Page 14 - Playtest_Square_Enix - EphemeralData

Natural Decay Analysis

What is Natural Decay:
N atural Decay is using a very simple yet powerful approach. The

natural decay is an approximation of the growth decline usually
seen in many phenomena (social, economical, scientifical,..).

The idea is that for a repeated situation through many periods (i.e. a
game with checkpoints) we will not observe a linear decrease of the
amount of player, but an exponential one.

Indeed, during the first checkpoints we should see a very small amount
of users leaving. This amount will begin to become drastically higher as
the game proceeds to finally become smaller again when we only got

very proficient users near the end.

How to Compute Natural Decay ?

To compute Natural Decay, we will use the following formula:

-g*t
Natural Decay = N (e ) with : N = %user still playing
g = decline rate
t = actual checkpoint

How to choose the decline rate ?

For this analysis, we chose a decreasing growth rate of 2% to represent

the natural decrease of the checkpoints game.

This choice is based on two principal facts:

- In a perfectly fair and balanced game with 30 periods, each period
should see a decrease of 3.33% of actual users

- Statistically, on a big enough (200 individuals) and representative
sample, we should retain at maximum 2.5% of our total population in
the less populated events (i.e. reaching checkpoint# 30)

To approximate the best these two assumptions, a 2%, decreasing
growth rate is an "ideal" theoretical fit.

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