Using Peer-to-Peer Downloading Behavior to Forecast Pre-launch Sales of Music:

A Bayesian Analysis

Il-Horn Hann, Joo Hee OhMarshall School of BusinessUniversity of Southern California

1. Research Motivation

Want to measure and understand the behavior of online system users and its linkage to the business forecasts from individual-level system usage data on Peer-to-Peer network (ARES)

2. Backgrounds

1. Lee, Boatwright and Kamakura (Management Science 2003)

-Bayesian model for Pre-launch Sales forecasting for Billboard 200s albums

2. Wendy Moe and Peter Fader (Marketing Science 2002)

-Using Advance Purchase Orders to Forecast New Product Sales

• Provides Pre-launch Sales forecasts for albums in Billboard 200s

• Does not provide pre-launch sales forecasts for NOT successful albums

• Does not provide point-estimate of first weeks’ sales after launch

• Generate Sales forecasts for music albums using advance-purchase orders

• Limited results for generalization for the special type of consumers

3. Research Question

How can we develop an empirical model utilizing downloading behavior data from peer-to-peer network to generate pre-launch sales forecasts of music for the first-week after launch?

4. Model Development

Hierarchical Random-Effects Model

tY ttQP ttt XbaPQ (Preference or Quality Variable)

,iiitit Xy ),,0(~ ii Nwhere ,,1,,,1 iTtni

iTii I2

1

: weekly sales of album i at week t

:- downloaded # from peer to peer network in the previous week

- total # of previous available dates for files in the previous week

- weekly dummy variables for 2nd, 3rd, and 4th release

it

it

y

X

week

: vector representing the album i's sensitivity to downloaded #si

4. Model Development

,iii z where ),,0(~ VNi

ni ,,1

: vector representing the album i's sensitivity to downloaded #s,

# of available dates, weekly dummies regarding launching datei

: vector representing the album i's characteristics

Total # of previous albums of artist,

Genre of music, Gender of artist

iz

i: matrix representing sensitivity of β to album i's characteristics

Second-level Model Hierarchy

4. Model Development

Conjugate Prior-Distribution for Hierarchical Linear Models

,For )),((~)( 1 AVvecNvec

0 ,200 I

:I Identity matrix

,For

Set &

where

statheAdopt ,priorgammainversendard

,VFor ),(~ 001

bb VWishartV

where kbbb IVandk 000 )11(4

),...,,( 221 mdiag

),(~ ii GammaInvertedtIndependen

Rossi & Allenby et al. (2005)Model hyper-parameters

4. Model Development

1y 2y 3y 50y 51y 74y

1 2 3 50 51 74

Downloading Behavior (X)

Album characteristics (Z)

VZ ),0(~'

VNiidvi

]',,,[ ''2

'1 m

Hyper-parameters),,( V

)( i

k ...,,, 21)( ity

)),((~)( 1 AVvecNvec

),(~ ii GammaInverted

,iiitit Xy ),,0(~ ii Nwhere ,,1,,,1 iTtni

iTii I2

]',,,[ ''2

'1 mzzzZ

),(~ 001

bb VWishartV

,' iii z

Estimation/Calibration set Hold-Out Sample

4. Model Development

)|,,,( tyVp ),(),(),|,(),|,()|( VppVpVpyp t

,,,,,,|1 VzXy iititi

211 ,,,| oiiitit sXy

AzV ii ,,,| 11

ii zV ,,| 11

Forecasting Model

,iiitit Xy ,,1,,,1 iTtni

Gibbs-Sampling

Draw

and

Draw

and Repeat, as necessary.

iiti Xy ̂ˆ 1

Point-Estimate of 1st week Sales

Average # of Downloads before launch, Available # of Dates, Weekly Dummy Var.

,' iii z ),0(~'VNiidvi

5. Hypotheses

H1 The more downloaded from the P2P, the higher sales of the album.

H2 The more dates available from the P2P, the higher sales of the album.

H3 The more previous total # of albums artist have, the higher sales sensitivity to the downloads #.

H4 Albums launched in the same rank of week have similar estimation coefficients of sales on downloads #.

H5 The genre of music, the gender of artist affect positively to the sales through downloads #.

6. Empirical Illustration

Description of the Data

Data Preprocessing

• Downloads data from the Ares P2P network (April 5, 2007-July 15, 2007)• Sales for Newly Released albums in billboard’s Top 200 (May 1-July 15,2007)• Album specific characteristics

- Previous total # of albums of the artist- Genre of music (Rap & Rock)- Gender of the artist (Male)

• Newly Released albums on Billboard 200s weekly chart : 98 albums Extracted Movie Soundtracks or Re-entered albums due to atypical patterns

• Ends up 74 newly Released-albums on Billboard 200s • Choose 50 for Calibration set/ 24 For Hold-out Sample

Calibration Panel set : 50 Cross sectional + 4 Time-series Hold-out Sample: Generate one point-estimate of first-weeks’ sales

6. Empirical Illustration

Sales_over_Aver#_sources

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Ave#_sources

Sales_over_Avel#_sources

6. Empirical Illustration

Average Downloads # on Sales (Weekly)

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RTD_Sales

May June

7. Results- Estimation

Estimation Results for Calibration set

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album

sa

les

Actual Sales Estimated Sales

[Figure 3] Total Estimation Results for Calibration set

7. Results- Estimation

Calibration_Results(First_week)

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Calibration_Results(Second_week)

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[Figure 4] Weekly Estimation Results for Calibration set

[Figure 5] Individual Album Sales Estimation: High, Medium, Low -Level of Success

7. Results- Estimation

BECAUSE OF YOU

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DOUBLE UP

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7. Results- Estimation

SNAKES & ARROWS

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AMERICAN DOLL POSSE

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[Figure 5] Individual Album Sales Estimation: High, Medium, Low -Level of Success

7. Results- Estimation

POISON'D

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ANOTHER SIDE

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Actulal Sales Estimated Sales

[Figure 5] Individual Album Sales Estimation: High, Medium, Low -Level of Success

8. Results- Forecasting

[Figure 6] Comparison of Forecast Results using Different Measure of Downloading #

Forecast_Results

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Absolute_Average Error

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Measure1 Measure2

8. Results- Forecasting

[Table 1] Comparison of Forecasts (MAPE) with Different Measure

Aver. Download # a week before Release (Measure 1) 0.689Aver. Number of total Download # before Release (Measure 2) 0.555Mean of Both Measure 1 & Measure 2 (Measure 3) 0.58

Comparison of MAPE with different Measure

[Table 2] Comparison of Fit (MAPE) with Previous Studies

Proposed ModelLee, Boatwright & Kamakura(2003)

Generalized Bass model

Generalized Gamma model

Forecasting 0.555 0.7 0.799 0.896Estimation 0.733 0.178 0.196 0.267

MAPE Comparison

(Lee, Boatwright, Kamakura 2003)

t

t

tt

A

FA

n

||1MAPE =

8. Results- Forecasting

[Figure 7] Point-estimate of Pre-launch Sales forecasts for the first-week

Pre-launch Sales Forecasts

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8. Results- Forecasting

[Figure 8] Sales-Coefficients ( i ) on Explanatory variables

Sales on # of Available Dates Sales on # of Average Downloads #

8. Results- Forecasting

Sales on 2nd week dummy variable Sales on 3rd week dummy variable

8. Results- Forecasting

[Figure 9] Downloads-Coefficient () on Album characteristics

Total # of previous albums Rap (Genre)

Rock (Genre) Male (Gender)

9. Future Work

Data

Methods

•Small sample-size for the # of Newly-Released albums•Lack of New-albums which is NOT on Billboard 200s’ chart

=> New release data purchased

•Does ARES network large enough to represent downloads behavior?=> Better prediction by using additional P2P network data

•Needs enhancement from simple standardized form of model •Need enhancement in the prior-distribution for using Barnard et al. (2000)V

Model•Does weekly cyclic pattern really exists in larger sample of albums?•Does supply side of data (audio_source) for downloads better than demand side of data (hash_request) for downloads # in forecasting sales?•Is there ommitted variable problem for not considering promotional-effect variable?