"[Analysis] Pinap berries ALWAYS yield more candy, on average, than Razz berries (simulated for Gen I)"

#PokemonGO: IntroductionWith the introduction of Generation II Pokémon, trainers are looking to quickly fill their Johto Pokédex and power up their strongest monsters. To help earn candy for evolutions and power ups, the new Pinap berry can be used to double the amount of candy earned for capturing a Pokémon. However, using a Pinap berry means that a Razz berry cannot be used, which decreases the chances of capturing the Pokémon, and ultimately increases the chance that it will flee. I set out to determine if there were any cases which using a Pinap berries actually resulted in LESS candies, due to the increased flee chance.MethodsTo define the problem, I made a decision tree (http://ift.tt/2m1JEu8). You choose which berry to use, and then the Pokémon is either caught or it flees. If you catch it, you receive a candy reward which depends on the berry used and the Pokémon’s stage of evolution. I also assume that you transfer the Pokémon after it is caught – though this might not always be the case, the results are the same. The expected value of each decision is simple – since no candy is gained if the Pokémon flees, the expected value of each choice is simply the Overall Catch Probability (OCP) times the candy reward. The expected value in this case represents the average amount of candy you will receive after making that choice. The math behind the OCP is nicely explained over at GamePress (http://ift.tt/2b16ONw). Briefly, it depends on the Pokémon’s base catch rate, flee rate, level, and on throw multipliers (ball type, curve, medals, berry, and coloured circle size). There are really only three independent variables here: Pokémon type, level, and throw multiplier. I chose the dependent variable to be the ratio of the Pinap and Razz expected candy values. Therefore, a ratio > 1 means that the Pinap berry yields more candy. Then, I simulated encounters with each Pokémon at levels 1-30 (the wild maximum) and throw multiplier before berry from 1 (straight pokeball throw outside circle, no medal) to 8.84 (excellent curved ultra ball with gold medal). I did this a second time, this time multiplying the throw multiplier by 1.5 as it would be with a Razz berry. At each point, I calculated the expected candy ratio between Pinap and Razz berries and plotted the point on a surface plot specific to that Pokémon.Results and DiscussionAn example surface plot can be seen here for Bulbasaur (http://ift.tt/2mfZLR6), and a picture of plots for the first 150 Pokémon can be found here (http://ift.tt/2lgFsVL). Throw multiplier before berry is on the x-axis, Pokémon level is on the y-axis, and Pinap/Razz candy ratio is on the z-axis. I also plotted the minimum Pinap/Razz candy ratio (Pokémon level 30 and throw multiplier of 1) from each surface against Pokédex number (http://ift.tt/2m1Qyjj). The one outlier on the plot is Abra, which has a 99% chance to flee if not caught on the first try (surface plot here http://ift.tt/2mfH8wk). Even here, the Pinap/Razz candy ratio is still greater than 1 at level 30 with no throw bonus. Importantly, there were NO cases where the ratio fell below 1, which indicates that using a Pinap berry, if you can spare it, will always yield the most candy.My MATLAB code can be found here (http://ift.tt/2m1QorQ) in case you want to check for errors.TL;DR in title :)E: My calculations were done using the old catch rates, from before they were increased. The result still stands though. E2: Replaced "EV" with "expected value" to prevent confusion with effort values. via /r/TheSilphRoad http://ift.tt/2mg21Ye