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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