# Pet Levels

Pets try to copy their owners in every way possible, and since they live and grow older as they gain more experience, they also have levels just like heroes. However, whilst hereos increase their levels by gaining more experience, pets increase their levels entirely by growing older. The growth rates of pets are not currently well understood but it is all under investigation.

This is the graph you get if you plot levels against age^{[1]}:

The trend-line passes through the top points for each level (the maximum age to have the level before it increases) and the curve is followed on despite the miscorrelation with higher level points. This is because as age increases, it becomes more approximate as it says 'about *** months' or something similar, so these points can just be used as a rough guideline. The main point is that it conclusively proves that pet levels are decided entirely by age. Now we just need the formula. It seems to be a power curve of some sort.

What do the vertical strips of dots mean then? each 'strip' is the **band** of ages which a pet must fit into to be that certain level. If pets of ALL ages had been plotted on the graph, the vertical strips would reach the trend line, but most do not since there are missing gaps in the data. However, the fact that some dots (each representing individual pets) are on the same level (ie. have the same age) but are in different strips (ie. have different levels) implies that the gradient of the growth curve varies with different species of pets (thus they grow at different rates). These anomalies usually occur near the top and bottom of the strips as would be expected since it is impossible to distinguish between the actual age bands and other growth curves (different age bands) superimposed on them, although they both seem to exist.

**Hypothesis 1:**From the stats that people have shared, we can see that the**gradient**of the pet growth curve is**directly proportional**to the level a hero must be to tame the specific pet species. For example, a Biowolf will level up faster than a Dust bunny.

In order to test this hypothesis we would have to plot the growth curves of many species of pets, which is not a task many would wish to undertake since it would be a lengthy process. However, we do in fact have the full growth data for one particular pet at the time of writing; the Solar bear. The graph below^{[2]} shows this data as originally plotted.

A rough line of best fit has been drawn over the top but we can clearly see that there is an underlying pattern of curves which has been ignored. Someone else decided that since a pet is just an animal, the pet growth curves would be a bit more like a real growth curve for an animal (a bit more curvy), so they decided to look for a better underlying trend by cumulating the days and putting this age of the pet/time since pet birth on the x-axis and the level on the y-axis, like might otherwise usually be expected. The result is shown below.^{[3]}

We can see that there is a definite power trendline with the equation **L = 1.98t ^{0.521}** where

**L**is the level of the pet and

**t**is its age (in days). You may instantly be concerned with the constants involved since you might expect them to be 'nicer' numbers as in other algorithms employed in the game of Godville. Our first hypothesis states that if were to plot the growth curve of another species, we would maybe get the same coefficient but a different exponent (to produce a different rate of gradient change), so we will know how accurate it is once somebody has done this.

**Hypothesis 2:**The growth curve of any pet follows a**power trendline**of the form**L = Gt**where^{k}**G**is a growth coefficient and**k**is a growth exponent (**L**and**t**already defined). The growth exponent varies with pet species while the coefficient stays the same. It is not known how exactly the exponent may vary, if at all.

To test Hypothesis 1 & 2 we must plot the equivalent growth curve for a pet species available to heroes at a lower [hero] level. We would then see if indeed different pet species have different growth curves (Hypothesis 1) by looking at the resulting growth exponenet and coefficient, if the growth curves of all pet species do in fact follow a power trendline (Hypothesis 2) since this has yet to be fully established (the maths may look right but there could be a more fundamental formula which remains undiscovered as yet). At the time of writing, nobody has done this yet.

## References

- ↑ Data collected from this forum thread then collated and plotted by Spode .
- ↑ Data collected, collated and plotted by BlueStapler , using his hero's own pet.
- ↑ The aforementioned data of BlueStapler was processed and then plotted by Spode .