1 Introduction

This paper seeks to describe common patterns in the life cycles of successful rock bands. Given the size of the industry and its impact on people, there are various studies that analyze the industry, its players, and the individual rock bands in more detail. A recent important contribution is Krueger (2019), which gives detailed and lucid insights in the music industry. Not many rock bands are successful, and many do not become successful (Strobel and Tucker, 2000), and even less rock bands become superstars (Rosen, 1981).

What seems to be lacking in the relevant literature is a generalization of descriptive features about the careers of successful rock bands. For example, how long after the entry in the music industry did it take for a now well-established rock band to have initial success? And how long did this success last? What happens when mainstream listeners adopt the music? If there is such a second generation, after how many years does that success peak?

As many rock bands have a long history, this paper focuses on rock bands like Metallica and Guns N Roses. A second choice in this paper is to measure the success of a rock band by the annual number of shows that have been performed. I consider the number of shows because accurate annual data are available for long periods of time, whereas for other indicators of success such lengthy series of data are not available.

To summarize the descriptive features of a range of rock bands, this paper puts forward a simple empirical model. The model includes two episodes of success. The first concerns entry, debut, and first shows, and is usually confined to early adopters of the music of a particular rock band. Without losing the first adopters, a second episode may associate with a broader audience, and it may be that this second period involves more success than the first wave.

The model is fitted to empirical data for forty-nine different but successful heavy metal bands. The bands cover a wide spectrum of subgenres, countries of origin, and years of debut, and hence there is substantial variation in the data. It is found that the model fits very well with the empirical data, and that various generalizing statements can be made. One of these is that the second wave of success peaks many years after the peak of the first wave. And the second wave of adopters, measured by the number of shows, outnumbers the amount of first wave adopters.

The outline of this paper is as follows. Section 2 provides a literature review on various measures of success. Section 3 describes the data and presents some basic statistics. Section 4 puts forward the empirical model. Section 5 presents the estimation results. Section 6 concludes with a discussion and various avenues for further research.

2 Literature review

There are various measures of success of creative performance. When we focus on the music industry, one can think of various measures of income. If artists have enough income, they can sustain and have a longer career. Income can be generated by album sales, concert ticket sales, merchandise sales, licensing deals and, in recent years, for example Spotify downloads. Enough income does not come overnight, and it may take a while to happen.

There are also various factors that influence the success, for example, of rock bands. One can think of external service providers, online platform searches, copyright revenues, social media impact, and the length of time that they stay high on hit lists, see for example, Cox, Felton and Chung (1995), Fisher et al. (2002), Giles (2007), Hughes et al. (2013), Krishnan (2010), and Smith (2013).

A recent example of the association of rankings and success is provided in Boughanmi and Ansari (2021), who consider Billboard 200 rankings for the period 1963–2016. Their focus is on specific albums of musical performers. Like the approach in Giles (2007), Elliott and Simmons (2011) consider vinyl and CD sales, live albums, soundtracks, and the total amount of albums sold. These data are viewed as a cross section, and then a power law is fitted to the data with various moderating factors. This latter approach is rather common across relevant studies, and that is the approach to translate annual or weekly observations into cross-sectional data. An exception perhaps is Albinsson (2013), where the analysis concerns yearly revenues for individual music IPR owners.

Studies on creative industries, other than the music industry, have similar characteristics. Study the growth and decline in mobile game diffusion, and these authors consider the number of days for a game to reach the top 20 in the Google Play game download chart. Walls (2019) looks at the market for DVDs and considers daily data for 2006–2009 on rank and sales revenues for a top thirty of DVDs. As concerning books, Gaffeo, Scocu and Vici (2008) study demand distribution dynamics, where they look at numbers of book sales in Italy 1994 – 1996, which are then treated as a cross section per book and included in the estimation of power laws.

In our present study we wish to explore the life cycles of rock bands over time, and hence we need a measure of success that can be observed for many years over time. Inspired by Connolly and Krueger (2005), who address concert revenues, we decided to consider the number of shows per year as a measure of success. Of course, such a measure also comes with its limitations, but on the positive side we will see that data are available ever since the start of the bands that we consider, that these data are relatively free from measurement errors, and that, due the sample length, it allows us to study various features of the life cycles of rock bands.

3 Data

In this paper, we measure success as the number of shows given per year by a rock band.Footnote 1 Next, it must be decided which successful rock bands will be considered. For that matter, a list of the forty-nine best metal bands is taken.Footnote 2

Table 1 presents the forty-nine bands in alphabetical order. To illustrate how the data look like, consider the annual number of shows from 1968 to and including 2017 for Black Sabbath in Fig. 1. There are years with zero shows and the peak year is 1970 with 171 performances. This is a measure of new success. Additionally, Fig. 2 presents the cumulative success for Black Sabbath. The Black Sabbath data are by no means exceptional, as can be learned from Fig. 3, which presents the cumulative success (here all measured as the cumulative number of annual performances) over the years for all forty-nine rock bands in the sample.

Table 1 Statistics on annual shows by forty-nine heavy metal bands
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Fig. 1
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Number of shows per year by Black Sabbath, 1968–2017

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Fig. 2
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Cumulative number of shows by Black Sabbath, 1968–2017

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Fig. 3
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Cumulative number of shows by all forty-nine heavy metal bands

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The forty-nine bands cover various subgenresFootnote 3 within the heavy metal genre,Footnote 4 like thrash metal (Slayer), industrial metal (Nine Inch Nails), rock and roll (Guns N Roses), death metal (Death), doom metal (Paradise Lost), and power metal (Helloween). Also, the forty-nine bands are from various countries. The US and UK dominate, but Brazil, Japan, Germany and even the Netherlands (Within Temptation) are represented. Furthermore, as Table 1 indicates, the starting year of the rock bands, which is here the year with their first show, can be any year between as early as 1968 (Black Sabbath) and as recent as 2010 (Babymetal and Ghost). The final column shows that there is also great diversity in the number of total performances, with 281 (Babymetal) as the minimum and 2754 (Motörhead) as the maximum. In sum, the data display substantial variety.

Some further statistics of the forty-nine rock bands are presented in Table 2. The maximum amount of shows in one year is obtained by Anthrax (with 213 shows). The highest average number of shows across the years is performed by Ghost (76.5). For some bands there is a substantial difference between the mean and median, and this is caused by the fact that some bands (like Alice in Chains, Disturbed, King Diamond) did not perform at all during a range of years, before they came back with a potential second wave of success. Trivium can be seen as the most active band over their years.

Table 2 Statistics on annual shows by forty-nine heavy metal bands
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4 The empirical model

It is now helpful to have a simple model that can be fitted to the data. The main idea in the present study is that there potentially are two waves of success. A generalization to three of more waves is conceptually straightforward and might be interesting for future work. A first wave could occur after the debut, where the first shows are booked, where positive critical appraisal appears in the relevant media, and where the first adopters embrace the rock band. This first wave success, measured by the cumulative number of annual shows, can be described for example by a logistic curve \(G_{1,t}\) like

$$G_{1,t} = \frac{{m_{1} }}{{1 + {\text{exp}}\left( { - \gamma_{1} \left( {t - \tau_{1} } \right)} \right)}}$$

where \(t = 1,2,3, \ldots ,T\), where \(m_{1} > 0\) is the total cumulative amount of success and where \(\gamma_{1} > 0\) measures the steepness of the curve around the inflection point \(\tau_{1} > 0\). At the inflection point \(t = \tau_{1}\), cumulative success equals \(m_{1} /2\). The logistic function is easy to analyze, and its parameters are easy to estimate.Footnote 5

After that first wave, new success may die out, maybe because a second or third album is not that good, there are problems within the band, some band members may go solo, and replacement must be found, amongst possible reasons. Issues with managers can appear, problems with drugs and money can emerge, and of course new competitive bands with perhaps similar music may enter the market. When reading the internet pages on various bands, one can encounter many anecdotal stories on almost every rock band. When a rock band persists, it may make a re-entry with a new album or albums which also may attract either a more mainstream audience or a new generation of younger adopters. Taking again a logistic function, this second wave of success may be described by a logistic function \(G_{2,t}\) as

$$G_{2,t} = \frac{{m_{2} }}{{1 + {\text{exp}}\left( { - \gamma_{2} \left( {t - \tau_{2} } \right)} \right)}}$$

where \(m_{2} > 0, \gamma_{2} > 0\), and \(\tau_{2} > 0\). When herding is at stake (Banerjee, 1992), it may be that \(m_{2}\) is much larger than \(m_{1}\). And, obviously, \(\tau_{2} > \tau_{1} .\)

It is proposed in this paper to take the sumFootnote 6 of the two waves,Footnote 7 like

$$G_{1,t} + G_{2,t} = \frac{{m_{1} }}{{1 + {\text{exp}}\left( { - \gamma_{1} \left( {t - \tau_{1} } \right)} \right)}} + \frac{{m_{2} }}{{1 + {\text{exp}}\left( { - \gamma_{2} \left( {t - \tau_{2} } \right)} \right)}}$$

to describe the total cumulative success. To illustrate, Fig. 4 presents the two separate waves of successes (not yet cumulative) for some hypothetical values for the six parameters (\(m_{1} ,m_{2} ,\gamma_{1} ,\gamma_{2} ,\tau_{1} ,\tau_{2} ),\) whereas Fig. 5 presents the two waves with cumulative success. More important is Fig. 6, which presents \(G_{1,t} + G_{2,t}\). As we saw from Fig. 3, this pattern is very often seen for rock bands and their annual shows. For data on the total number of shows \(G_{t}\), with \(t = 1,2,3, \ldots ,T\), and with an error term, the empirical model reads as

$$G_{t} = \frac{{m_{1} }}{{1 + {\text{exp}}\left( { - \gamma_{1} \left( {t - \tau_{1} } \right)} \right)}} + \frac{{m_{2} }}{{1 + {\text{exp}}\left( { - \gamma_{2} \left( {t - \tau_{2} } \right)} \right)}} + \varepsilon_{t}$$

where \(\varepsilon_{t}\) is an error term with mean 0 and constant variance \(\sigma^{2}\). The six unknown parameters (and their associated standard errors) can be estimated using Nonlinear Least Squares (NLS).

Fig. 4
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Theoretical pattern of new success, measured by two stages: Hypothetical data for 1960 to 2020

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Fig. 5
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Theoretical pattern of cumulative success, measured by two stages: Hypothetical data for 1960 to 2020

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Fig. 6
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Theoretical pattern of cumulative success, measured as the sum of the two stages: Hypothetical data for 1960 to 2020. Note that it is this type of data that we observe in practice

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The six estimated parameters for \(N\) (here forty-nine) cases provide the basis for some empirical generalizations. A first generalization concerns the values of \(\tau_{1}\)(the peak moment of the first wave of success), and \(\tau_{2}\) (the peak moment of the second wave of success), and their ratio or difference. That is, how long does it take to have a second wave of success? A second generalization concerns the values of \(m_{1}\) and \(m_{2}\), and specifically their ratio or difference. That is, how much larger (or smaller) is the second wave of success relative to the first? A third generalization concerns the values of \(\gamma_{1}\) and \(\gamma_{2}\). If the first wave of success happens fast, then growth (and decline) of new success around the peak moment can be steep. And, when it takes a while for the second wave of success to occur, then one may perhaps expect that \(\gamma_{2} < \gamma_{1}\). Finally, one may look at the relation between \(m_{2}\) and \(\tau_{2}\), that is, it is perhaps not unexpected that the later the second wave of success comes, the larger is the total cumulative success.

5 Estimation results

The estimation results for \(m_{1}\) and \(m_{2}\), with their associated standard errors, are presented in Table 3. Summary statistics for the forty-nine cases are presented in the first two rows of Table 5. In eight cases for both parameters, the associated t statistics are smaller than 2, but in all other cases, the maturity levels are estimated with substantial precision. This is also reflected by the (unreported) estimated values for the errors \(\varepsilon_{t}\) which are very small.

Table 3 Estimation results (Estimated standard errors in parentheses)
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A regression of forty-nine values of \(m_{2} - m_{1}\) on a constant term, gives (with an estimated standard error in parentheses)

$$m_{2} - m_{1} = 465 \left( {81.7} \right)$$

Hence, \(m_{2}\) is estimated as significantly larger than \(m_{1}\). The mean of the ratio \(\frac{{m_{2} }}{{m_{1} }}\) is 2.76 and the median is 1.83. In short, the first empirical generalization for these forty-nine successful metal bands is that the second wave of success is about twice as large as the first wave.

Table 4 first reports the estimation results and associated standard errors for \(\gamma_{1}\) and \(\gamma_{2}\). In forty and forty-one cases, respectively, the t statistics are larger than 2. A regression of \(\gamma_{1} - \gamma_{2}\) on a constant, gives

$$\gamma_{1} - \gamma_{2} = 0.724 \left( {0.117} \right)$$
Table 4 More estimation results (Estimated standard errors in parentheses)
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This means that the speed with which the first peak of new success is attained is 0.724 larger than the speed with which the second wave success is attained. This provides a second empirical generalization. The first wave of fans apparently adopts the music of a band much faster than the second wave of fans.

The last two columns in Table 4 present the estimation results for the timing of the peaks of the two waves. A traditional t statistic is of not much value here (as the null hypothesis that \(\tau_{1} = 0\) is not meaningful) but comparing the estimates with the estimated standard errors shows that the inflection points are estimated with substantial precision. Table 5 shows that the \(\tau_{1}\) is estimated on average as 7.28 years, while the average of the forty-nine estimates of \(\tau_{2}\) is 20.6 years. The mean of the ratio \(\frac{{\tau_{2} }}{{\tau_{1} }}\) is 3.22 and the median is 2.83. In short, the third empirical generalization is that the first wave of success takes seven years to occur, and it takes around twenty-one years for the second wave of success.

Table 5 Summary statistics of the estimated parameters
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Finally, in a regression of the forty-nine estimates of \(m_{2}\) on an intercept and the estimates of \({\tau }_{2}\), the slope parameter is estimated equal to 34.4 with standard error 9.73. The \(R^{2} = 0.210\). Hence, the fourth feature of the life cycles is that the longer it takes to have the second wave peak, the larger is the second wave success.

6 Discussion and conclusion

Based on a simple empirical model that matched well with the data on cumulative annual shows of forty-nine heavy metal bands, this paper has established four common features of the life cycles of successful rock bands. The first is that the second wave of success is about twice as large as the first wave. The second is that first wave of fans adopts the music of a band much faster than the second wave of fans. The third feature is that the first wave of success, on average, takes seven years to occur, and it takes about three times as many years for the second moment of peak success. Finally, the fourth feature is that the later the second wave peaks, the larger is the second wave (and total) success.

This paper has studied only forty-nine rock bands, and this analysis can of course be extended to other genres and to individual performers. Upon doing so, one may follow the lines of thought in Rossman, Chiu and Mol (2008) and introduce a second layer in the model, which contains the characteristics of the rock bands, to see which of those characteristics influences the parameters in the logistic curves.

All in all, the main conclusion of this paper is that the life cycle of a successful rock band is a lengthy one. In terms of years, initial success does not come fast, nor does the second wave of success. Next to quality and other factors, apparently it is perseverance that seem a key factor for a successful career in the music industry.

This paper studied the market for heavy metal music. It is of course interesting to study other markets, like those for books, video games and movies, where there are sequels to early works. It is not the same issue as we have discussed here, but it may well be that sequels arouse attention to initial releases and earlier work of film makers and authors.

What is it that artists can learn from the results in this study? It seems that success spreads over a long period of time. Immediate success is rarely seen, and the second wave of success can take a long while. So, it seems that not giving up is an important factor of success. This associates with the recognition that rock bands are a joint effort, see Phillips & Strachan (2016), and Ceulemans et al. (2011), and that success assumes perseverance.

An obvious limitation of this study is that we have measured success just by the numbers of shows per year. Of course, the amounts of shows do not tell the full story. The size of the venues will be different, and some bands would prefer small venues while others are attracted to festivals. More detailed data would be useful, while also having insights into the prices paid by the attendees could be useful. Collection of such relevant data is definitively an interesting issue for further research.