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School of InformationUniversity of Michigan

The dynamics ofviral marketing

Lada Adamic

MOCHI

November 9, 2005

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Collaborators Jure Leskovec (CMU) Bernardo Huberman (HP Labs)

Outline prior work on viral marketing & information diffusion incentivised viral marketing cascades and stars network effects product characteristics timing

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Information diffusion

Studies of innovation adoption hybrid corn (Ryan and Gross, 1943) prescription drugs (Coleman et al. 1957) poison pills and golden parachutes (Davis and

Greeve, 1997)

Models (very many) Rogers, ‘Diffusion of Innovations’ Watts, information cascades, 2002

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Using online networks for viral marketing

Burger King’s subservient chicken

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Motivation for viral marketing

viral marketing successfully utilizes social networks for adoption of some services hotmail gains 18 million users in 12 months,

spending only $50,000 on traditional advertising gmail rapidly gains users although referrals are the only way to

sign up

users becoming less susceptible to mass marketing mass marketing impractical for unprecidented variety of

products online

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Marketing in the long tail

Chris Andreson, ‘The Long Tail’, Wired, Issue 12.10 - October 2004

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The web savy consumer and personalized recommendations

> 50% of people do research online before purchasing electronics

personalized recommendations based on prior purchase patterns and ratings Amazon, “people who bought x also bought y” MovieLens, “based on ratings of users like you…” Epinions, “based on the opinions of the raters you trust”

(Richardson & Domingos, 2002)

ratings have been shown to affect the likelihoodof an item being bought Resnick & Zeckhauser, 2001: eBay Judith Chevalier and Dina Mayzlin, 2004: Amazon and BN

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Is there still room for viral marketing next to personalized recommendations?

We are more influenced by our friends than strangers

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

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Incentivised viral marketing

Senders and followers of recommendations receive discounts on products

10% credit 10% off

Recommendations are made to any number of people at the time of purchase

Only the recipient who buys first gets a discount

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Product recommendation

network

purchase following a recommendation

customer recommending a product

customer not buying a recommended product

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the data

large online retailer (June 2001 to May 2003)

15,646,121 recommendations 3,943,084 distinct customers 548,523 products recommended 99% of them belonging 4 main product groups:

books DVDs music VHS

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data attributes

recommendations sender (shadowed) recipient (shadowed) recommendation time buy bit purchase time product price

additional product info categories reviews ratings

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identifying viralmarketing cascades

t1 < t2 < … < tn

buy bit

t1

t3

buy edge

t4

late

reco

mm

enda

tion

t2

legend

bought but didn’treceive a discount

bought andreceived a discount

received a recommendationbut didn’t buy

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summary statistics by product group

products customers recommenda-tions

edges buy bits buy edges

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

high

low

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observations on product groups There are relatively few DVD titles, but DVDs account for ~ 50% of recommendations.

recommendations per person DVD: 10 books and music: 2 VHS: 1

recommendations per purchase books: 69 DVDs: 108 music: 136 VHS: 203

Overall there are 3.69 recommendations per node on 3.85 different products.

Music recommendations reached about the same number of people as DVDs but used only 1/5 as many recommendations

Book recommendations reached by far the most people – 2.8 million.

All networks have a very small number of unique edges. For books, videos and music the number of unique edges is smaller than the number of nodes – the networks are highly disconnected

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measuring cascade sizes

delete late recommendations count how many people are in a single cascade exclude nodes that did not buy

100

101

10210

0

102

104

106

= 1.8e6 x-4.98 R2=0.99

steep drop-off

very few large cascades

books

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100

101

102

10310

0

102

104

= 3.4e3 x-1.56 R2=0.83

cascades for DVDs

shallow drop off – fat tail

a number of large cascades

DVD cascades can grow large possibly a product of websites where people sign up to

exchange recommendations

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CD and VHS cascades

Music and VHS cascades don’t grow large

100

101

10210

0

102

104

= 4.9e5 x-6.27 R2=0.97

100

101

10210

0

102

104

= 7.8e4 x-5.87 R2=0.97

music VHS

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simple model of propagating recommendations(ignoring for the moment the specific mechanics of the recommendation

program of the retailer)

Each individual will have pt successful recommendations. We model pt as a random variable

At time t+1, the total number of people in the cascade, Nt+1 = Nt * (1+pt)

Subtracting from both sides, and dividing by Nt, we have

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simple model of propagating recommendations(continued)

Summing over long time periods

The right hand side is a sum of random variables and hence normally distributed.

Integrating both sides, we find that N is lognormally distributed

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simple model of propagating recommendations(continued x 2)

For high variance in # of recommendations sent

The lognormal behaves like a power-law with exponent 1

We observe fat tails in cascade sizes

small if large

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participation level by individual

100

105

100

102

104

106

108

Number of recommendations

Co

un

t= 3.4e6 x-2.30 R2=0.96

very high variance

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individual purchase activity

100

101

102

103

104

100

102

104

106

108

Number of purchases

Co

un

t

= 4.1e6 x-2.49 R2=0.99

also highly skewed

The most active person made 83,729 recommendations and purchased 4,416 different items!

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0 1 2 3 4

x 106

0

2

4

6

8

10

12x 10

4

number of nodes

size

of

gia

nt

com

po

ne

nt

by monthquadratic fit

0 10 200

2

4x 10

6

m (month)

n

# nodes

1.7*106m

adoption of viral marketing program& social network connectivity

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viral marketing programnot spreading virally

94% of users make first recommendation without having received one previously

linear growth: ~ 165,000 new users added each month size of giant connected component increases from 1% to

2.5% of the network (100,420 users) – small! some subcommunities are better connected

24% out of 18,000 users for westerns on DVD 26% of 25,000 for classics on DVD 19% of 47,000 for anime (Japanese animated film) on DVD

others are just as disconnected 3% of 180,000 home and gardening 2-7% for children’s and fitness DVDs

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network densification

105

106

106

107

n (# nodes)

e (

# e

dg

es)

data

e ~ n1.26

the number of connections per user (network density) increases over time as users recommend to additional friends

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Network effects

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does sending more recommendationsinfluence more purchases?

10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

Outgoing Recommendations

Nu

mb

er

of

Pu

rch

ase

s

20 40 60 80 100 120 1400

1

2

3

4

5

6

7

Outgoing Recommendations

Nu

mb

er

of

Pu

rch

ase

s

BOOKS DVDs

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the probability that the sender gets a credit with increasing numbers of recommendations

consider whether sender has at least one successful recommendation

controls for sender getting credit for purchase that resulted from others recommending the same product to the same person

10 20 30 40 50 60 70 800

0.02

0.04

0.06

0.08

0.1

0.12

Outgoing Recommendations

Pro

ba

bili

ty o

f C

red

it

probability of

receiving a credit levels off for DVDs

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does receiving more recommendationsincrease the likelihood of buying?

BOOKS DVDs

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

ba

bili

ty o

f B

uyi

ng

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saturation in response to incoming recommendations for DVD purchases

5 10 15 20 250

0.01

0.02

0.03

0.04

0.05

0.06

Incoming Recommendations

Pro

ba

bili

ty o

f B

uyi

ng

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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

ba

bili

ty o

f b

uyi

ng

5 10 15 20 25 30 35 400.02

0.03

0.04

0.05

0.06

0.07

Exchanged recommendations

Pro

ba

bili

ty o

f b

uyi

ng

BOOKS DVDs

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pay it forward

product category number of buy bits forward recommendations

percent

Book 65,391 15,769 24.2

DVD 16,459 7,336 44.6

Music 7,843 1,824 23.3

Video 909 250 27.6

Total 90,602 25,179 27.8

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product characteristics

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fading interest compare

# book reviews written during 2 periods: Jan 2001 – Dec 2003 (3 years) Jan 2005 – Jun 2005 (6 months)

completely sustained interest would give a ratio of 6

what we observe (averages per book given in parentheses) persistent

children (7.38) & teens (7.08) reference (9.96), religion (8.93), parenting & families (8.39)

middle history (11.81), arts & photography (12.27), travel (12.15) engineering (11.76) comics (11.94)

pulp fiction mystery & thrillers (14.71) romance (15.52)

so 2001 computers & internet (21.06)

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telling the world vs. telling your friends

consider # reviewers per book # recommenders per book

what we observe (ratio of recommendations to reviews given in parentheses) tell the world but not your friends

literature & fiction (0.57) mystery & thrillers (0.36) horror (0.44)

tell the world and your friends biographies (0.90) children’s books (1.12) religion (1.73) history (1.27) nonfiction (1.89)

tell just your friends about personal pursuits health, mind & body (2.39) home & garden (3.48) arts & photography (3.85) cooking, food & wine (3.49)

tell your colleagues about professional interests professional & technical (3.22) computers & internet (3.10) medicine (4.19) engineering (3.85) law (4.25)

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recommendation success by book category

consider successful recommendations in terms of av. # senders of recommendations per book category av. # of recommendations accepted

books overall have a 3% success rate (2% with discount, 1% without)

lower than average success rate (statistically significant at p=0.01 level) 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 sports (2.26) home & garden (2.26) travel (2.39)

higher than average success rate (statistically significant) 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)

nonfiction – general (3.28) in the middle

literature & fiction (2.82) religion & spirituality (3.13) outdoors and nature (2.38)

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professional and organized contexts

In general, professional & technical book recommendations are more often accepted(probably in part due to book cost)

Some organized contexts other than professional also have higher success rate, e.g. religion overall success rate 3.13% Christian themed books

Christian living and theology (4.7%) Bibles (4.8%)

not-as-organized religion new age (2.5%) occult spirituality (2.2%)

Well organized hobbies books on orchids recommended successfully twice as often as

books on tomato growing

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book recommendation networksare typically sparse

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DVD recommendations Three colors: blue, white & red showing purchasers only

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Anime

47,000 customers responsible for the 2.5 out of 16 million recommendations in the system

29% success rate per recommender of an anime DVD

giant component covers 19% of the nodes

Overall, recommendations for DVDs are more likely to result in a purchase (7%), but the anime community stands out

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regressing on product characteristics

Variable transformation Coefficient

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

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

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products most suitedto viral marketing

small community few reviews, senders, and recipients but sending more recommendations helps

pricey products

rating doesn’t play as much of a role

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0 5 10 15 20 250

2

4

6

8

10x 10

5

Hour of the Day

Re

com

me

nd

tion

s

when recommendationsare sent

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when purchasesare made

0 5 10 15 20 250

0.5

1

1.5

2x 10

4

Hour of the Day

All

Pu

rch

ase

s

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when discountsare to be had

0 5 10 15 20 250

1000

2000

3000

4000

5000

6000

7000

Hour of the Day

Dis

cou

nte

d P

urc

ha

ses

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lag between time of recommendationand time of purchase

1 2 3 4 5 6 7 > 70

0.1

0.2

0.3

0.4

0.5

Lag [day]

Pro

po

rtio

n o

f P

urc

ha

ses

0 24 48 72 96 120 144 1680

100

200

300

400

500

600

Lag [hours]

Co

un

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

po

rtio

n o

f P

urc

ha

ses

0 24 48 72 96 120 144 1680

500

1000

1500

2000

2500

Lag [hours]

Co

un

t

Book DVD

40% of those who buybuy within a day

but > 15% wait morethan a week

daily periodicity

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observations

purchases and recommendations follow a daily cycle

customers are most likely to purchase within a day of receiving a recommendation

acting on a recommendation at atypical times increases the likelihood of receiving a discount

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Conclusions

for a vast majority of products, incentivized viral marketing contributes marginally to total sales

occasionally large cascades occur, most often for DVDs simple threshold models (a fraction of one’s friends buys a

product) and individual interactions do not capture the saturation phenomenon we observe in recommendation networks

sending out large numbers of recommendations has limited returns → we tend to influence just the people we know well

viral marketing may sabotage its own effectiveness if social network links are overused

professional and organizational contexts improve the recommendation effectiveness

price influences how attractive the recommendation discount is small communities enjoying expensive products are most

conducive to viral marketing

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For more information

short version of the paper: http://www-personal.umich.edu/~ladamic/papers/viral/viral-market-short.pdf

long version of the paper: http://arxiv.org/PS_cache/physics/pdf/0509/0509039.pdf

my publications: http://www-personal.umich.edu/~ladamic

Jure’s publications: http://www.cs.cmu.edu/~jure/pubs/

Bernardo Huberman’s Information Dynamics Lab at HP: http://www.hpl.hp.com/research/idl