Hello fellow trainers!

So I know that this is most probably a fairly simple question to answer and I'm sure we all agree that the rarer the Pokémon is, the better its overall performance points should be right? Well, although it's pretty fair to answer this question by just saying "yep" and moving along, I decided to use this question as the basis of my IB Math Studies Internal Assessment and delve deeper into the statistics that are involved in answering this question. Now first off I would like to state that I am no mathematician, hence the fact that I decided to take the IB Math Studies course over any of the higher level courses. That being said, most if not all of what you see done in this internal assessment might seem like a piece of cake to you. However, for me it was a great feat to get this assignment done right and I am very proud with the result, which is why I am sharing it with all of you. I would very much appreciate those who are interested to take a look at the internal assessment and let me know what you think!

Note: Some parts are very dumbed down and I explain step-by-step what I did with the calculator as part of the assessment. Although this might be redundant information to some, hopefully it will serve to be helpful for those who are like me and also have a hard time following the math.

Another Note: This assessment focuses solely on the original 151 Pokémon for two reasons: they are the ones that are near and dear to my heart and I didn't have the time to do all 721.

One Last Note: I did some bonus math to further prove my result by finding the correlation between a Pokémon's overall performance points by type and overall catch rate by type. Conclusion: I had hypothesized at the beginning of the assessment that there would be a "very strong" correlation between the Pokémon's performance points in battle and its catch rate. I ended up disproving that only slightly by calculating a strong correlation instead. It is safe to say that the correlation is strong, however based on the data I collected it is evident that there are some instances in which this correlation is not valid.

TL:DR - I'm no mathematician but I did some fairly simple math to answer this question regarding the original 151 Pokémon. I had a lot of fun and would appreciate your comments! Conclusion: Yes, there is a strong correlation as you probably suspected, however it is not "very strong" as I and most others probably hypothesized.