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Modeling of players activity

June 20th, 2013

Michel Pierfitte Director of Game Analytics Research

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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

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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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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 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)

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Lifetime Retention benchmark

Web Mobile Facebook HD Online Multiplayer

Q average lifetime

Criteria for launch : Q ≥ 3 (black line)

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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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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

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Playtime Retention of a F2P game

non-paying payers

• 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 log-

normal distribution

KPI : median playtime

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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

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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

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑒𝑟𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑠𝑒𝑟𝑠

𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑦𝑒𝑟𝑠

𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑠𝑒𝑟𝑠

= * *

= * *

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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

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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

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Purchasing Days

KPI : percentage of one-shots

• In most games, the % of payers that have 1, 2, …. n purchasing days follow a logarithmic distribution with parameter p, 0 < p < 1

• Pr(n) = - 𝑝𝑛

𝑛∗log 1−𝑝

• PF = 𝑝

𝑝−1 ∗log 1−𝑝

• 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)

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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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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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Thank you for your attention