One of the things that Pokemon Go doesn't tell you is its catch mechanics. Players seem to just enjoy random tossing of PokeBalls to catch a wild Pokemon. But if you look hard into it, there are certain patterns and computations on how a creature is caught the moment that ball lands into that shrinking ring guide thing.
Recently a YouTube channel dedicated to helping everyone out with Pokemon Go, Trainer Tips, has summarized how the app calculates the chances of catching a wild Pokemon in Pokemon Go the moment you throw that PokeBall. Now, I will write it the best I can but I bet I couldn't beat how it is being explained on the video below, so better play that one too.
Basically the catch rate is now unified throughout all parties and it says: Catch Rate = 1 - (1 - (BCR/2*CPM))^M. In words it would say something like the Catch Rate is equal to 1 minus 1 minus Base Catch Rate over 2 times CPM to the power of Multipliers.
CPM, or combat power multiplier is a number assigned per Pokemon, it is in the game data used for calculating combat powers (obviously) and it's also used for calculating the catch rate. The value varies from one Pokemon to the other.
BCR, or Base Catch Rate, is the unit assigned for a Pokemon's chances of being caught. The range for Base Catch Rate is found out to be from 4% for the fully evolved Pokemon to 56% for the easy ones.
Multiplyers (M in the formula) are affecters that help increase or decrease your catch rate. They are your PokeBall types - better balls mean better catch rates, wether or not you use Berries, Curve Ball throw or just swipe straight, Medal Bonuses, and if you hit a throw bonus - Nice, Great, Excellent.
If you observe in the formula, the multiplier is used as an exponent, meaning this greatly affects the equation. For Pokeballs you will have 1.0, 1.5, 2.0 respectively for ordinary red, Great Ball, and Ultra Ball. Raspberry gives you a multiplier of 1.5 while a curveball gives 1.7. For the bonuses, you will have 1.15, 1.5, 1.85 respectively for Nice, Great, and Excellent. For medals, since its new, they weren't able to completely define the multipliers except for gold which is 1.3, which speculates to give silver 1.2 and bronze at 1.1. With those said, the more points you can stack up, the better the chances you will catch that wild Pokemon in Pokemon Go.
Well, the mathematical stuff mentioned in the video has no practical use really except for proving mathematically the numbers and calculations that work behind Pokemon Go's catch mechanics. The video was able to prove that higher level Pokemon are harder to catch by using the formula. As an example, a level 30 Pidgey's chances of being caught is 27.33%, a level 20 gives 33.48%, and a level 10 has 47.34%, all using an ordinary red PokeBall. As of this point, it is better to keep higher items from PokeStops and just get rid of the basic ones if you want a higher capture rate..
At this point, my vision is starting to go purple so I'd just leave you with the video below on further discussions about more numbers and mathematical stuff for Pokemon Go's catch rate. If you finish the video, I congratulate you, all my brain can take was up until 4:29 on the timeline. Have fun.