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  • 标题:The whoop curve: predicting entrepreneurial and financial opportunities in the performing arts.
  • 作者:Wacholtz, Larry ; Wilgus, Jennifer
  • 期刊名称:Academy of Entrepreneurship Journal
  • 印刷版ISSN:1087-9595
  • 出版年度:2011
  • 期号:January
  • 语种:English
  • 出版社:The DreamCatchers Group, LLC
  • 摘要:Albert Einstein (Songwriters Resource Network, 2010)
  • 关键词:Economic conditions;Entrepreneurship;Industries;Industry;Performing arts

The whoop curve: predicting entrepreneurial and financial opportunities in the performing arts.

Wacholtz, Larry ; Wilgus, Jennifer

"If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music."

Albert Einstein (Songwriters Resource Network, 2010)

"If we do our job ... Music's not black or white, it's green."

Jim Caparro, PGD (Knab, 2001)

"The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free and good men die like dogs. There's also a negative side."

Hunter S. Thompson (Rudolph, 2010)


A performance art product such as a film, sculpture, painting, musical recording or live concert emulates what we are often thinking, our hearts are feeling and our souls are judging. We often express, through our selection of artistic products, our introspective emotional thoughts by laughing, crying, feeling heartbreak, love, sadness, longing and other emotions we can sense or feel. Determining demand for performance art is thus complicated; it is based on emotions. One person may experience a film, computer game, recording or a live performance as positive and exciting, while another may find it revolting and still others may not even notice. It's the same for those who create, own, and manage the acts, recordings, videos, films, computer games, cell phone applications and songs we love, hate and ignore.

While preference formation is complicated, there is a financial motivation for its prediction. The entrepreneurs behind the artists or the entrepreneurial artists themselves are financially motivated to create entertainment products that satisfy consumer wants and needs (emotions). Additionally, they are encouraged to economize on products that have a high probability of not satisfying consumers. Towards this end, the authors develop a framework for entrepreneurial evaluation of entertainment products. The framework which we label "the whoop curve" represents an estimate of the ex-ante probability of success of the entertainment product. By whoop curve, we mean to say a relationship that predicts the current and future enthusiasm of an entrepreneurial product. We illustrate that these probabilities can be derived by considering the revealed strength of the emotional connections consumers have to the act.

The whoop curve model has two beneficial characteristics. First, the actual measure of success is a probability that some defined benchmark outcome will be achieved at a future specified date. The benefit of this feature is that probabilities are easily understood. Second, the benchmark of success can be modified to fit the entrepreneurial activity. In our example, we adapt the model to the music industry where success might be measured by unit sales at some future date. However, it can be adapted to include ticket sales, tour dates and other measures of success.

The technique used to derive the whoop curve is not new. Called duration analysis in other fields (i.e. engineering, economics and sociology), this method is a time honored and well established statistical technique (Hosmer & Lemeshow, 1999; Hald, 1990; Lancaster, 1997; Van den Berg, 2001). Our contribution is to develop, at an introductory level, the technique and concepts of duration analysis applied to an entrepreneurial problem in the music industry. Following Genc's (2004) duration modeling for introductory econometrics, an example problem is worked out using Microsoft Excel; a software program accessible to entrepreneurial students and music industry practitioners. Our choice of the whoop curve terminology (as opposed to duration analysis) is intended to signal that the topic can be easily incorporated into undergraduate entrepreneurial curriculum.

The paper is structured as follows. The next section develops the entrepreneurial problem. Section 3 introduces the whoop curve. An example of the derivation of the whoop curve employing Microsoft Excel is developed in Section 4 and Section 5 concludes.


The traditional entertainment and performance arts industries are large and complex. They are a collection of artists, entertainment conglomerates, film companies, record labels, consumers, the mass media (radio, television and print), cell phone networks, and Internet portals that together form the industry. There are local, regional, national and world markets. The artists are typically composed of songwriters, musicians, producers, recording artists, singers, audio engineers, graphic artists, actors, film directors, union members, and computer technicians.

For the purpose of this paper, we consider the entrepreneurial problem of record labels. They have to find and sign artists to their labels and songs to their publishing companies. They provide hundreds of thousands of dollars to recording artists to pay for advances, producers, musicians, audio engineers, background singers and studio rental time. Additionally, they provide money to market the recordings to various types of consumers through promotion, publicity and distribution to retail outlets. Labels range in size from worldwide distribution companies (entertainment conglomerates), such as Bertelsmann, Disney, Sony, Universal, and TimeWarner to the one-person operation that offers digital downloads over the Internet.

According to the Bureau of Economic Analysis' Survey of Current Business (2010), personal consumption spending on entertainment and recreation is a large part of the U.S. economy representing $929.3 billion real dollars in 2009. This is approximately 7% of our $12.9 trillion dollar U.S. economy when adjusted for inflation as measured by the Gross Domestic Product (GDP). During the same time period, the Recording Industry Association of America (2010) reports that the music industry accounts for $7.7 billion dollars or about 1 percent (0.06%) of the U.S. economy.

Figure 1 illustrates U.S. Bureau of Labor Statistics' Consumer Expenditure Survey (2010) data of mean quarterly household consumption spending on physical platforms (records, CDs, audio tapes), 1984-2008. We see that since 2000 the households in the sample have dramatically reduced their consumption of physical platforms. Presumably, the lost revenue has gone to online streaming, downloaded files, and piracy. In fact, research appears to support this conclusion (Andersen & Frenz, 2008; Bhattacharijee, et. al., 2005; Dejean, 2009; IIPA, 2010; McKenzie, 2009; Peitz & Waelbroeck, 2004; Stevans & Sessions, 2005; Zetner, 2006).

The large size of the entertainment and music industries and the impact of technological innovation suggest two main points. First, there exists a financial motivation for predicting talent success; a small proportion of a large market results in high revenues. Second, while technological innovation has negatively impacted revenues, it has also created a means to better track consumer preferences and thus their emotional connections to the act.

There are several examples of how technology can allow entrepreneurs to estimate consumer preferences. For example, data collected from per-to-per (P2P) search queries, Billboard charts, Nielson SoundScan, website hits, and social networking sites represent revealed consumer choices. Some recent examples of the use of these data in various studies include Andersen & Frenz (2008), Bhattacharjee, et. al. (2005), Bradlow & Fader (2001), Koenigstein, Shavitt & Zilberman (2009), Liebowitz (2007), Oberholzer-Gee & Strumpf (2007), and Stevans & Sessions (2005).


Traditional ways of identifying talent include tracking consumer trends through demographic and psychographic research. Demographic research is an analysis of comparison based on gender, age, income, and education. Psychographic research is a deeper analysis that groups individuals by their lifestyles tied to zip codes. The results are used by labels to market tours, corporate sponsorships and merchandise. However, shouldn't there be a way to predict success for labels before they sign an act and spend the money? And, once they are signed, what is the likelihood that they will be successful in a given time period?

The tools of economics and access to new data (i.e. P2P search queries, SoundScan, social networking sites) can be used to help answer the prediction of success problem. While it may be difficult to predict emotional responses to performance arts presentations and products, consumer preferences for those products and services are revealed in terms of units sold, tickets purchased, or venue attendance. These revealed preferences can be proxied by web page hits, air play, online streaming, social network hits and publicity hits, for example. Therefore, applying the tools of economics and utilizing accessible consumer data, the authors are able to predict the preferences illustrated in the whoop curve model in the following section.


Figure 2 illustrates the essential prediction problem: possible artist outcomes. The vertical line displays the success of the artist that can be measured in a variety of ways (the example utilizes unit sales). The horizontal line indicates time. The 45 degree line represents the investment project line. A curve extending above the 45 degree line indicates acceptance of the entertainment products. A curve extending below the 45 degree line indicates rejection over time. To be more specific, Line A illustrates a type of powerful emotional response by consumers. This of course, indicates the act is already being noticed and accepted by consumers. Artist development time, marketing and promotion will be shorter and potential profits are greater. Line B illustrates that the act is becoming successful yet it has taken far too long and lies below the investment project line. Thus, the act is being noticed, yet it is still not popular enough to be signed, as the label cannot make any profits. Sadly, Line C illustrates the act had some emotional connection to consumers, yet it quickly faded and would not even be considered.


The tension for the entrepreneur is that the success curves are not known before the endeavor is undertaken. That is, it is unknown which curve the artist will eventually be on. Over time the artist's success (or lack thereof) will be revealed. However, as previously stated, industry pressures make prior prediction of the direction essential. For the prediction problem, the authors suggest using variables to explain the likelihood of success and thus develop "the whoop curve". Much like Forbes Magazine uses to determine their Celebrity 100 List, our approach is similar in spirit. For example, the Forbes list includes salary, TV/radio, press rank, web rank and social rank. Our procedure uses conceptual benchmarks such as past units sold, web page responses, publicity hits in local or national media, events, tours or shows, social websites and broadcasts or digital streaming as predictive variables. These data are available through such sources as Nielson SoundScan, Broadcast Data Services (BDS/The Monitor), Billboard Charts and Big Champaign.

Unlike the Forbes ranking, however, the whoop curve probabilistically weights the predictive variables by correlations based on how quickly or slowly (weeks or months) the acts and their recordings are able to gain rankings based on the strength of the emotional connections consumers have to the act (displayed by the purchasing, using or stealing of the acts products).

To demonstrate the predictive problem, consider the release of a recording by two previously unknown artists--Taylor Fast and Taylor Slow. Initially, Taylor Fast has 25,000 social network hits on her website from individuals interested in her music. Alternatively, Taylor Slow has only 250 network hits. Based on this information the label (large conglomerate or one-man show) is trying to determine how successful each will be within two years. Success is defined as unit sales exceeding 500,000 by two years. The probabilities of their successfully achieving the goal of 500,000 unit sales within one and two years are plotted against time in Figure 3.

Based upon the example, Taylor Fast gains consumer acceptance quickly; the probability that she will achieve the entrepreneurial goal is almost 100% after one month. Taylor Fast's unit sales are represented by Line A in Figure 2. Taylor Slow never really gains consumer acceptance. As such, Taylor Slow's unit sales look more like Line C in Figure 2. Figure 3 is indeed the whoop curve; the probabilistic weights of success. If you are entrepreneurial, who would you be more "whooped" about after 1 month? Who would you be more "whooped" about after a year? Which artist would you be more likely to spend your time and resources on?


Because the whoop curve measures probabilities over time, the curve can be illustrated in other intuitive ways--perfect for classroom illustration. One method that illustrates the essence of the whoop curve is decision tree analysis. Figures 4A and 4B illustrate the decision tree representation for the probability of success (in terms of consumer acceptance) in 1 month, 12 months and 2 years for Taylor Fast and Taylor Slow, respectively. Like the whoop curve, decision tree analysis provides a basis of comparison between the two artists. Taylor Fast's probability of success rises with each time period more rapidly than Taylor Slow's probability of success. In fact, within 1 month Taylor Fast is highly likely to reach the goal of 500,000 units sold while Taylor Slow is likely to never reach that goal. Obviously the keys to Figures 4A and 4B are the probabilities.



By applying the predictions of the whoop curve, entrepreneurial efforts could shift from using costly traditional marketing, promotion, and publicity campaigns to help consumers discover new acts towards a more favorable decision making process of artist selection. Thus, industry leaders improve their decision making ability and ultimately improve their profit margins. The next section illustrates how to estimate the probabilities, and thus the whoop curve, so that if you are an entrepreneur, you can determine who to be "whooped" about.


To illustrate how the whoop curve is derived, the authors construct a hypothetical example using the data presented in Figure 5. The columns within Figure 5 represent previous artists (Taylor A through Taylor M), the length of time to achieve the goal of 500,000 units sold, whether the goal was reached within 24 months, and the number of social website hits. The table shows that the artists with the majority of social website hits, on average, successfully and rapidly attained the goal within the specified period of time.

The correlations between the explanatory variable (social website hits) and the attainment of the goal can be exploited to derive the whoop curve via the theory of maximum likelihood. In this case, the likelihood function is known in other fields of science as a Weibull distribution (Lancaster, 1997). The log-likelihood function defined on the Weibull distribution to be maximized is given in equation (1):


Here the functions f and F are the probability and cumulative density functions for the Weibull random variable. The variables [t.sub.i], [social.sub.i], and [d.sub.i] are, for each artist i, the number of months needed to achieve the goal, the number of social website hits, and attainment goal indicator. The parameters to be estimated are [alpha], [beta], and c.

Statistically, the parameter [beta] represents the correlation between the probability of goal attainment within 24 months and social website hits. In the example, [beta] is most likely positive. The parameter c represents how likely the goal will be achieved holding social website hits constant at zero. The parameter can be positive or negative. The parameter [alpha] measures the influence of time on the probability of goal attainment. In our example, it appears that the goal is more likely to be achieved as time passes. It is expected that [alpha] will be greater than one ([alpha] < 1 implies time negatively effects the probability). The specific formula for the Weibull density is given in equation (2):

f([t.sub.i] | [social.sub.i], [alpha], [beta], c) = exp(c + [beta][social.sub.i])[alpha][t.sup.[alpha]-1.sub.i] exp(-exp(c + [social.sub.i])[t.sup.[alpha].sub.i]) (2)

while the cumulative density is defined by (3):

1-exp (-exp(c + [beta][social.sub.i])[t.sup.[alpha].sub.i]) (3)

New variables and, hence correlations, can be added to the formula to strengthen the predictability of the model. Figure 6 specifically documents how the likelihood is constructed in Microsoft Excel given the hypothetical data set found in Figure 5.

Figure 7 illustrates how the likelihood function is maximized by choice of [alpha], [beta], and c using Microsoft Excel solver. The maximization reveals three parameters given in Rows 19-21 of Column B. The most relevant parameter estimate, defined as [beta], is the effect of social website hits on the probability of goal attainment. The estimate of 1.2881 indicates that an increase in social website hits will positively influence goal attainment.

Figure 8 is the whoop curve that was defined by the previous parameter estimates and equation (3). In this case, we ask two hypothetical questions. First, suppose that a talent had 25,000 social website hits (Taylor Fast), what would we expect her whoop curve to look like over time? Second, suppose a competing talent (Taylor Slow) had 250 social website hits, what would her whoop curve look like over time? Figure 8 depicts the results whereby Taylor Fast is highly likely (87.8% chance) to obtain the entrepreneurial goal within one month while Taylor Slow is unlikely to fulfill the goal attainment (probability of attainment is never above 39.8% in the example). A conclusion can be determined from this analysis. Based on past correlations of this example, artists with high social website hits are more likely to attain goals. Therefore, entrepreneurs would have a vested interest in identifying talent with this attribute.





Given the large size of the entertainment and performance arts industries and the pressure to identify successful acts, the authors have shown that a basic whoop curve can provide creative artists and entertainment industry entrepreneurs with a powerful, yet inexpensive process to predict financial success. Utilizing industry constructs, the whoop curve probabilistically weights the predictive variables by correlations based on how quickly or slowly the acts are able to gain rankings given the strength of emotional connections consumers have to the acts. As a result, the predictive problem of success encountered in the industry is addressed enabling entrepreneurs to spend their time and resources more efficiently on acts most likely to satisfy consumer desires. Thus, industry leaders improve their decision making ability and ultimately improve their financial success.

Because the whoop curve model measures success in probabilities, the model is easily understood. This enables educators the opportunity to motivate their students in the decision making process while incorporating tools that are applied in the industry. As a result both industry leaders and students (future industry leaders) benefit by learning the whoop curve methodology.


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Larry Wacholtz, Belmont University

Jennifer Wilgus, Belmont University
Figure 5
Hypothetical Data Set

         A           B          C             D

1     The Data
2                Months to   Attained     Social Web
3       Name      500,000      Goal     Hits (thsands)
4     Taylor A       1          1             25
5     Taylor B       2          1             15
6     Taylor C       3          1             16
7     Taylor D       7          1             10
8     Taylor E      10          1             6
9     Taylor F      12          1             5
10    Taylor G      14          1             4
11    Taylor H      13          1             3
12    Taylor 1      20          1             3
13    Taylor J      22          1             2
14    Taylor K      23          1             1
15    Taylor L      24          0            0.5
16    Taylor M      24          0            0.25

Figure 8
Whoop Curve Results for Taylors Fast and Slow

         A           B             C         D

40    Prob of reaching goal
41    Months      Taylor         Taylor
42    Elapsed      Fast           Slow
43       0      0.B77B297B2   2.B0BB6E-14
44       4           1        1.1955IE-07
45       3           1        3.15006E-05
45      12           1        0.001029342
47      16           1        0.013024S51
4S      20           1        0.092669534
49      24           1        0.39B363139