[Superimp]

Response to MeteorMiss:

Originally Posted by Fat MeteorMiss

Might it be better to use log(2)? This would make it easy to calculate resistances and weaknesses. (For example, if grass arceus switches in on a water spout, its tier number increases by 1. If Palkia switches in, its tier number increases by 2.)

Here is Dragontamer’s reasoning for why he set the Defense Tiers at the logarithmic scale of base 1.1.

Originally Posted by Fat Dragontamer

I took my own advice and created the exponential tier list. The tier number is the floor(log_1.1(value)) . Essentially, every tier is a group of pokemon that are within 10% of each other's defense*hp value. (…) The exponential scale of 10% was chosen pretty much at random. However, I did first split the pokemon into 6 tiers. But ****ing EVERYONE is in the sweeper tier. I mean seriously, EVERYONE is in a single tier. As you can see here, even with a 10% difference between tiers (again, not that much) the tier lists get a little big in the middle. SOURCE

Keep in mind MeteorMiss that one of the main goals of these numbers are to compare the relative strength of numerical bulk between Pokemon in an easy to understand manner. Resistances and weaknesses are calculated separately through simple addictive modifications.

Although it is true that a log(2) scale might make it easier to calculate the modifiers for resistances/weaknesses, such a scale makes it far more difficult to compare the relative defensive capabilities between Pokemon (100% V.S. 10% difference between tiers). That and other modifiers such as Calm Mind, entry hazards, etc. might not be fully suited for a log(2) scale.

Here is the database using a log(2) scale. Compare it with the database using a log(1.1) scale. Which do you prefer? The log(2) scale, or the log(1.1) scale?

In the end, it really comes down to how much of a “zoom” you want for the data. I thought a 10% difference between tiers would provide sufficient in-depth information while still retaining enough of the big picture, so this is why I kept the scale. There’s nothing wrong about preferring a 100% difference though :).

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Originally Posted by Fat MeteorMiss

Also, I don't think the adjectives cut it. How "superb" does something have to be to take a scarfed Water Spout? How about a specs Spacial Rend?

Maybe it would be better if we drew lines in the sand. In other words, we could take some common attacks in ubers and say, "bulk has to be above xxx to avoid being 2HKO'd by scarf water spout". This is where the log(2) scale would come in; it would be easy to adjust the scale for a resisted attack, rather than a neutral attack.

It seems you have stumbled upon the limitations of these Defense Tiers MeteorMiss. Although these Defense Tiers are quite useful for comparing the relative strength of numerical bulk between Pokemon, they alone are unable to provide the answers you seek. Perhaps you might be interested in a combination of Attack Tiers and Defense Tiers instead?

Although Attack Tiers are outside the scope of this thread as of the moment, here are some links from Dragontamer (along with discussion from users like X-Act) which explain Attack Tiers in more detail:

Practical Introduction to Attack Tiers

Attack Tiers: The Counterpart to Defense Tiers

Although these threads are from Generation IV, they should be adequate for your purposes.

As a small demonstration on the potential of Attack Tiers, let’s use your example of Choice Scarf Kyogre’s Water Spout.

Originally Posted by Fat Superimp

Choice Scarf Kyogre has a Special Attack Tier score of 63.81 since log 438/log 1.1 = 63.81 where 438 is Kyogre’s Special Attack stat.

A full power Water Spout has an Attack Tier score of 52.57 since log 150/log 1.1 = 52.57 where 150 is Water Spout’s Base Power.

Let's assume the following modifiers are in play.

Rain = 50% boost AKA 4.25 score
STAB = 50% boost AKA 4.25 score

Adding all these numbers up, we get 63.81+52.57+4.25+4.25 = 124.88.

From this point on, we decide how "strict" we want Kyogre's chance of a XHKO to be.

EX: Suppose we want a guaranteed chance of an OHKO. Therefore, we subtract 3.53 (The "magic" number for a guarantee) and do not apply any XHKO modifiers (Base form is OHKO).

124.88 – 3.53 = 121.35

Therefore, any Pokemon that is neutral to Kyogre’s full power & rain Water Spout and has a Special Defense Tier score lower or equal to 121.35 will be OHKOed guaranteed in general.

And we see this is true when we look at a 4 HP Arceus with a neutrality to Water Spout (EX: Arceus-Bug), which has a Special Defense Tier score of 121.35.

252+ SpA Kyogre Water Spout vs. 4 HP / 0 SpD Arceus-Bug in rain: 382-451 (100 - 118.06%) -- guaranteed OHKO

A similar process as seen above can be applied to situations with stat boost changes, entry hazards, 2HKOes, 3HKOes, Leftovers, average chance to XHKO, bare minimum chance to XHKO, etc. through the use of modifiers.

NOTE: These calculations assume the logarithmic scale of 1.1.

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As you previously said MeteorMiss, perhaps I could "draw lines in the sand" for common attacks through a combination of Attack Tiers and Defense Tiers. However, I did not provide Attack Tiers in this thread for the following reasons:

1. Attack is relatively more straightforward than bulk.
2. Honko’s Mass Damage Calculators exist. Although they are currently a bit weak compared to Defense Tiers for comparing the relative strength of numerical bulk between Pokemon, they are extremely strong at giving information on how well one Pokemon does against the rest. That and they’re really easy to use.
   
   NOTE: Attack Tiers are still useful for not requiring calculator/online support, being possibly faster given enough experience, the ability to take into account Leftovers, stat changes from moves such as Draco Meteor for XHKOes, etc. for mass damage calculations, and more.
3. This thread as of the moment focuses on one thing – Defense Tiers.

If there are enough people who are interested in an updated Uber Attack Tier list though, then I see no reason not to provide them. It might help us better understand bulk as a whole, improving the list like you previously said.

Hope this answers your question MeteorMiss.

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Thanks for all the support Poppy, Faint, and MeteorMiss! As well as all possible readers - I hope you guys found this resource to be of use.