Interestingly enough I was thinking about the "Down + B" method the other day because a friend of mine was asking me about the method and calculations of catch rates on certain pokeballs. I used to follow the Down + B method starting in generation 3 all the way until generation 5. It was actually RNG tracking and ROM Hacking that taught me that the Down + B method was built on a logical idea, but still did not improve catch rate.
That logical idea is the idea of using RNG tracking for the purpose of guaranteeing a specific result in the game. If anybody doesn't know what RNG tracking is, it's when you press a specific set of buttons and activate specific actions in order to prompt the RNG to create specific numbers within the games data in order to produce a very specific result within the game such as a perfect pokemon, or a shiny pokemon. It's basically cheating without actually cheating.
The idea of using Down + B to guarantee a catch, although it does sort of make sense based on RNG tracking, it's still not true since tracking RNG is significantly more complicated than guaranteeing a specific result by doing the same simple code over and over again within that one situation.
In other words, once I learned how the RNG in pokemon games works, I stopped doing the Down + B trick while catching pokemon.
Another really interesting myth in pokemon that is also related to catching pokemon is, have any of you guys ever heard of "Ball Shock"?
The idea of Ball Shock works like this, when you are trying to catch a pokemon with an incredibly high catch rate, you're supposed to throw pokeballs that have a high catch rate over and over again, such as Ultra Balls, Timer Balls, Dusk Balls, Dive Balls, etc., however when the pokemon you are trying to catch breaks out of the high catch rate pokeballs without even shaking once, you're supposed to throw one regular Pokeball or a Premier Ball at the pokemon, the moment they break out of the regular pokeball, you immediately go back to using the pokeballs with the higher catch rate again. This pattern is called Ball Shock.
The supposed theory of how this works is that the pokemon with the high catch rate is constantly having to hit a growing percentage to break out of each pokeball you throw at it, at first it will struggle to meet that percentage as it goes through each pokeball shake, but once it hits that percentage to break out, it will then have a higher likelihood of hitting that previous percentage without hitting the lower numbers that would cause the pokeball shakes on the next thrown pokeball with a high catch rate. Supposedly, when the pokemon can break out of the pokeball without a single shake, it means it has hit the highest percentage for that pokeball which guarantees an automatic break out. Throwing a regular pokeball at the pokemon, which has the lowest catch rate, requires the pokemon to hit a significantly lower percentage number in order to break out of the pokeball, when it breaks out of the regular ball, it holds onto that percentage and carries it over to the next pokeball you throw at the pokemon. This means that when the next pokeball you throw at the pokemon has a higher catch rate, the pokemon will have to meet all of those higher percentages all over again in order to beat the shakes and break out once more.
In other words, Ball Shock is a method that supposedly resets the catch rate value of the pokemon you're trying to capture. I found out about this supposed method back in generation 4, but to this day I have absolutely no idea if it is true or not. Sometimes I use the method in hopes it is true, mostly when I am trying to capture a Legendary pokemon that is being incredibly frustrating to catch. However, I have been successful even without using this method, so I really have no idea if it works or not.