"Answering the fastest way to catch legendaries."

This is an answer to the post from /u/thisisredditnigga, it can be found here.So, first of all, from the last part of your post I assume you want to calculate things on the 7th Gen, so based on that I tried to find out things with resetting time etc. on this generation.The calculator I used for it is synx.ws. It is german only sadly, but calculation can be made up to 7th gen.In all methods I will equally ignore a critical catch as it just makes just a minor difference. Method #1: Quick Ball and soft-resettingLets take a look at method #1, quick ball and resetting after first catch. As it is important to know how long the soft reset is taking, we have to time this first. The whole soft reset, the cycle, goes like this:The actual pressing of buttons, from where the soft reset startsThe time we can interact with the legendary pokemon (like, the stationary ones).The first time we can actually access the menu in the fight.The time we make the "order" to throw the ball So after we reset we have to mash A to get through the intro sequence and select our profile, including loading times, which maybe varies on different versions of the handheld.For testing purposes a NPC was talked to, it got the job done for the timing.After that, legendary pokemon normally have a little scream before you can enter the fight. This time differs from pokemon to pokemon and from gen to gen. Some even have cutscenes before. I think if we take 3 seconds for the scream and assume we don't have a long cutscene before, we are about right.Then the fight starts with the message, the pokemon appeared and you as the trainer bring up your pokemon to fight, it gets a camera scene, then we can finally access the menu on the bottom screen.You can reduce the time you need to select the pokeball you need. Before you start to soft reset your pokemon over and over I recommend catching a few pokemon in quick balls before, so Y, the quick access item slot gives you a quick ball. Seclecting the ball viaTimeBag3sQuickmenu (Y->Y)less than 1s I recorded and measured the times myself on a normal 3DS XL on Pokemon Sun. I took the cycle from above, timed and wrote it down into this table: TimestampsTime passedThings donePerfoming soft reset0sPressing L, R, Start, Select ButtonsInteracting with pokemon15sMashing A through the intro, selecting profile, loading into game, "talking" to pokemonFight menu accessible32sHear the pokemon's scream, getting into battle, bringing out your pokemonOrder to throw a ball33sAccessing menu, pressing Y->YPokemon breaks out40-45sDepends on how many times the ball shakes before it breaks outSoft reset table(Numbers are rounded slightly upwards to compensate speed difference and little measuring errors) In method #1 though we can say, as soon as we see the pokemon break out the ball, we can soft reset.So we can take a rough estimate time of 48 seconds per cycle.Now we have to make calculations on the catch rate. Taking the numbers from synx.ws , I took an Articuno (german: Arktos), which has a catch rate 3, and put every single state we will need to calculate the catch rates in all 3 methods. StatusHP[%]BallProbability(r)Tries neededNone100Quick Ball2%51Paralyzed1Ultra Ball3.5%28Paralyzed1Timer Ball7%14Sleeping1Ultra Ball4.7%21Sleeping1Timer Ball9.3%10Catch chance tableProbabilities are rounded, Tries needed are calculated to reach 100% We will come back to this table again later in all 3 methods, don't forget this table.Now we take the first case in the table above and multiply the 51 tries with 48 seconds and we get the result of around 40 minutes with method #1.Of course, like everything with probability, it is NOT ENSURED to have a catch after 40 minutes, it can also happen after 2 minutes or 60 minutes.But it gives us a reference we can measure the other methods on. Method #2: Paralyzed pokemon For method #2 and #3 we assume we have a perfect pokemon.It doesn't matter which pokemon it is exactly but it can learn False Swipe, Nuzzle and is preferably bulky against Articunos attacks (Ice, Fly, Rock).There are some pokemon that fulfill these things almost, but my self-created perfect pokemon also brings down Articuno to 1HP with 1 False swipe, but practically there is none.As there is no "perfect pokemon" though we will assume that we need 3 turns to set up Articuno to 1 HP and paralyzed, after that though we can spam balls.We still need to declare which balls we want to use. Here are the balls that will probably net Articuno faster than all others. Quick Ball excluded for now of course. BallCatch RateNotesMaster Ball......Ultra Ball2Timer Ball1 / 44 in turn 11+Repeat Ball1 / 33 if you have the poxedex entry I assume the Articuno appears at level 50, so the Level Ball will make same effect as an Ultra Ball as long as you use a pokemon over level 50. Is the pokemon we want to catch lower than level 50, we can instantly get a catch rate of 4 as long as our pokemon is level 100.Heavy Ball does not come into this table because with the low weight of Articuno it gives us, even at 1HP and paralysed, a chance of 0,9% per throw.The timer ball does, like you corrected me right, evolve into his full potencial in turn 11.The Repeat Ball helps us if we already have the entry in our pokedex, which I will NOT assume in this example.So, the plan goes as following: TurnMoveNotes1Paralyze2False Swipe3Extra set up roundExtra paralyze/False Swipe4Ultra Ball5Ultra Ball6Ultra Ball7Ultra Ball8Ultra Ball9Ultra Ball10Ultra Ball11Timer Ball......xTimer BallCatch turn So we have 8 chances with the Ultra Ball before we change to the Timer Ball for the rest of the fight to increase our chances.Taking data from the Catch chance table again, we try to get to 100% to have an "average" of balls needed.This leads us to the equation:8 [Ultra Balls] x 3.5% + 10.2[Timer Balls] x 7% = 100% -> rounded up 11 Timer BallsAccording to this, we should need 8 Ultra Balls and additional 11 Timer Balls.Further leading us to the conclusion that we need about 22 turns. Now I don't need more calculations on this to say that Method #2 is DEFINETELY faster than method #1.For clarification, to get to this 100% point (which is no 100% safe catch but a reference we can compare both methods with) method #1 takes 40 minutes, method #2 takes 22 turns.I don't have to tell anyone that 22 turns go WAY faster than 40 minutes.At this point we are done with method 2, but how fast is method #3? Method #3: Sleeping pokemon Like in method 2 we assume we have a perfect pokemon with False Swipe, this time an attack to put Articuno to sleep and is bulky enough to tank Articunos hits.The advantage of a sleeping 1HP Articuno is, it gives us a higher catch rate at the cost of having to refresh the sleep over and over again.Another disadvantage is that most sleep moves are very inaccurate compared to paralyzing moves, taking more time because moves sometimes won't hit.There would be one 100% accuracy move [Spore] but only few pokemon can learn, but they are all vulnerable to Articunos Ice-moves, though this is just a problem because we catch an Articuno in this example. Generally our plan looks a lot like in method #2: TurnMoveNotes1False Swipe2Extra set up roundExtra False Swipe3Spore4Ultra Ballsleeping5Ultra Ballsleeping6Spore7Ultra Ballsleeping8Ultra Ballsleeping9Spore10Ultra Ballsleeping11Timer Ballsleeping12Spore13Timer Ballsleeping......xTimer BallCatch turn The pokemon will wake up after 1-3 turns of sleeping, so I am taking an average of a 2-turn sleep.So, with this in mind, we can start our calculations as followed:5[Ultra Ball] x 4.7% + 8.2[Timer Ball] x 9.3% = 100% -> rounded up 9 Timer BallsWith our 2 turn sleeps in mind, we come to turn 23 where we should get to 100% and have a reference to the other methods. Comparing method #2 and method #3Looking at the last 2 methods, they seem to be equally fast, though there are some things that haven't been said yet.The paralyze-method is way more brainless in a sense that you need technically only need to press Y all the time, maybe B to speed text boxes up.The sleep-method requires you to look your screen every turn and decide if you have to Spore the pokemon or if you can throw a ball.Additionally, the amount of pokemon that can learn 100% or 90% accurate paralyze moves (TM Thunder Wave) is way higher than the amount of pokemon that can learn accurate sleep moves.Sadly there is no pokemon that learns both 100% accurate sleep moves, Yawn and Spore so you can't optimize the first turns into Yawn -> False Swipe -> Ultra Ball.Both status moves make the pokemon not attacking at all (sleep) or partially (paralyze with a 25% chance), meaning that you would skip the animation of the pokemon's attacks, but you should turn off animations off anyways. TL;DRSoft reset + Quick Ball is not worth at all, it takes a HUGE amount of time, depending on your luck (+40 minutes, calculations above).Sleep and paralyze methods both are almost equally fast with around 22 turns, sleep-method can be faster if pokemon sleeps longer than 2 turns and if your sleep-moves hit every single time.Paralyze is way more comfortable, you can spam Y (and B to speed up text boxes) and it works itself, sleep-method requires you to check status every single turn and alternate between attacking and catching.The best choice is the combination of method #1 and #2 as they don't cancel out each other, you just sacrifice one turn for the first turn quick ball. Things you should do before you start:Bring Ultra and Timer Balls with you, if you have the pokemon registered, replace Ultra Balls with Repeat Balls.Take bulky pokemon with you, at least one with a paralyzing move, others should resist the pokemon's attacks.Saving (to reset for a good nature/shiny/IVs)Turn off animations And, yes, you can still catch any given pokemon with Beast Ball, you just need to be lucky enough.Happy catching via /r/pokemon http://ift.tt/2pJQZQU