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# A Defense to Reach the Stars - A Numerical Glance at the Bulk in the Uber Tier

Discussion in 'BW Ubers' started by Superimp, Oct 14, 2012.

1. ### Superimp

Joined:
Feb 7, 2012
Messages:
62
What defines bulk? Is it the mere combination of both the Defense and HP stats of a Pokemon? Or is it something much more?

A Defense to Reach the Stars
A Numerical Glance at the Bulk in the Uber Tier
An Uber Extension of the Efforts from both Ulevo and Dragontamer
Introduction

When one plays the game of Pokemon, bulk is often a key topic. Many players have a general sense of how bulky a Pokemon is; you know that Blissey has very impressive special bulk for example.

But when one begins to dive into the specifics of bulk comparison or definition, the issues begin to surmount. How much greater is the special bulk of specially defensive Giratina when compared to tank Tyranitar under sandstorm? What is the difference between the physical bulk of Evolite Chansey and support Ferrothorn? When does a lack of numerical bulk become unacceptable for a defensive Pokemon?

When such questions are asked, it comes as no surprise that many players often fall short. It is not common knowledge; very few players memorize this information from the top of their head. Still, there must be some way to objectively compare and define the bulk of such Pokemon.

It is through a glance within the world of numbers that we may find our answer, a way to objectively rank the physical, special, and mixed bulk of the Pokemon used in the Uber tier. More specifically, Defense Tiers will prove our means to the end.

The Numbers

What is a Defense Tier? Simply put:

Although this calculation might be a bit crude, its accuracy should be adequate for our purposes.

To provide the most accurate reflection of the defensive capabilities of the Uber metagame, only the official sets currently on site or in C&C will be used. For instance, you wouldn't expect to find a physically defensive Reshiram despite the theoretical possibility.

The following charts were derived from a spreadsheet detailing all the defensive stats and tiers of all the Pokemon used in the Uber tier. The link is as follows:

All the charts below are arranged from highest to lowest, not taking into account any special modifications such as weaknesses, stat boosts, and resistances - these are calculated separately. However, the nature, possible item boost, possible sandstorm, and ability are taken into account.

The average of each chart has been set to 118 based on previous experience and that the average for all the defense tiers was coincidentally calculated to be around 118. I hope these charts prove convenient for your purposes.

NOTE: If there is no set name in front of the Pokemon's name, assume that tier score is true for all cases unless otherwise noted.

Physical Bulk Tier Chart:
Special Bulk Tier Chart:
Overall/Mixed Bulk Tier Chart:
The Interpretation

With just a mere glance, these charts provide a quick and easy method for comparing the numerical bulk of one Pokemon to another. Just take two relevant Defense Tiers and note their values; whichever has the greater value has the stronger defensive capability in general. However, a little more effort may be required to gleam other information.

For those who wish to find an accurate adjective to describe the numerical bulk of a Pokemon in accordance with the Defense Tiers, the following chart will allow easy comparison.

Ranking Chart:
Simply take the relevant Defense Tier of the Pokemon in question and then match it up with the relevant number in the chart to obtain the desired adjective. More accurate sentences which detail the numerical bulk of Pokemon used in the Uber tier can possibly be created as follows:

For those who prefer a numerical analysis between the numerical bulk of two Pokemon, the Defense Tiers themselves will prove crucial.

Because the Defense Tiers were calculated using the logarithmic scale base 1.1, a difference of 1 Defense Tier corresponds to a general 10% difference in the ability to take damage.

For instance, a Pokemon in Defense Tier 127 would generally take around 10% more damage than Defense Tier 127+1 = 128, yet would generally take around 10% less damage than Defense Tier 127-1 = 126. Around the same amount of damage would be taken when compared to another Pokemon in Defense Tier 127.

For those who desire a more specific comparison, a little arithmetic may be required. An equation for a quick estimation of percent difference is as follows:

$Percent Difference = ((1.1^{\left | Tier Difference \right | })-1) \times 100$

An example of a possible calculation is below:
If you wish for a more accurate percent difference value, the following equation might prove useful:

$Percent Difference = \frac{\left |1.1^{DefenseTierA}-1.1^{DefenseTierB} \right |}{\frac{1.1^{DefenseTierA}+ 1.1^{DefenseTierB}}{2}} \times 100$

Here is the same example using this equation instead:
It is to be noted though that looking at the big picture is quite important when calculating these percent difference values. Many player would probably be content with just an approximate value. There is also a bit of already existing uncertainty with the entire Defense Tier system due to their crude method of obtainment. Still, it doesn't hurt to provide a more accurate percent difference value every once in a while.

The Beginnings of a New Analysis - Your Turn

Through the interpretation of the raw data obtained through the Defense Tiers, we are now in a position to dive into the heart of the matter. What really defines "bulk" in Ubers?

This question may prove more difficult than it might seem. Conceivably, a look into the Defense Tiers themselves to see which Pokemon outright are notable for their numerical bulk might work. Yet if such an approach were made, we might fail to recognize the Pokemon which use other strengths to overcome their otherwise inadequate numerical bulk.

Take for example Skarmory. Skarmory is clearly inferior when compared to an Uber titan such as Lugia in essentially all regards numerically. Yet Skarmory has an extraordinary useful defensive typing, and carries valuable utility in Taunt, Spikes, and much more. Clearly, the bulk score isn't everything by itself.

There are so many factors to be taken into account for bulk. Entry hazard susceptibility, resistances, weaknesses; all of these factors are incredibly important in the Uber metagame. Luckily, there is a method for taking these modifications into account.

The special modification chart using Dragontamer's efforts as a base is as follows:
Code:
```4x weak : -14.27 (EX: Ice Attacks Dragon/Flying)
2x weak : -7.27 (EX: Fire Attacks Grass, 4x Stealth Rock weak)

-25%    : -3.02 (3x Spikes, 2x Stealth Rock weak)
-18.75% : -2.18 (2x Spikes)
-12.5%  : -1.40 (1x Spikes, neutral Stealth Rock)
-6.25%  : -0.68 (2x resist Stealth Rock)
-3.125% : -0.33 (4x resist Stealth Rock)

+50%  : 4.25 (Calm Mind, Bulk Up, etc.)
+100% : 7.27 (Amnesia, Barrier, Reflect, Not Very Effective, etc.)
+150% : 9.61 (3x Calm Mind / etc. etc.)
+200% : 11.53 (2x Amnesia, etc.)
+250% : 13.14 (5x Calm Mind / etc. etc.)
+300% : 14.55 (Max Amnesia/Barrier, 4x Resists, etc.)```
NOTE: Leftovers is meaningless for taking actual hits, so is not included. Spikes / Stealth Rock only applies on the switch-in if applicable.

When using this modification list, take the relevant Defense Tier in question and then add/subtract the desired bonus. For instance:
Still, a focus on just the Defensive typing and Defense Tiers might prove too limiting for our answer. Movepool, offense, Speed, utility - many intrinsic factors come together to define the use of bulk for a Pokemon. It is in this sense that perhaps only an interdisciplinary approach can truly bring about a solution for our problem.

If you are interested, please take a look at the Uber Threat List. More specifically, the Defensive Threats. Are they any connections between that list and the Defense Tiers? What kind of Pokemon are on these lists? Utility? Niche? Overwhelming bulk?

Please take a look at the Offensive Threats after. Do you notice any patterns between the list and the Defense Tiers? Is there a certain "balance" between bulk and offense that distinguishes one Pokemon from the next? External factors? Movepool?

For example, you might notice that some Pokemon such as Deoxys-A who are typically associated with offense are not in Tier 1. Why is this the case? Is there a certain "threshold" in bulk that must be achieved in order to truly distinguish the great Pokemon from the rest?

Likewise, what defines an acceptable bulk for a defensive Pokemon? What is the bare minimum Defense Tier that a bulky Pokemon may lower itself before it becomes useless? How much of a "balance" is required?

Of course, analyzing the Defense Tiers themselves might bear some fruit. What misconceptions do we currently have about the numerical bulk of certain Pokemon? Conversely, when were we correct?

For instance, Chansey with her Evolite has always been associated with an increased Physical Defense when compared to Blissey. But have you tried comparing her physical bulk with the rest of the Uber tier? A quick glance into the charts reveal that standard Chansey is quite similar in physical bulk to Pokemon that we typically associate with good Physical Defense, such as standard Gliscor and support Ferrothorn. This isn't even the end of it though, as a full Physically Defensive Chansey actually has a Defense Tier of 123.16. To put this into perspective, Chansey actually has more physical bulk than physically defensive Kyogre and 252 HP Arceus! Clearly, there are many surprises to be found within the data.

Final Thoughts

When one really stops to reflect about the data provided from this resource, you might realize that there are many ways to interpret this information. Maybe you will try identifying key trends and connections between this resource and the others. Maybe you will use this data to supplement your own posts when you start to describe bulk. And of course, maybe you will focus on finding information that you personally find interesting. It matters not though; it's really up to you to determine how best you will use it. But no matter the path you eventually embark on, I hope this resource proves useful as we all strive together to better understand the Uber metagame as we know it today.
Last edited: Jan 2, 2014

Joined:
Jul 29, 2010
Messages:
2,947
super(p)imp is awesome and i am stickying this

a very thorough and amazing continuation of dragontamer's work, bravo

everyone who glances through this at least have a look at the database of defense tiers as it is marvelous

edit: whoever thinks this isn't worthy of stickying ..... whatever, as long as it stays somewhere where it will be noticed
3. ### FaintValar morghulisModerator

Joined:
Dec 23, 2007
Messages:
1,862
My friend, I have not seen defense tiers since ADV.

You clearly put tons of work into this. I doubt it will be of any help to me but thank you. It's pretty rare that I'm actually impressed with things, especially in the Ubers forum.

Luvdisc'd.

edit: I love Latias too. :)
4. ### MeteorMiss

Joined:
Oct 19, 2012
Messages:
126
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.)

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.

Anyway, great job; these are a few things that would make the list even better.
5. ### Superimp

Joined:
Feb 7, 2012
Messages:
62
Response to MeteorMiss:

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

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 :).

----------------------​
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 members like X-Act) which explain Attack Tiers in more detail:​

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