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Pokémon Research

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  • Between Diamond and Soul Silver, I have developed spreadsheets of data; probably the most interesting of them is my compilation of the stats of individual Pokémon.  I used it to create a measure of the overall power of a Pokémon for comparison purposes.  I first normalized each of the Pokémon's six individual stats by subtracting the mean, or average, and dividing by the standard deviation for each stat.  The purpose of this step is to allow direct comparison between say HP and Attack, for example, as a 50-point difference in HP is not as significant as a 50-point difference in Attack.  After normalizing the individual stats, I used the average of all six normalized stats as a measure of a Pokémon's overall power.  I've also toyed with a model that instead averages HP, Defense, Sp. Def, Speed, and the higher of Attack and Sp. Atk, as a Pokémon with a high Attack that only knows physical moves doesn't need Sp. Atk and vice versa.  These methods provide a good measure for a Pokémon's power, but this does not take into account the level differences between Pokémon.

    This more significant problem has given me some difficulty.  I know, for example, that my level 100 Blastoise is far more powerful than my level 58 Raikou, but I have sought to determine a way to make a valid comparison of overall power while accounting for these level differences.  The best model I have developed so far is based on a least squares quadratic that determines approximately what an average Pokémon's power is expected to be at every given level.  Then, it is just a matter of determining the deviation between what is expected and what is computed for an individual Pokémon to see how powerful that Pokémon is relative to other Pokémon at its level.  This provides a means for comparing Pokémon of different levels, but a problem I have noticed is that Trainers, myself included, are far more inclined to raise powerful Pokémon to high levels than they are to raise weak Pokémon to high levels.  This shifts the expected power rating for high-level Pokémon, as predicted by the model, to a much higher value than it should be, which results in high-level Pokémon being rated using this metric as weaker than they are.  For example, the model shows my level 100 Blastoise as being weaker than my level 44 Ariados on the level-adjusted scale, which appears instinctively to me to be erroneous.

    I am, at this time, unsure as to the best way to restructure my model to provide better comparisons of Pokémon of unequal levels.  One idea I have had is to use power computations from level 1 to 100 based on the normalized stats of a roughly average Pokémon such as Skarmory to create a baseline to compare all the other Pokémon to, but this method doesn't really utilize the available data very well.

    In some respects though, the stats exhibited by Pokémon after level reduction such as in the Battle Tower may be more valuable, particularly as all of these Pokémon can be directly compared because they are all the same level.  I've made some progress in this area, but this list is certainly much shorter because a Pokémon must be at least level 50 to be included.  I have not been able to compare any of the most powerful legendary Pokémon as yet by this method because the Diamond Battle Tower, which is what I have been utilizing, doesn't allow them entry.  Another difficulty I have is determining when a Pokémon's stats are as high as they will go.  I have a theory as to how this can be determined, namely that the cap has occurred when a Pokémon will no longer accept stat-boosting items, but I do not know for certain whether this is the case.  I do know that if this point is not reached before a Pokémon goes into the Battle Tower, its stats could be different if it goes into the Battle Tower at a later time after it has been raised further.

    In addition to my primary project discussed above, I have also been working on compiling a comprehensive list of moves that includes an overall power computation for each move using both its power and accuracy.  This power computation is based on the expected value.  For example, if the move's power is 100 and its accuracy is 75, the expected power of the move is 75 because it delivers 100 power 75% of the time and 0 power 25% of the time.

    I've also recently delved into some type research.  I began with a table I created delimiting the particular strengths and weaknesses of all attack types compared to all Pokémon types.  If the world had only consisted of single-type Pokémon, my analysis need not have gone much further; however, as we know, dual-type Pokémon add a tremendously greater depth to the strategy involved.  The difficulty is that because there are dual-type Pokémon, rather than there existing 17 distinct Pokémon types, there are in fact 289 different possibilities, which requires the analysis to be tremendously more extensive.  I have made an initial attempt to account for this variety, but my current computations are flawed.  From a defensive perspective, my table implicitly assumes that a dual-type Pokémon would be equally likely to use either of the attack types with which it is naturally most effective.  The reality is that a knowledgeable Trainer will choose the attack type that is most potent against the defending Pokémon's type set.  This means, for example, that a Charizard is not equally likely to employ both Wing Attack and Flamethrower against a Dialga; from a purely type-based perspective, the Charizard will use Flamethrower.

    From my offensive analysis, I assumed that a Pokémon will use attacks according to its strengths, meaning that a Charizard will use either a Fire- or Flying-type attack, which I believe is reasonable for the scope of this analysis.  Be that as it may, what I failed to account for in this instance was the interactions that occur between the two types of a dual-type Pokémon.  Therefore, what my offensive analysis implicitly assumed was that all Pokémon were single-type Pokémon, or at the very least, the average of the effects of a type of attack against two distinct single-type Pokémon was equivalent to the effectiveness of that type of attack against a Pokémon that had both of the defending types, which is not the case.

    Thus, all of this is still a work in progress, but I intuitively believe the results of my defensive analysis may work out to be fair approximations for the time being.  To that end, it might be interesting to note that Ghost/Steel is the most defensive type that is possible, according to my incomplete analysis, even though I am not certain there are any Pokémon with that type set.  Other highly defensive types include Steel/Flying (e.g. Skarmory), Steel/Dragon (e.g. Dialga), Steel/Water (uncertain if this exists), Steel (I think Mawile is of this type), and Ghost/Dark (e.g. Sableye).  Weak defensive types include Ice/Rock (uncertain if this exists), Bug/Grass (e.g. Parasect), Ice/Grass (e.g. Abomasnow), and Bug/Ice (uncertain if this exists).

    I know how to fix my offensive analysis from a mathematical perspective, but it is computationally tedious and my limited programming skills are probably not up to the task at this time.  I believe I can also work the defensive analysis to completion, but once again, determining how to instruct the computer to perform the calculations will be the primary challenge.  When I finish the type research, I am considering using a type modifier to adjust my stat power computations to account for the Pokémon's type strength.  I believe this may work well to achieve a more robust determination of a Pokémon's potential battle prowess.  Other factors such as the scope of moves a Pokémon can learn and a Pokémon's ability are far more difficult to quantify.

    I have shared this information in the hope that someone else might be able to benefit from it.  Questions, comments, and suggestions are welcome.  I'd be willing to share this data with anyone who was interested; perhaps I might even post some or all of it here depending on the practicality of doing so.

    And, if anyone sees a Dragonite named Estle, please let me know.

  • Wow, that's some research. Y'know there's a site called Bulbapedia, a Pokemon site that's COMPLETELY into this kinda stuff. Visit it sometime, it's pretty good.

    And I've never heard of an Estle. Sorry

  • I made some progress on the type research; my comprehensive offensive analysis is complete.  The top ten offensive type sets are as follows:

    1. Ice/Ground (e.g. Piloswine)
    2. Ground/Rock (e.g. Rhydon)
    3. Fire/Ground (e.g. Camerupt)
    4. Ground/Flying (e.g. Gligar)
    5. Rock/Fighting (no known species)
    6. Ice/Fighting (no known species)
    7. Ground/Fighting (no known species)
    8. Fighting/Flying (no known species)
    9. Bug/Ground (e.g. Nincada)
    10. Fire/Fighting (e.g. Infernape)

    It may be interesting to note why Piloswine's type set is so lethal; the only known Pokémon that is resistant to both Ice and Ground attacks is Surskit.  Every other known Pokémon can be hit for full, double, or quadruple damage by either an Ice or a Ground attack.  This doesn't mean that we should all go out and catch Piloswines for our parties though, as this is an offensive analysis only and the Ice/Ground combination doesn't fare so well defensively.

    The results for the low end of the spectrum are a bit less interesting; most of the single-types are included in the worst ten list because we expect that a Pokémon with one attack type to choose from rather than two is going to be less effective offensively.  The worst ten type set list is as follows:

    1. Poison (e.g. Arbok)
    2. Normal (e.g. Snorlax)
    3. Normal/Poison (no known species)
    4. Grass (e.g. Meganium)
    5. Electric (e.g. Raichu)
    6. Bug (e.g. Pinsir)
    7. Ghost (e.g. Banette)
    8. Psychic (e.g. Alakazam)
    9. Steel (e.g. Mawile)
    10. Dark (e.g. Absol)

    The reason Poison is so offensively deficient is that it is not quadruply effective against any type set at all and is doubly effective against only 12 of the 153 different possible type sets (the 289 different possible type set figure I mentioned earlier was inaccurate, as it counted set pairs such as Ground/Rock and Rock/Ground as distinct type sets when clearly they are the same type set).  Furthermore, the 17 type sets that include the Steel type are completely immune to Poison attacks.

    On a side note, I visited the Bulbapedia site.  There is indeed a wealth of valuable information there; I used some of it to make a calculator that determines how many balls on average a Trainer would have to throw to catch a given Pokémon.

  • The defensive type analysis is complete; the top ten defensive type sets are:

    1. Dark/Ghost (e.g. Sableye)
    2. Steel/Dragon (e.g. Dialga)
    3. Steel/Ghost (no known species)
    4. Steel/Flying (e.g. Skarmory)
    5. Normal/Ghost (no known species)
    6. Water/Steel (e.g. Empoleon)
    7. Steel (e.g. Mawile)
    8. Poison/Dark (e.g. Skuntank)
    9. Steel/Psychic (e.g. Bronzong)
    10. Water/Dragon (e.g. Kingdra)

    The Dark/Ghost type set has no weaknesses at all and it is completely immune to Normal, Fighting, and Psychic attacks, so it is not difficult to see why it is an excellent defensive type set.

    The ten worst defensive type sets are as follows:

    1. Ice/Rock (no known species)
    2. Bug/Grass (e.g. Parasect)
    3. Ground/Rock (e.g. Rhydon)
    4. Grass/Ice (e.g. Abomasnow)
    5. Bug/Ice (no known species)
    6. Grass/Psychic (e.g. Exeggutor)
    7. Fire/Rock (e.g. Magcargo)
    8. Grass/Dark (e.g. Cacturne)
    9. Dark/Rock (e.g. Tyranitar)
    10. Dark/Ice (e.g. Sneasel)

    Since there are currently no known Ice/Rock Pokémon, let's discuss the Bug/Grass type and what your poor Parasect has to hope he never faces.  Any Fire or Flying attacks will net quadruple damage while Bug, Ice, Poison, and Rock attacks will all do double damage; that is a plethora of weaknesses for one Pokémon to suffer with.

    Now that the offensive and defensive dissections are complete, I can present the best and worst type sets overall.  The worst ten type sets are as follows:

    1. Bug/Grass (e.g. Parasect)
    2. Grass (e.g. Meganium)
    3. Grass/Psychic (e.g. Exeggutor)
    4. Dark/Grass (e.g. Cacturne)
    5. Poison (e.g. Arbok)
    6. Grass/Dragon (no known species)
    7. Bug/Ice (no known species)
    8. Normal/Grass (no known species)
    9. Grass/Ice (e.g. Abomasnow)
    10. Ghost/Psychic (no known species)

    Notice how many times Grass appears on this list; this is largely due to the fact that Grass is one of the only two basic types to have as many as 5 weaknesses and there are 7 basic types that are resistant to Grass attacks while only 3 basic types are weak to it.  This generally makes most type sets that include Grass vulnerable to a lot of attacks and unable to launch effective Grass attacks in retaliation.  A Grass-type Pokémon's strength is generally in its Status moves such as Leech Seed and Sleep Powder, but it will frequently have a substantial type disadvantage to overcome.

    I have saved perhaps the most exciting list for last, namely the ten best all-around type sets:

    1. Dark/Fighting (no known species)
    2. Steel/Ground (e.g. Steelix)
    3. Fire/Ground (e.g. Camerupt)
    4. Ground/Flying (e.g. Gligar)
    5. Steel/Flying (e.g. Skarmory)
    6. Ghost/Fighting (no known species)
    7. Fighting/Psychic (e.g. Medicham)
    8. Ice/Ground (e.g. Piloswine)
    9. Electric/Fighting (no know species)
    10. Fighting/Steel (e.g. Lucario)

    The Steel/Ground type set is quite solid defensively, while it is also the only type set including Steel that is above average offensively.  Steelix enjoys immunity to both Electric- and Poison-type attacks while it has resistance to many other types.  Steelix's Attack may leave something to be desired, but it is fast and will often deliver its potent Earthquake before it can be assaulted in return.  It is noteworthy that if a Dark/Fighting Pokémon did exist, it would be weak only to Fighting-type attacks; immune to Psychic, one of the Fighting-type's greatest obstacles; and able to pummel Ghost-types without the use of Foresight as well as being capable of delivering devastating blows to a wide variety of other type sets.

    So, there you have it, the most comprehensive type breakdown I have seen to date.  I will eventually explore the possibility of utilizing a suitable method for combining a type factor with my stat power parameter in order to determine a Pokémon's battle facility based on its type set and stats combined.

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