1. Modeling of players activity
June 20th, 2013
Michel Pierfitte
Director of Game Analytics Research
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2. Lifetime Retention
Metaphor
Day 0
1
2
3
n
a cohort gets
in the bus
Game Bus
Lifetime = time spent in the bus, Retention = % of remaining users at each stop
• Lifetime is a random variable, X = last active time - first active time
• Retention(t) = Pr(X > t), probability of lifetime greater than t
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3. Lifetime Retention
typical lifetime retention curves of non-paying and payers
negligible
drop-off
significant
drop-off
50% on average
KPI : 1st day drop-off (50% on average)
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4. Lifetime Retention model
Life to date operation of the game
?
modeling retention curves
R(t) = 1 – d * t1/α
t
horizon
parameters d and α are found with estimation techniques
vanishing time T = d-α , when R(T) = 0
• The area under the retention curve is the average lifetime, E[X]
• KPI : quality of retention Q = log(area)
4

5. Lifetime Retention benchmark
Q
average lifetime
Web
Mobile
Facebook
HD Online Multiplayer
Criteria for launch : Q ≥ 3 (black line)
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6. First day quitters in a mobile game
ZOOM in the first day of the lifetime retention
Decomposition of the 21% drop
•
3% leave within the first 15 seconds
•
4% leave during the next 4 minutes
•
14% leave during the remaining 24 hours
•
•
A lot of variation between games
Can help designers to understand why
users leave
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7. Playtime Retention
activity
event
Lifetime view
Playtime view
• Playtime is a random variable, X = total active time of a user
• Retention(t) = Pr(X > t ∣ lifetime > 1), probability of playtime greater than t
for users with lifetime > 1
•
Users with same playtime can
have a very different lifetime,
depending on the intensity
and the frequency of play
•
Example : hardcore user
10 h / day on average !
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8. Playtime Retention of a F2P game
•
•
non-paying
We only consider users with a lifetime > 1
day, complementary to 1st day drop-off
Impossible to read on a linear time scale
•
Playtime follows approximately a lognormal distribution
payers
KPI : median playtime
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9. Playtime Retention of a
HD single player game of 20h
•
•
mode #2
mode #3
Automated resolution using excel solver
•
mode #1
Modeling of the playtime retention by a
mixture of 3 population with log-normal
playtime distributions
Gives information to perform classification of
users (supervised learning)
Population #1 : 39%, mode 0.8 h
Population #2 : 21%, mode 11.7 h
Population #3 : 40%, mode 21.9 h
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10. RpU =
Revenue
per User
=
𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑠𝑒𝑟𝑠
=
from June 4th, 2012
Revenues
CR *
AP
Conversion
Rate
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑒𝑟𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑠𝑒𝑟𝑠
*
PF
Purchasing
Frequency
*
Average
Payment
*
*
𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
*
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑒𝑟𝑠
to June 3th, 2013
growth
quickly
stabilized
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11. Purchasing Frequency (PF)
•
Trend is known in 5 days
of observation
•
Potential PF is predicted
by a model based on the
current known value
•
Can’t predict wether the
potential will be achieved
•
When the curve turns
sharply, most of the time
it’s because of poor
retention of payers
= current value
achieve potential
quick
start
slow
start
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12. Probability of Purchase
•
Spiral of probability of (re)purchase : 30 days dial
representation
•
Each probability point is the % of payers relative to
the previous point
•
The interval between two points is the median time
probability of 1st purchasing day = CR
KPI : probability of 2nd purchasing day
• The probability to purchase increases
with each purchase
• 1st & 2nd purchases are critical to success
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13. Purchasing Days
•
•
In most games, the % of payers that have
1, 2, …. n purchasing days follow a
logarithmic distribution with parameter p,
0<p <1
𝑝𝑛
Pr(n) = -
•
PF =
•
On average, 50% of one_shots  PF ≈ 2.5
•
Setting default expectations :
CR = 5%, AP = 20€, PF = 2.5  RpU = 2.5€
one-shots (single purchasing day)
𝑛∗log 1−𝑝
𝑝
𝑝−1 ∗log 1−𝑝
KPI : percentage of one-shots
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14. Progression
•
Ideal case: flat histogram (constant acquisition
of users who keep leveling up)
•
Outsanding bars signal levels where users quit
the most
•
Main reasons to quit (based on experience) :
 unpredictable time interval between levels
 peak of difficulty in the gameplay
 boredom
•
Very often the CR reaches 100% for high levels :
this is a symptom of efficient monetization
hooks
KPI : no outstanding bars in the
histogram of levels
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15. Summary of KPIs
• 1st day drop-off
• Q : quality of lifetime retention
• median playtime
• RpU : revenue per user
• CR : conversion rate
• AP : average payment
• PF : purchasing frequency
• probability of 2nd purchasing day
• percentage of one-shots
• outstanding bars in the histogram of levels
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16. Thank you
for your attention
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