The Dynamics of Viral Marketing

Jure Leskovec Lada Adamic Bernardo A. Huberman Stanford University University of Michigan HP Labs

Presented by Leman AkogluMarch 2010

Targeted marketing

Personalized recommendations

Cross-selling“people who bought x also bought y”

Collaborative filtering“based on ratings of users like you…”

Viral marketing

We are more influenced by our friends than strangers.

68% of consumers consult friends and family before purchasing home electronics (Burke 2003)

Our friends know about our needs/tastes better.

Why need Viral Marketing?

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The paper in a nutshell• Analysis of a person-to-person recommendation network

(June 2001 to May 2003)– 4 million people– 0.5 million products– 16 million recommendations

Contributions:• Data statistics• Propagation, cascade sizes• Network effects• Effectiveness of viral marketing on product and

pricing categoriesApril 20, 2023 3

products customers recommenda-tions

edges buy + get

discount

buy + no discount

Book 103,161 2,863,977 5,741,611 2,097,809 65,344 17,769

DVD 19,829 805,285 8,180,393 962,341 17,232 58,189

Music 393,598 794,148 1,443,847 585,738 7,837 2,739

Video 26,131 239,583 280,270 160,683 909 467

Full 542,719 3,943,084 15,646,121 3,153,676 91,322 79,164

people recommendations

I. Music CDs and DVDs have the most/least number of items, respectively.II. Still, DVDs account for than half of all recommendations.III. Number of unique edges for Books, Music and Videos is less than number of

customers –suggests many disconnected components

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1. Largest connected component at the end contains ~2.5% of the nodes.2. Total number of nodes grow linearly over time.

The service itself was not spreading epidemically.

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products customers recommenda-tions

edges buy + get

discount

buy + no discount

Book 103,161 2,863,977 5,741,611 2,097,809 65,344 17,769

DVD 19,829 805,285 8,180,393 962,341 17,232 58,189

Music 393,598 794,148 1,443,847 585,738 7,837 2,739

Video 26,131 239,583 280,270 160,683 909 467

Full 542,719 3,943,084 15,646,121 3,153,676 91,322 79,164

people recommendations

IV. Influence: 1) Books (1/69) 2) DVDs (1/108) 3) Music (1/136) 4) Video (1/203)

buy+get discount

… buy+no discount

V. People tend to buy books when they can get a discount whereas for DVDsdiscount does not matter much.

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Lag between time of recommendation and time of purchase

1 2 3 4 5 6 7 > 70

0.1

0.2

0.3

0.4

0.5

Lag [day]

Pro

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0 24 48 72 96 120 144 1680

100

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Lag [hours]

Co

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t

1 2 3 4 5 6 7 > 70

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Lag [day]

Pro

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0 24 48 72 96 120 144 1680

500

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Lag [hours]

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Book DVD

40% of those who buybuy within a day

but > 15% wait morethan a week

daily periodicity

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Contributions of the paper:Data statistics• Propagation, cascade sizes• Network effects• Effectiveness of viral marketing on product and

pricing categories

April 20, 20238

Identifying cascades

…

t

t

tt

+t’

t+t’’

t’’’ > t’’ > t’Cascade size:

6

t+t’’’

steep drop-off

very few large

cascades

shallow drop off

DVD cascades can grow large

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Propagation model (produces power-law cascade-size distribution)

• Each individual will have pt successful recommendations.

– pt:[0,1]

• At time t+1, the total number of people in the cascade,

Nt+1 = Nt * (1+pt)

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• Summing over long time periods

– The right hand side is a sum of random variables and hence normally distributed. (Central Limit Theorem)

• Integrating both sides, N is log-normally distributed

if large resembles power-law

Propagation model (produces power-law cascade-size distribution)

April 20, 2023

Contributions of the paper:Data statisticsPropagation, cascade sizes• Network effects• Effectiveness of viral marketing on product and

pricing categories

April 20, 202312

2 4 6 8 100

0.01

0.02

0.03

0.04

0.05

0.06

Incoming Recommendations

Pro

ba

bili

ty o

f B

uyi

ng

10 20 30 40 50 600

0.02

0.04

0.06

0.08

Incoming Recommendations

Pro

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Question: Does receiving more recommendations increase the likelihood of buying? (receiver’s perspective)

BOOKS DVDs

Book recommendations are rarely followed. A peak at 2, and then a slow drop (!) For DVDs, saturation is reached at 10 –diminishing returns

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Question: Does sending more recommendations yield more purchases? (sender’s perspective)

10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

Outgoing Recommendations

Nu

mb

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of

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rch

ase

s

20 40 60 80 100 120 1400

1

2

3

4

5

6

7

Outgoing RecommendationsN

um

be

r o

f P

urc

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BOOKS DVDs

To too few –changes of success is low versus to everyone –spam effect For Books, the number of purchases soon saturates. For DVDs, the number of purchases increases throughout.

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Question: Do multiple recommendations between two individuals weaken the impact of the bond on purchases?

5 10 15 20 25 30 35 404

6

8

10

12x 10

-3

Exchanged recommendations

Pro

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5 10 15 20 25 30 35 400.02

0.03

0.04

0.05

0.06

0.07

Exchanged recommendations

Pro

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bili

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BOOKS DVDs

YES! --Less is more…

April 20, 2023

Contributions of the paper:Data statisticsPropagation, cascade sizesNetwork effects• Effectiveness of viral marketing on product and

pricing categories

April 20, 202316

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Recommendation success by book category

• Success rate: # of purchases following a recommendation / # recommenders

• Books overall have a 3% success rate

• Lower than average success rate– Fiction

• romance (1.78), horror (1.81)• teen (1.94), children’s books (2.06)• comics (2.30), sci-fi (2.34), mystery and thrillers (2.40)

– Nonfiction (personal & leisure)• sports (2.26)• home & garden (2.26)• travel (2.39)

• Higher than average success rate– professional & technical

• medicine (5.68)• professional & technical (4.54)• engineering (4.10), science (3.90), computers & internet (3.61)• law (3.66), business & investing (3.62)

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What determines a product’s viral marketing success?

Modeling recommendation success-- by linear regression

# recommendations

# senders

# recipients

product price

# reviews

avg. rating

xi :βi : Coefficients : success

Over 50K products

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Modeling recommendation successVariable transformation Coefficient βi

const -0.940 ***

# recommendations ln(r) 0.426 ***

# senders ln(ns) -0.782 ***

# recipients ln(nr) -1.307 ***

product price ln(p) 0.128 ***

# reviews ln(v) -0.011 ***

avg. rating ln(t) -0.027 *

R2 0.74

# senders and receivers have negative coefficients, showing that successfully recommended products are actually more likely to be not so widely popular more expensive and more recommended products have a higher success rate avg. rating does not affect success much

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significance at the 0.01 (***), 0.05 (**) and 0.1 (*) levels

Contributions of the paper: Data statistics Propagation, cascade sizes Network effects Effectiveness of viral marketing on product and pricing categories

Questions & Comments

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