1. 1
Modeling of players activity
June 20th, 2013
Michel Pierfitte
Director of Game Analytics Research

2. 2
Lifetime Retention
Day 0 1 2 3 n
Game Bus
a cohort gets
in the bus
Metaphor
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

3. 3
Lifetime Retention
typical lifetime retention curves of non-paying and payers
negligible
drop-off
significant
drop-off
50% on average
KPI : first day drop-off (50% on average)

4. 4
Lifetime Retention model
?
horizon
Life to date operation of the game modeling retention curves
R(t) = 1 – d * t1/α
t
parameters d and α are found with estimation techniques
• The area under the retention curve is the average lifetime
• KPI : quality of retention Q = log(area)

5. 5
Lifetime Retention benchmark
Web
Mobile
Facebook
HD Online Multiplayer
6 13 months
5 5 months
4 55 days
3 20 days
2 7.4 days
1 2.7 days
0 1 day
Q average lifetime
Criteria for launch : Q ≥ 3 (black line)

6. 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

7. 7
Playtime Retention
• 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 !
Lifetime view
Playtime view
activity event
• 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

8. 8
Playtime Retention of a F2P game
non-paying payers
• We only consider users with a lifetime > 1
day, complementary to first day drop-off
• Impossible to read on a linear time scale
• Playtime follows approximately a log-
normal distribution
KPI : median playtime

9. 9
Population #1 : 39%, mode 0.8 h
Population #2 : 21%, mode 11.7 h
Population #3 : 40%, mode 21.9 h
Playtime Retention of a
HD single player game of 20h
• Modeling of the playtime retention by a
mixture of 3 population with log-normal
playtime distributions
• Automated resolution using excel solver
• Gives information to perform classification of
users (supervised learning)
mode #1 mode #2 mode #3

10. 10
Revenues
from June 4th, 2012 to June 3th, 2013
quickly
stabilized
growth
RpU = CR * AP * PF
Revenue
per User
Conversion
Rate
Average
Payment
Purchasing
Frequency
= * *
= * *

11. 11
quick
start
slow
start
achieve potential
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

12. 12
Probability of Purchase
probability of 1st purchasing day = CR
KPI : probability of 2nd purchasing day
• 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
• The probability to purchase increases
with each purchase
• 1st & 2nd purchases are critical to success

13. 13
Purchasing Days
KPI : percentage of one-shots
one-shots (single purchasing day)

14. 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

15. 15
Summary of KPIs
• first 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

16. 16
Thank you
for your attention