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Game Progression in Graphs - The Golden ratio

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The "Player Progression" follows a path dictated by The Game, what I call the in-built "Game Progression".


We all noticed how fast the progression is at the beginning and then how it becomes slower and slower.
How slower ? For how long ?  ... and when will I reach Level 40 ? That is the question.


We can have a glimpse of what happens by analysing how the Levels are connected to the XP along this Game Progression.

For this I used the Level indicator which shows how many XP one needs to reach the next level.

Putting all these raw data on a table and then a graph, we get this:







Note 1: Level 29 and 43 are just highlighted to show how it works.

Note 2: You see that the curve looks flat till level 23 or so, but the zoom reveals that it's only a matter of scale (look at the scales).


There are some strange spikes at Level 20 and 40, confirmed by the table, where the requirement is much higher than during all the rest of the progression.
I couldn't figure out why developers put these breaks in place.


Well, the curve is a bit chaotic but altogether it has a nice look, something like an exponential.

Fiddling with Excel, I found out that, after "cleaning" the series from its two alien spikes, we can get something that can be approximated by a coherent mathematical formula:
- just multiply the "number of XP you need to the next level" by 1.25 and you get close to the "next Level requirement".

For instance, if you needed 200.000 XP from Level 28 to 29, you will need 250.000 from 29 to 30.


In most cases it's not immediately obvious, particularly in the low levels, so let's put this on the graph also.





The pink curve has been generated artificially and the result looks really very similar to the raw data (it would be significantly different if it was multiplied by something else than 1.25).

The correlation between the two sets of values is 0.997, close to the 1.000 that would be a perfect match.


Note: this is a step to step approach, not an absolute mathematical curve. It means that it gives a good visibility from one step to the next but you cannot infer accurately from a level 20 how it will look at a level 40 by just multiplying many times by 1.25.


Now, even more interesting than analysing this Game Progression from Level to Level, let's see the overall cumulated game progression, i.e. the total XP one needs from Level 1 to Level 48.

For instance, you need 2.5 millions XP from Level 29 to 30, and at that stage you will have harvested a total of 11.5 millions XP since the beginning.


Let's sum up the same raw data as initially, after cleaning the 2 spikes.
And, while we are here, let's also add a curve with the summing up of the raw data multiplied by 1.25.
This gives the following table and curves:








Now the correlation is even better: for the "summed up data vs its mathematical representation" it reaches 0.9989 ! A quasi perfect match.


All this long story to demonstrate that            1.25  is the Golden ratio of RF4 progression.


We will see next what we can infer from that discovery.



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