Is Levelling Up in Pokemon Go Exponential?

Unless you have been living under a rock over the last few weeks, you've probably heard of Pokemon Go. If you are not aware, the general premiss is that you wander your neighbourhood (physically) with the App open. The app is linked to GPS and Google maps so as you walk around you see your streets but overlying those streets are various Pokemon characters to capture and along the way you collect points by visiting PokeStops (to also collect items) and PokeGyms (to also have battles). Along the way you "Level Up" by accumulating experience (XP) points. As you increase your level, the number of points needed to go to the next level also increases. But how? Is it linear, quadratic, exponential or something else? Well, get the data and have your students decide.

Analysis

As far as anyone knows (right now) there are only 40 levels. To move past the 1st level you need to accumulate 1000 pts but by level 40 you need five million. So the question might be "How does the number of points change as you go from level to level?".

As players are in the game, they will level up. What they will see is the number of points needed to get to the next level (not the total number of points accumulated). The first 15 levels can be seen to the right. The middle column shows the total number of points at the beginning of each level (constructed from the points needed to level up for each level). The right most column indicates how many points are needed in each level to get to the next level (this is what players would actually see). It is essentially the 1st difference of the total points. But to clarify, players never see the Total number of XP in the game. It was just constructed here because that is usually what we would be graphing. So to keep your street cred with the kids, you may want to only refer to the XP needed at each level and construct the total (like I did) for mathematical purposes.

Regardless, this is one of the first places you can have students do some analysis. By looking at the points need to level up you can see that as you go from level to level, the number of points needed goes up 1000 pts per level until level 11 where it starts to stabilize for a few levels.

As you look at all the levels there are a couple of ways you can look at it. By plotting all 40 levels you can see that an exponential model is almost a perfect fit with a geometric progression of little more than 25% each time you level up, though not exactly. A different view could be by putting the levels in groups of 5. Doing this shows that as you go up levels you need significantly more XP points to get to the next group of levels.

But a closer look at the data shows that the first 11 levels have a constant 2nd difference and thus are quadratic. And then the next few levels have constant first differences and thus go up linearly. After that the increases are not as consistent. 

So there are many places in the curriculum that this data set can relate to. On the simple end you can look at it as a non linear data set. Or you can just focus on the first few levels and keep it quadratic or contrast that with the linear portion. The fact that we are talking about discrete levels means that you can think about this in terms of sequences and series. So take from it what you need. Below are some possible prompts you can use with students and the entire set can be downloaded from this Google Doc for easy consumption.

Sample Questions

• If it took you one day to get to level 5, how long would it take you to get to level 10? Level 15? Level 40?
• What type of relationship exists between the points for each level in the first 10 levels? 15 levels? all levels?
• Do the levels follow a constant sequence?

Download the Data

• Original Data set 
• Google Sheet version Google sheets with graphs CODAP file
• Desmos Exponential Regression
• Desmos First 14 Levels

Let me know if you used this data set or if you have suggestions of what to do with it beyond this.