940.58 All > 0.05 Collabo 69 92.86 95.19 1.09 14.58 989.81 Domestic 669 93.34 95.64 0.80 13.74 947.25 r , r , t : 0.000*** Nationality init max pre Foreign 20 62.65 73.45 3.60 15.45 891.60 tpost, Success > 0.05 Ballad 182 94.51 96.13 0.72 14.02 960.70 R&B 40 94.45 95.975 0.80 15.53 1070.18 Genre Rock 38 91.63 95.76 0.63 13.63 903.95 All > 0.05 Dance 217 93.77 95.75 0.76 13.30 947.16 Hiphop 106 93.85 95.71 0.71 14.27 953.06

Pop. Take by and Party Rock An- (p > 0.05). However, domestic and foreign artist groups them by LMFAO, for instance, that are the outliers in exhibit significant differences regarding rinit, rmax, and Fig. 4(a) and (b). New Thang entered the chart at rinit = tpre (p < 0.0001). Although the overall success are not 83, rising in the chart quite slowly (see Fig. 4(c) C), pea- significantly different, foreign songs have lower rinit and king at rmax = 65 and staying on the chart for a to- rmax, and take longer times to reach their peaks. These tal of 11 weeks. , on the other hand, observations regarding hit songs and their artist proper- took tpre = 24 weeks to peak, but exited the chart in ties imply that while non-musical extrinsic properties of tpost = 8 weeks. In fact, the other outliers in the plots of popular songs do in general matter for songs’ on-chart Fig. 4(a) and (b) tend to be foreign songs as well, taking behaviors, their effects become weaker when successful a longer time to reach their peaks than K-Pop songs : songs are considered and the intrinsic, musical qualities Six out of eight songs below diagonal x + y = 100 in of the songs become more important. Fig. 4(a) are foreign songs, and below y = x in Fig. 4(b) (meaning tpre > tpost), four out of the seven songs were foreign although only 5.41% (260) of the songs analyzed B. Chart dynamics of K-Pop vs foreign songs (4 810) are foreign. The Kruskal-Wallis test also reveals significant diffe- We now at the differences between rences between domestic and foreign songs with the group K-Pop and foreign songs. To do so we analyze two se- of 689 songs that stayed on the chart for more than ten parate subcharts of Gaon, primarily due to the small weeks. The average trajectory parameters of these groups sample size of foreign songs in the original data : Of the and p-values from the Kruskal-Wallis tests are given in N = 7 560 songs that ever appeared in the main Gaon Table II. Here, unlike the entire group of songs, artist digital chart, only three percent (260) are foreign. The features and genres do not show significant differences subcharts we use here are the digital top-100 charts ex- 5

(a) All ( > 10 weeks on chart) (b) All ( > 10 weeks on chart) 1 80

0.4 Neoui Uimi 0.4 (Meaning of You, IU) 20

60 x=y 0.3 0.3 40 max post 0.2 40 Gangnam Style 0.2 60 r Neoui Uimi t (PSY) New Thang (Meaning of You, IU)

(Redfoo) / Gangnam Style 0.1 20 0.1 80 (PSY) Party Rock Anthem (LMFAO) x=y 0.0 0.0 0 100 100 80 60 40 20 1 0 20 40 60 80 r init t pre (c) Peaks in the initial phases Peaks in the middle phases A. Gangnam Style (PSY) C. New Thang (Redfoo) 1 65 20 40 75 60 85 80 95 5th 10th 15th 20th Week 2nd 4th 6th 8th 10th Week B. Neoui Uimi (Meaning of You, IU) D. Party Rock Anthem (LMFAO) 1 50 20 60 40 70 60 80 80 90 100 10th 30th 50th 70th Week 10th 20th 30th Week

Figure 4. The life trajectory parameters of 689 successful songs (defined as longer than ten weeks on the chart). (a) The bulk of the songs are located on the top right, meaning that a majority of songs that appear on the chart are ranked high in the early phases. (b) For most songs tpre ranges up to ten weeks while tpost is much more wide-ranging with a maximum of 71 weeks. clusively for K-Pop and foreign songs. This yields a much the Max. Foreign songs on the other hand, while fewer larger set of foreign songs for us to analyze : 7 602 for K- than half the number of K-Pop in total, show a wider dis- Pop (there is not much difference, since the main chart tribution of the parameters in Fig. 4(c) and (d) : 18.7% was dominated by domestic songs to begin with), and entered the chart ranked 40th or lower, and 46 songs took 3 855 for foreign songs. Again focusing on those that sur- more than ten weeks to reach their peaks, with maximum vived for more than ten weeks on each chart (702 K-Pop tpre = 220 by Adele’s Someone Like You that entered the and 327 foreign songs), we find that the total life on the chart at rinit = 98. chart already show significant differences : K-Pop songs The question is, then, which factors are behind such survive on average 15.7 ± 0.4 weeks with maximum 73 visible differences between K-Pop and foreign songs. One weeks by IU’s Neoui Uimi, while foreign songs survive could argue that it could be the music itself, if there really 37.3 ± 1.0 with a maximum of 235 weeks by ’s are intrinsic differences between K-Pop and foreign pop. (Fig. 5(e) B). Even if such differences from a musical standpoint did Their life trajectories are plotted separately in exist at all, however, they would be quite subtle, given Figs. 5(a) to (d). They again confirm that K-Pop songs that nearly all modern popular genres–rock and roll, bal- reach their peaks early, with only 2.14% entering the lads, synth pop, electronica, etc.–in foreign pop are also chart under the 40th place, and the longest tpre is equal well represented in K-Pop. We therefore find it uncon- to ten, for Geu namjan marya (Because of You) by M.C vincing that the musical differences would be the sole 6

K-Pop ( > 10 weeks on chart) 20 1 (a) (b) 80

0.4 15 0.4 10 20 60 0.3 0.3 05 40 0510 15 20 40 max 0.2 post 0.2 Geu Namjan marya 60 r Neoui Uimi t (Meaning of You, IU) (Because of You, M.C the Max)

0.1 20 0.1 80

0.0 0.0 0 100 100 80 60 40 20 1 0 20 40 60 80 r init t pre Foreign ( > 10 weeks on chart) 20 (c) 1 (d)

0.35 Moves Like Jaggar 15 0.25 (Maroon 5) 10 200

20 0.30 0.20 0.25 05 150 40 0510 15 20 0.15 0.20 max post

0.15 100 r 60

t 0.10

0.10

50 0.05 80 0.05 Someone Like You (Adele) 0.00

0.00 0 100 100 80 60 40 20 1 0 50 100 150 200 r init t pre (e) Peaks in the initial phases Peaks in the middle phases A. Neoui Uimi (Meaning of You, IU) C. Geu Namjan marya (M.C the Max) 1 20 20 40 40 60 60 80 80 Domestic 100 10th 30th 50th 70th Week 10th 20th 30th Week B. Moves Like Jagger (Maroon 5) D. Someone Like You (Adele) 1 20 20 40 40 60 60

Foreign 80 80 100 50th 100th 150th 200th Week 50th 100th 150th 200th Week

Figure 5. The analoguous scatter plots for K-Pop (domestic) songs (red) and foreign songs (blue). Foreign songs are compa- ratively more spread out, probably due to less influence of extrinsic factors. 7 determinant of the differences in the chart dynamics of First, Fig. 6(a) shows the S values of the ten most songs. If not the intrinsic properties, then some external successful artists by the last week in our data set. Most factors may be in play here. While there could be many, artists display a pattern of alternating rises and plateaus here we study two that are widely believed to be defining in the growth of S, the plateaus meaning the time bet- characteristics of contemporary K-Pop, the artists and ween successive songs. While it is the band that generally the machinery of production companies. occupy the top positions, IU is a notable exception. Se- cond, Fig. 6(b) shows the S values of the top ten produc- tion companies. Most companies display linear growth III. ARTISTS, PRODUCTION COMPANIES OF patterns unlike their artist, with YG, SM, and Loen En- K-POP tertainment corporations being the major three as of the last week in our data. To view the relationship between an The observed fact that most songs reach their peaks in entity’s influence and the life trajectory of the songs they the very early phases of their lives does seem unnatural release, we compute the correlation between final value and counterintuitive–this means that the songs have al- of S and the four curve parameters plus overall success of ready realised potential for success during the one short each song (the area under its trajectory curve). The er- week before entering the chart or, even more bizzare, be- rors are estimated using the jackknife method [30, 31]. fore its release. We believe that the clues to the origin of Here we note that we consider the life trajectories of such behavior comes from a dominant recent trend in how songs from debuting artists, since unknowns in the mar- new K-Pop songs are produced and marketed : Produc- ket their production companies’ abilities and clout would tion companies are increasingly focusing on pre-release be the only major external, non-musical factor behind marketing to rally the fandom that prop up online strea- their chart performance. Of the 934 production compa- ming counts and downloads in the very early stages of nies that produced at least one new artist on the chart, the song’s release [17]. This happens in tandem with the 514 produced only one. To eliminate similar errors ori- actions of the fan base of the artist who are not passive ginating from such small players, we consider 193 artists consumers in music industry but active disseminators of (out of 1 680) that put more than ten songs, and the 55 the songs to the general public outside the fan base. This companies that put nine or more debuting artists on the means that production companies in K-Pop–influential chart. The results are shown in Fig. 6(c) and (d). entities that recruit, train, finance, manage, and market All parameters but the pre-peak time (tpre) show artist–and huge fan bases that reflect the artists’ prior strong positive correlations with S. This means that success and reputation may hold significant sway over the being a renowned artist or having powerful production chart success of new songs [27, 28], possibly even more company behind one’s back is highly correlated with ge- than their qualities may. Artists and producers of foreign neral chart success (i.e. long duration on chart and high pop songs, on the other hand, generally do not main- peak rank), but regardless of the prior reputation or com- tain such a strong presence in Korea which explains their pany’s influence the artist hits their peak early. To a skep- more natural dynamics on the charts (Fig. 4(e) and (f)). tical eye, this phenomenon may be a reason for doubting We now investigate the influence of artists and pro- the role of the “quality” of a K-Pop song in its chart duction companies on a song’s chart dynamics. We start performance ; since early peaking (short tpre) is universal by defining a quantity that represents the influence of while rmax is positively correlated with S, rmax could be an artist and a production company. Possible candidates due simply to the marketing and the established fan base could include the size of the fan base, the company’s sales of a company–because it suggests that a K-Pop song’s volume, stock price, and number of affiliated artists in success was somewhat determined even before its release, companies. But here we focus on chart performance as before it had a chance to be introduced to the larger the measure of an artist and a company’s influence. In consumer base–and tpost would also be a straightforward other words, we posit that a history of chart success is consequence of that (the higher the rank, the more time an indicator of the entity’s influence and future success. it takes to leave the chart). It should be noted, however, This is inspired by the so-called “Matthew effect”, the that this is not a complete picture, and there is still evi- rich-get-richer phenomena often observed in social sys- dence that quality and musical properties do matter in a tems [29]. We define the Chart Success Index Si of an song’s chart success. Ironically, one could make the point artist and a company i as the sum total of the weekly from the dynamics of foreign songs in the Korean mar- ranks of all songs produced by the subject in the history ket that lack such a level of support and marketing from of Gaon Digital Chart, i.e. production companies : Foreign songs are slow to gain   popularity, but they tend to have more staying power. It X w may be an unsatisfactory state of affairs for the business Si ≡ 101 − rs , (1) w∈All Weeks that the effect of marketing may eclipse the importance w s∈Ωi of musical quality for K-Pop, and it remains to be seen w how much role quality plays in the long run [32–34]. where Ωi = {s} refers to all songs from artist or company w i ranked on the chart on week w, and rs refers to the weekly rank of the song. 8

Artists Production Companies (a) (b) 35000 IU 120000 YG Entertainment SM Entertainment Big Bang IU Loen Entertainment 30000 100000 2NE1 JYP Entertainment Beast YG 25000 SNSD Busker Busker 80000 Core Entertainment T-ara FNC Entertainment 20000 Plan A Entertainment SM 60000 15000 Loen 40000 10000 Big Bang Chart Success Index Chart Success Index 5000 20000

0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Week Week (c) Pearson Correlation Coefficient (d) Pearson Correlation Coefficient Spearman Correlation Coefficient Spearman Correlation Coefficient Success Success (of a song) (of a song)

tpost tpost

t pre t pre

rmax rmax

r init r init

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 −0.2 0.0 0.2 0.4 0.6 0.8 1.0

Figure 6. (a)–(b) The growth of chart success index S of top 10 artists and production companies. (c)–(d) Correlation between the chart success index and average life trajectory parameters of song released by the artists and the production companies. The errors are estimated using the jackknife method [30]. All parameters except tpre are positively correlated.

1−2θ IV. ENDOGENOUS VERSUS EXOGENOUS descend slowly proportional to 1/|t − tc| where t = 0 PEAKS corresponds to the peak maximum and tc is an additional positive parameter. On the other hand, the relaxation of 1−θ Our analyses on the the impact of extrinsic properties exogenous peaks behave like 1/(t − tc) which decays separate from the intrinsic ones of popular songs are in much faster than endogenous peaks. Sornette also found line with earlier studies on the two types of dynamical an average value of the exponent θ ∼ 0.3 ± 0.1. Howe- features in complex networks : exogeneity and endoge- ver, Lambiotte [39] observed that the relaxation process neity [35–37] that are believed to cause critical peaks. can be as well seen as an exponential one that saturates Exogenous peaks occur in response to external kicks, toward an asymptotic state when focusing on the short- while endogenous peaks are spontaneous internal fluctua- time scale after a sales maximum (∼ 1 month). He sugges- tion formalized by the theory of self-organized criticality. ted a thermodynamic model to represent the decays with It is therefore well understood that it is important to a relaxation coefficient λ which is inversely proportional distinguish between exogeneity and endogeneity to mea- to the relaxation time, and found that the initial decay sure their respective effects to ultimately understand the of exogenous and endogenous peaks occurs on different fundamental dynamics underneath a system. In parti- time ranges : < λ >exo∼ 2 < λ >endo= 0.14. cular, Sornette et al. [38] introduced a model of epide- We apply these models to our data, limited to the 689 mic propagation which specifies that exogenous peaks oc- songs that stayed on the chart more than ten weeks for cur abruptly and are followed by a power-law relaxation sufficient data points. First, we transform a time series of while endogenous peaks are characterized by approxima- the rank R of a song into a time series of instantaneous tely symmetrical power law growth and relaxation. Ac- sales flux through the relation S = R−γ , γ = 0.5 follo- cording to the model, the endogenous peaks ascend and wing Sornette et al.’s approach. We fit the relaxation of 9

(a) Neoui Uimi (Meaning of You, IU) (a) 20 Power Law Fit 0.5 Exponenetial Fit -2 0.4 2 - 0.5 - 0.5 0.3 2-2 0.2 Sales ( R ) -2

0.1 Sales ( R ) 2 Endogenous, 1 - 2θ = 0.271 0 10 20 30 40 50 60 70th Week Exogenous, 1 - θ = 0.655 (b) 2-2 Early Peaker, 1 - θ = 0.669 0 2 4 8 16 0.10 Power Law Fit Exponenetial Fit (Weeks) 0.08 (b)

0.06 1.0

0.04 0.8 0.02

Mean Square Deviation 0.00 0.6 0 5 10 15 20 25 30 35h Week 0.4 t post (rank ordered)

0.2 Endogenous Figure 7. (a) Power-law (blue) and exponential (red) fits Exogenous Cumulated Probability to IU’s Neoui Uimi, the longest-surviving song on the chart. Early Peaker The power law-fit appears better matched. (b) The change of 0.0 root-mean-square deviation along the relaxation time, tpost. 0.0 0.1 0.2 0.3 0.4 0.5 At smaller tpost, the exponential fit (red) shows similar or better results than the power-law fit (blue), but the power- Relaxation Coefficient law fit shows smaller residual errors at large tpost. Figure 8. (a) Relaxation of sales after peaks obtained by averaging over songs in each class classified according to the life trajectories with power-law and exponential models precursory acceleration. (b) The cumulated histograms of re- respectively, and measure the root mean square deviation laxation coefficient λ for three classes : endogenous (blue), in order to quantify the goodness of fit. Lower values of exogenous (red), and early peaks (black). The vertical lines point to the average values 0.076 (endogenous), 0.178 (- the deviation imply a better fit. Fig. 7 (a) shows the genous) and 0.181 (early peaks). The exogenous and endo- power-law and exponential fits of the song Neoui Uimi, genous classes are markedly distinguishable, and early peak the longest-ranked on the chart, and Fig. 7 (b) shows group shows a similar behavior to exogenous peaks. the changes in the root-mean-square deviation along the relaxation time, tpost. At smaller tpost (< 5 weeks), the exponential fit (red) showed similar or better results than observe whether they show behaviors similar to those of the power-law fit (blue), but the power law seems to have endogenous or exogenous peaks. Fig. 8 (a) shows relaxa- lower residual errors at large t , implying that the re- post tion of sales after peaks obtained by averaging over songs laxation process behave exponentially at the shorter time in each class, and Fig. 8(b) present the cumulated proba- scale. bility of the relaxation coefficient λ in the three classes. In addition, we extract endogenous and exogenous Both figures clearly indicate difference between endoge- peaks inferred from their initial acceleration defined as nous and exogenous peaks being separated significantly. r−0.5−r−0.5 max init here based on the assumption that exogenous tpre The power law exponents in Fig. 8 (a) also approxima- peaks occur abruptly while endogenous peaks are formed tely obey Sornette et al.’s prediction, 1 − θ, and 1 − 2θ. relatively slowly. 30 high-ranked and low-ranked peaks In addition, the average relaxation coefficient of exoge- are respectively classified as exogenous and endogenous. nous peaks (0.178) is over that of endogenous peaks Meanwhile, as most songs (607 out of 689 songs) reach (0.076), implying that the relaxation time is significantly their peaks immediately as they are released, the initial shorter in exogenous shocks. Interestingly, the early pea- acceleration is not defined (rmax − rinit = 0, tpre = 0), so ker songs without any precursory pattern also show a we classify them as a separate “Early Peaker” group to similar behavior to exogenous peaks in both the power 10

(a) law exponent and relaxation coefficients, leading us to Wiarae (Up and Down) infer that their early peaks can indeed be attributed to 1 20 external forces rather than spontaneous fluctuations. 40

Rank 60 80 Release 100 Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan 2010 2010 2011 2011 2012 2012 2013 2013 2014 2014 2015 2015 2016 V. DISCUSSIONS (b) Reset 1 In this paper we have studied the life trajectories of K- 20 40

Pop and foreign songs on Korea’s Gaon Charts. We have Rank 60 80 shown that a large majority of life trajectories could be 100 Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan represented with four parameters of their peak rankings 2010 2010 2011 2011 2012 2012 2013 2013 2014 2014 2015 2015 2016 and duration on the charts. Many songs, especially K- (c) Gaseum sirin iyagi (Words That My Heart) Pop, were found to attain their peaks in the early phases, 1 20 which indicated the influence of non-musical external fac- 40

Rank 60 tors such as the power of artists and production compa- 80 100 nies. Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan We have demonstrated the possibility of utilizing po- 2010 2010 2011 2011 2012 2012 2013 2013 2014 2014 2015 2015 2016 pularity data to describe how the state of an industry (d) Yanghwa daegyo (Yanghwa Bridge) affects the success of products, and we believe that the 1 20 application is not necessarily limited to popular songs. 40

Rank 60 We have explored only a small range of possibilities, and 80 100 we hope to see our methods applied to more systems in Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan a wider gamut of products and markets. 2010 2010 2011 2011 2012 2012 2013 2013 2014 2014 2015 2015 2016 (e) We now conclude this paper by introducing two classes All I Want For Christmas Is You 1 of songs that do not follow the general trends of Fig. 4 20 but could still be interesting. The first class is “Late Bloo- 40

Rank 60 mers” that take an relatively long time since debut to 80 100 climb up the chart. This would be a very rare feat indeed : Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Only 1.5% of the songs (112 in total) manage to climb in 2010 2010 2011 2011 2012 2012 2013 2013 2014 2014 2015 2015 2016 (f) rankings for three straight weeks. A good example is Wi- Beotkkoch ending (Cherry Blossom Ending) 1 arae (Up and Down) by EXID : having failed to make it 20 40 to Gaon upon release, it went viral on other social net- Rank 60 working sites before taking the 1st place several weeks 80 100 Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Jan later, as shown in Fig. 9(a). Another example is Reset 2010 2010 2011 2011 2012 2012 2013 2013 2014 2014 2015 2015 2016 by Korean-American rapper Tiger JK. The song was in- tended as a soundtrack to a TV drama whose popularity Figure 9. Two types of notable outlier types observed in pushed up the song on to the charts, and its peak in the chart dynamics. (a)–(b) The first type are “Late Bloomers,” middle of its trajectory matches with the ratings peak for referring to songs that climb up the chart or peak noticeably the TV show, see Fig. 9(b). The second class of extraor- later than their market releases, often due to belated media dinary patterns is “Re-entrants”, referring to the songs exposure. (c)–(f) The second type are “Re-entrants,” refer- that return to the chart after falling from it the first ring to the songs that re-enter a chart after leaving it. Media time (we consider a song’s life trajectory on the chart exposure and seasonal changes are the main factors. has come to an end when it exits the chart and does not return within five weeks.). A very small percentage of the songs (1.5%, or 116 songs) are such cases, and an even smaller number (39) stay on the chart for longer than five weeks after re-entry. A detailed review of the forces behind such behavior tells us that there are broadly two effect, which is very straightforward : Christmas carols kinds : The first is renewed media exposure and broadcas- such as All I Want For Christmas Is You by Mariah ting. Particularly, getting featured on audition programs Carey (Fig. 9(e)) is a good example. The K-Pop song such as K-Pop Star (Korean version of American Idol) or Beotkkoch Ending (Cherry Blossoms Ending) by Busker game shows centered on songs is a common way by which Busker, popular upon its release, is an example that be- an old song experiences a surge of interest. Gaseum Si- came a spring carol of sorts that re-enters the chart every rin Iyagi (Words That Freeze My Heart) by spring in Korea, as seen in Fig. 9(f). To conclude, there (Fig. 9(c)) and Yanghwa daegyo (Yanghwa Bridge) by were evidence that, absent powerful production compa- Zion.T in Fig. 9(d) are famous examples helped by the nies, quality and other factors such as media exposure mass media, sometime gaining even more popularity af- could lead to chart success resulting in extraordinary life ter re-entry than upon its release. The second is seasonal trajectories such as the late bloomers and the re-entrants. 11

ACKNOWLEDGMENTS funded by the Korean government (MSIP-R0115-16- 1006), and National Research Foundation of Ko- This work was supported by the BK21 Plus Post- rea (NRF-20100004910, NRF-2016S1A2A2911945, and graduate Organisation for Content Science, IITP grant NRF-2016S1A3A2925033).

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