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...and why is the number 3.41% significant in the way competitors tend to use Pokemon?

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By seeing their usage.

The tiers as of such do not qualify the Pokemon as "strong" or "weak", but rather how much people use them. It indirectly shows the viability of the Pokemon as a good Pokemon will always be opted over a weaker one. Smogon as such only has a semi-control over these tiers.

The Smogon tier system classifies Pokemon into how much they are used. If they ever turn out to be too highly used (or too strong in layman's language) then they step it up one tier. For example Mega Mawile was considered too strong for the OU tier, so it was banned to the Uber realm. Mega Rayquaza was too strong even for the Uber tier, so they banned it to "Anything Goes".

The reason why these Smogon tiers are so popular among trainers is because it was one of the first systems to actually rank Pokemon as per their strengths accurately enough. It standardized competitive play in a way the official system did not, promoting fair-play in battles.

You like legendary Pokemon (in a competitive sense unlike some newbies)? Try the Uber tier, and eat your fill against others with your opinion. Like strong Pokemon, but avoid all those hot shot legendaries? The OU (and maybe UU) is filled with it. Like using those underwhelmed Pokemon but don't want it to get crushed by the strong ones? Try RU/NU or even PU. People get a huge amount of choice like this, and get attracted to it.

And then there's also those novices that want to look like the other experts, and they think Smogon is for the cool gang.

Hope I helped!

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But what exact amount of usage shifts a Pokemon up or down a tier?
I'm pretty sure they have Suspect Tests, and then vote whether or not to move a Pokémon out of a tier. If it reaches a 60% majority then it rises / falls.
3.41% I believe is the requirement to be in a tier. For example, say if Zapdos (OU) dropped below 3.41% in OU usage, it would drop to BL
How does something drop out of BL?
I wanted to ask how does the number 3.41% have any significance.
To clarify, the number 3.41% has significance in the sense that a pokemon would be used enough in a tier to be seen a certain number of times when facing an opponent out of an X number of battles. It isnt too high, to the point where "crappy" or niche stuff would remain OU (such as mandibuzz and Mamo), and it isnt too low that everything and its evolution tree is in a specific tier.

Also, direct data tiering has NOTHING to do with borderline (BL). If something did not meet the 3.41% cutoff in OU, it would directly go to UU. BL is a place Tier Councils use to place pokemon deemed "too strong" for the tier. Hawlucha, by direct data tiering, should be UU or lower. However, the UU council has suspected Hawlucha and came to a general agreement that it is sinply too strong and lacks a fair amount of checks and/or counters for it to be healthy to the metagame.

For a mon to drop out of BL and into the tier it was originally banned from, the tier council must be willing to resuspect the pokemon, usually after tier shifts (every 3 months), when a number of mons either leave the tier or drop down to it or the addition of a new clause. Such is the case with Venemoth, whose brokeness in UU was being a great Quiver Dance Passer in a tier with powerful special attackers such as Nidoking and Hydreigon. Now, thanks to the new Baton Pass Clause, Venemoth has lost its primary usefulness in being a Baton Passer, and is being allowed in UU for the time being unless it is found to be overpowering (unlikely).

Also, for a mon to leave BL and go a tier up, all they must do it achieve the 3.41% cutoff, which happens every 3 months.

Usage data only transfers a pokemon through Official tiers.
Suspect tests remove a pokemon (or in the case of Megas, stones) from an official tier into a borderline tier, an in between of the tier it dropped from and the tier is was suspect tested out of.