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

Day 0

1

2

3

n

a cohort gets
in the bus

Game Bus
Lifetime = time spent in the bus, Reten...
Lifetime Retention
typical lifetime retention curves of non-paying and payers

negligible
drop-off
significant
drop-off
50...
Lifetime Retention model
Life to date operation of the game

?

modeling retention curves

R(t) = 1 – d * t1/α

t
horizon
...
Lifetime Retention benchmark
Q

average lifetime

Web
Mobile
Facebook
HD Online Multiplayer

Criteria for launch : Q ≥ 3 (...
First day quitters in a mobile game
ZOOM in the first day of the lifetime retention
Decomposition of the 21% drop
•

3% le...
Playtime Retention
activity

event

Lifetime view
Playtime view

• Playtime is a random variable, X = total active time of...
Playtime Retention of a F2P game
•

•

non-paying

We only consider users with a lifetime > 1
day, complementary to 1st da...
Playtime Retention of a
HD single player game of 20h
•

•

mode #2

mode #3

Automated resolution using excel solver

•

m...
RpU =
Revenue
per User

=

𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑠𝑒𝑟𝑠

=

from June 4th, 2012

Revenues
CR *
AP
Conversion
Rate
𝑛𝑢𝑚𝑏𝑒...
Purchasing Frequency (PF)
•

Trend is known in 5 days
of observation

•

Potential PF is predicted
by a model based on the...
Probability of Purchase
•

Spiral of probability of (re)purchase : 30 days dial
representation

•

Each probability point ...
Purchasing Days
•

•

In most games, the % of payers that have
1, 2, …. n purchasing days follow a
logarithmic distributio...
Progression
•

Ideal case: flat histogram (constant acquisition
of users who keep leveling up)

•

Outsanding bars signal ...
Summary of KPIs
• 1st day drop-off
• Q : quality of lifetime retention
• median playtime
• RpU : revenue per user
• CR : c...
Thank you
for your attention
16
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Modeling of players_activity_michel pierfitte_ubisoft_septembre 2013

  1. 1. Modeling of players activity June 20th, 2013 Michel Pierfitte Director of Game Analytics Research 1
  2. 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 2
  3. 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) 3
  4. 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. 5. Lifetime Retention benchmark Q average lifetime Web Mobile Facebook HD Online Multiplayer Criteria for launch : Q ≥ 3 (black line) 5
  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 6
  7. 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 ! 7
  8. 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 8
  9. 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 9
  10. 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 10
  11. 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 11
  12. 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 12
  13. 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 13
  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 14
  15. 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 15
  16. 16. Thank you for your attention 16

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