Predicting not only the effects of music promotion, but also a cult following. April 4, 2018 MKTG/STAT 476/776 Prof. Peter Fader Abstract This paper analyzes the purchase processes of two obscure alternative rock albums by fitting 28 timing models. By drawing insights from music history and the music industry, the author determines that a “Weibull 2- Segment Finite Mixture Model with covariates associated with music promotion (airplay, the holiday season, tours and EPs)” can be an actionable tool for music promoters at record labels to both assess the efficacy of different promotional tactics and gain insights about consumer behavior. Finally, one segment of the final model’s positive duration dependence appears to have been able to predict that Sparklehorse would develop a cult following. 1 Contextualizing the Data: Alternative Rock and the Music Industry With the breakthrough phenomenon of Nirvana’s Nevermind album in 1991, alternative rock entered the mainstream. Previously, major record labels such as Capitol, EMI and Warner Bros had deemed “alternative” rock unprofitable and left them to indie labels. However, in response to the changing landscape of popular music, the major record labels greedily signed talented alt-rock bands. Popular radio and MTV (Music Television) aggressively increased the genre’s airplay in their weekly rotations per audio and music video formats, respectively. Ironically, even though that and other mainstream album and tour promotional tactics were against the do-it-yourself ethos of alternative rock, bands such as Pearl Jam, Soundgarden, and Radiohead nevertheless achieved notoriety. Yet, many other alternative rock bands have since faded into obscurity. Two such bands, both signed by Capitol Records, are Dink and Sparklehorse. Dink released one self-titled album, Dink (1994) with noticeable promotion upon debut, before Capital decided that the band no longer had commercial viability and dropped it. Sparklehorse’s debut album, Vivadixiesubmarinetransmissionplot (1995), was well-received by critics and eventually gained some attention from college radio stations. Ultimately, Sparklehorse developed a cult following that was remarkable enough for the band to be the subject of a documentary, The Sad & Beautiful World of Sparklehorse, in 2016. This history is reflected in the sales and airplay data of the first 27 weeks of the bands’ respective debut albums. It is evident that Capitol believed in Dink but not Sparklehorse. Dink was met with immediate radio attention, likely due to Capitol’s promotional efforts, but rapidly lost the attention of radio stations after approximately three months. Conversely, Sparklehorse’s album did not receive any airplay until its nineteenth week, after which its airplay drastically increased for nearly two months before plateauing. Notably, even at its maximal weekly airplay in its first 27 weeks, Sparklehorse’s album did not receive as much airplay in one week than Dink did in its first week. This is unsurprising; college radio simply does not have the same reach as mainstream radio. These observations suggest that using probability models to understand the underlying purchase processes of their albums may both confirm intuitions about the music industry and yield fascinating new insights into the fundamental drivers of album promotion. 2 A Baseline for Comparison: Basic Probability Models The album purchase data matches the criteria of timing models. The number of purchases per week has an integer value. Furthermore, the assumption that each consumer only purchases one album simplifies modeling. Fitting basic exponential models provides a baseline for comparison with future models: Dink Model λ Total LL BIC MdAPE Exponential 0.0295 -255510.63 511032.77 24.90% Sparklehorse Model λ Total LL BIC MdAPE Exponential 0.00156 -31036.88 62085.27 50.60% Dink Sparklehorse Exponential Exponential 4000 1000 2000 500 0 0 1 4 7 10 13 16 19 22 25 1 4 7 10 13 16 19 22 25 Actual Expected Actual Expected 2 3 Understanding Heterogeneity: Gamma Mixture and Zero-Inflation No justification was provided for the assumption that the population size (N) is 100,000. It is unclear whether N includes all music buyers, popular music listeners, casual alt-rock fans, or only hardcore alt-rock diehards. Given that Capitol is a major record label in this era of music history in which “alternative” is also mainstream, this assumption is particularly frustrating and questionable for understanding what significance the population’s heterogeneity actually holds. Fitting Exponential-Gamma models, both with and without “non-buyers,” helps to elucidate the nature of the data’s heterogeneity without breaking the N = 100,000 assumption: Dink Model p(buyer) λ Total LL BIC MdAPE Exponential (Zero-Inflated) 0.999 0.0296 -255514.10 511051.22 24.911% Model p(buyer) r α Total LL BIC MdAPE Exponential-Gamma -- 23814.46 8751199 -255692.00 511407.12 28.40% Exponential-Gamma (ZI) 0.999 19051229 64486053 -255514.10 511062.73 24.91% Sparklehorse Model p(buyer) λ Total LL BIC MdAPE Exponential (Zero-Inflated) 0.999 0.00157 -31036.90 62096.83 50.60% Model p(buyer) r α Total LL BIC MdAPE Exponential-Gamma -- 1361635 870854408 -31036.90 62096.78 50.60% Exponential-Gamma (ZI) 0.999 1.837 1169.78 -31051.5 62137.62 49.29% Two worthwhile observations can be made regarding these models: first, “non-buyers” do not exist under the population-size assumption because the probability of being a buyer is essentially 100%. Second, the Exponential-Gamma spews out nonsensical parameters; this implies that the population is rather homogeneous. Both of these observations suggest that N merely represents the (fairly homogeneous) population of alternative rock fans who are passionate enough to buy albums by bands like Dink and Sparklehorse. This result would be consistent with the actual history of the albums; Dink failed to attract a mainstream audience and Vivadixiesubmarinetransmissionplot only caught on with the college radio niche. 3 4 Factoring in Duration Dependence: Weibull & Weibull-Gamma Intuitively, album sales should be duration dependent. A highly competitive music scene with innumerous musicians releasing new albums year-round makes it is difficult for an individual album to maintain consumer attention. So, it is important to observe whether the findings regarding heterogeneity from the exponential models hold true when duration dependence is factored in: Dink Model p(buyer) λ c Total LL BIC MdAPE Weibull -- 0.0105 1.335 -253012.50 506048.02 24.98% Weibull (Zero-Inflated) 0.645 0.00793 1.692 -251989.70 504014.02 14.72% Model p(buyer) r α c Tot. LL BIC MdAPE Weibull-Gamma -- 0.9227 154.923 1.650 -252485 505004.8 19.37% Weibull-Gamma (ZI) 0.645 11260.09 1420563 1.692 -251990 504025.7 14.72% Sparklehorse Model p(buyer) λ c Total LL BIC MdAPE Weibull -- 0.0002108 1.609 -30637.65 61298.33 31.99% Weibull (Zero-Inflated) 0.999 0.000211 1.609 -30637.66 61309.87 31.99% p(buyer α c Model r Tot. LL BIC MdAPE ) Weibull-Gamma -- 1576.58 7478873 1.609 -30637.7 61309.87 31.98% Weibull-Gamma (ZI) 0.999 1782.42 8448099 1.609 -30637.7 61321.39 31.99% The results of the Weibull and Weibull-Gamma models suggest that zero-inflated and Weibull-Gamma models are unreliable: Dink’s zero-inflated Weibull and Weibull- Gamma models contradict all other models. Its zero-inflated Weibull-Gamma model fails to improve on its zero-inflated Weibull model. All of the Weibull-Gamma models exhibit absurd parameters. Although the Weibull-Gamma models appear to improve BIC and MdAPE for Dink, they have virtually no effect on Sparklehorse’s models. Logically, the same model ought to fit both albums because they are both alternative- rock albums released by Capitol at around the same time. Even though the Weibull- Gamma appears to remarkably improve BIC and MdAPE values for Dink, it would be short-sighted and against intuition to base future Dink models off of Weibull-Gamma and future Sparklehorse models off of the Weibull— given all of these inconsistencies and concerns with interpretation of N, zero-inflation and the Weibull-Gamma. Overall, it is best to be conservative and use the regular Weibull model as the basis of future models. 4 5 Segmenting Consumers: Finite Mixture Models Though heterogeneity is difficult to capture with a Gamma mixture, it still may be possible to understand the make-up of the consumer population with finite mixture models featuring two to four segments: Dink Model Seg 1 % Seg 2 % Seg 3 % Seg 4 % Tot. LL BIC MdAPE Weibull FM 2 50.67 59.33 -- -- -251075.1 502219.3 10.64% Weibull FM 3 50.67 49.33 0.00 -- -251075.1 502253.8 10.64% Weibull FM 4 33.89 60.43 0.06 0.00 -251276.0 502690.2 11.27% Sparklehorse Model Seg 1 % Seg 2 % Seg 3 % Seg 4 % Tot. LL BIC MdAPE Weibull FM 2 30.00 70.00 -- -- -30449.5 60968.1 19.99% Weibull FM 3 0.007 74.70 24.53 -- -30431.7 60966.9 12.30% Weibull FM 4 32.04 35.03 32.10 0.00 -30435.0 60988.1 12.20% Excitingly, the Weibull 2-Segment and 3-segment Finite Mixture models are virtually the same, and their behaviors are consistent across both albums. Though Sparklehorse’s MdAPE rises with the Weibull 2-Segment Finite Mixture, it may be misleading because the BIC is about the same and MdAPE drops considerably in comparison to previous models. Overall, the simplest and most consistent model moving forward is the Weibull 2-Segment Finite Mixture. 6 Speculating about Covariates: Album Promotional Tactics For the purpose of fitting probability models, covariates related to album promotion are likely to be the most predictive and actionable.