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I know that it measures how often a Pokemon is used in a specific tier or metagame, but how is it measured?

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I think it's how often that Pokémon appears on a team.
I didn't answer this expecting someone else to answer faster.

Dang it.

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Doctor Disco's got it right. Smogon's tiers are based on usage, which is the percentage of teams a Pokemon appears on in the surveyed time period, which is usually one month. So if you look at some of the usage stats from November, for example, and you see Clefable scored 10% in OU, that means it appeared in 10% of all OU teams used in matches.

As for how this applied to Smogon's tiering system, every three months they compile all the usage stats from the past three months in a specific tier, weighted to favour more recent statistics, more experienced players and handle suspect test data appropriately. Then, using this data, they do a mass "tier shift" in which Pokemon may go up or down one tier based on usage. Smogon's official explanation for this is:

The cutoff for each tier is the point at which you're more than 50% likely to encounter that Pokemon at least once in a given day of playing, if you play 20 battles a day. For those that don't feel like doing the math themselves, that number is approximately 3.41%. So that means if a Pokemon is used on 4% of OU teams, it's considered OU and is banned from UU, RU and NU. (source)

Simply put, if a Pokemon drops below 3.41% in its tier, it drops to the tier below the one it is currently in. If a Pokemon gains more than 3.41% in the tier above, it will move up to that tier. These moves completely bypass suspecting testing processes, unless there's an obvious problem with the move. Ubers is exempt to this process, and to my knowledge, the only way for a Pokemon to drop to OU from Ubers is if it gets a suspect test and the change wins a 60% majority vote.

As you would know, Smogon's tiers are not run entirely according to usage stats. If they deem it necessary, Smogon way hold a suspect test, in which they will test for an amount of time whether a certain Pokemon, item, ability etc. should be allowed. Those who achieve a sufficient rank on the suspect test ladder will vote for or against the proposal. If the proposal gets 60% approval amongst voters, it will be accepted and the change will occur. Smogon will also "quick-ban" a Pokemon if it's so broken that no suspect test is required to determine a fair result.

The most recent tier update, from December and thus using data from November, October and September, can be found at this address. For whatever reason, the rise and drop percentages were different this month (6.7% and 1.7% respectively) which may or may not have to do with a recent change they made, where Mega Pokemon are ranked separate to their standard forms.

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I think i might be able to make my own tier system with this information. Be sure to check out my new battle simulator in about 20 years.