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RBY The Option Value of Self-KO

Discussion in 'Analysis and Research' started by P5726, Dec 26, 2017.

  1. P5726

    P5726 Member

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    pt2017_10_19_21_08_39.jpg pt2017_11_14_08_29_43.jpg pt2017_11_21_14_12_12.jpg pt2017_12_18_15_29_26.jpg pt2017_11_21_14_10_48.jpg


    Background

    As an academic at an early stage of my career I have the tendency to be more theoretical than practical. However, I hope this may help me to contribute in a unique way. Today I wish to propose a view point known as "option value" and infer its relevance to the game. I imagine many players already hold the main precepts (perhaps subconsciously) and utilize them extensively in matches, yet I believe there is perhaps still value in formally developing and analyzing this concept.

    The theory of option valuation is widely applied in economics, finance and project management, which refers to the monetary value placed upon choices. In everyday example we observe that short-term contracts (e.g. for mobile phone deals) cost more than long-term contracts because by taking the long-term contract you lose the option of switching or terminating the contract at an earlier date and therefore must be compensated. This is an example where you pay more for the option of switching earlier. Note this is an option meaning a choice which does not have to be exercised. Should you have little or no intention of changing the contract then the option is probably worth little and it makes sense to commit to longer contract where it would be cheaper.

    Real estate economists observe the strange phenomenon that central urban locations are often used for low value activities such as car parking. The standard economic theory of opportunity cost could not explain such development since according to such theory prime central locations should be devoted to retail or office. The alternative theory of option valuation as applied to urban land usage was proposed in several influential journal articles (e.g. Titman, 1985; Quigg, 1993).

    Titman, S. (1985). Urban land prices under uncertainty. The American Economic Review, 75(3), 505-514.

    Quigg, L. (1993). Empirical testing of real option‐pricing models. The Journal of Finance, 48(2), 621-640.

    The basic idea is that by not immediately developing the land into retail/office, the owner of the land retains the option of developing the land at a later date, when land value may appreciate even higher. They lose this option the moment it is exercised. For this particular example, the value of the option would be influenced by the relative importance of the following:

    1. The benefit of immediately developing the land - the higher the current land price, the higher the opportunity cost of not immediately developing, and it is less attractive to wait.

    2. The potential to develop at a later date. This would be highly dependent on the belief of future land prices and trends. If house prices are believed to rise rapidly, the option to wait has large economic value and vice versa if the economic situation is bleak.

    It was argued that the economic value of the option of developing at a later date (i.e. the second aspect) was what caused urban land in prime locations to be devoted to seemingly economically suboptimal usage. This is true especially in speculative markets where current high prices fuel expectations for further increase.


    Application to RBY

    Now applying the above to pokemon RBY there are five major mons with self-KO powers - Exeggutor, Golem, Snorlax, Cloyster and Gengar. With the exception of perhaps Gengar which has a weak explosion without critical hit, all of these can be considered as the option to destroy (or at least severely damage, to the point where it would not be so difficult to revenge-kill) a pokemon of your choice at a time of your choosing.

    Applying the same principles the value of this option are governed by the relative importance of the following:

    1. The benefit of exploding on any given turn

    2. The prospect of exploding later in game.

    So on the first point - the benefit of explosion at any given turn is governed first of all by the likely damage. This is ranked in the following order - Snorlax, Golem, Cloyster and Exeggutor roughly tied, and Gengar (although crit hit rates should be considered). The higher the damage the larger the benefit. It should be pointed out here however that the actual difference between all the bombs as Ortheore rightly pointed out is not of major significance due to the relative ease of revenge kill, especially by Tauros. What really differentiates the benefits are two things:

    1. The target - if the targeted pokemon poses severe risk to your team then the benefit of its destruction is clearly higher.

    2. The opportunity cost of sacrificing a mon. Snorlax and Exeggutor are very valuable mons hence the OC of exploding are very high. The OC of Golem exploding would be highly influenced by the number of electrics (Jolteon/Zapdos) on the opposing team. The OC of Gengar and Cloyster exploding are relatively low, particularly the former after something has already been put to sleep.

    Onto the second point of exploding at a later time. It should be noted that during later stages of the game the potency of self-KO moves generally diminishes for the following reasons:

    1. The exploding mons are on low health, which means that the exact timing of explosion becomes more predictable - if you wait too late you may hit the hard shoulders of Goldon or Gengar's smoke. Perhaps you will get KO-ed by an unexpected critical hit thus unable to boom as planned

    2. Related to the above, as the game goes on there will be more useless mons around - asleep, frozen or heavily injured mons, which are perfectly content in taking the blast at little or no cost to its team

    3. The exploding mon is paralyzed, meaning you will be slower and perhaps killed before you have a chance to boom. Or more commonly perhaps full paralysis spoils the plan. However, this may be compensated by more opposing mons being paralyzed also.

    For the above reasons, the prospect of blowing up later in the game is normally negative - you want to boom as early as possible, subject to certain constraints. The execption to this is would be at the very early stages of the game where waiting for the opponent to reveal their team before deciding which mon to target has some value. Therefore, at any particular turn if the sum of the OC plus the option value (the cost of exploding) falls below the benefit of taking out a target, then you should should boom. As the game progresses, the OC generally declines when the mon's health is depleted, yet the negative option value becomes larger (more negative, i.e. more costly as you wait, meaning it may be more difficult to hit something useful).

    The control aspect

    For simplicity assume that the five mons are roughly equal in their ability to take out the target of your choice if you manage to explode on it. Clearly the 'if' hangs on the balance and determines how true the statement "self-KO = the ability to take out any pokemon at any time of your choice" is. Of course under no circumstance will this statement be completely true yet since it is a process you have some degree of control over, this degree of control will determine the degree of truth carried by this statement and thus the usefulness of self-KO in any particular situation. I believe the degree of control boils down fundamentally to three things:

    1. The state of the pokemon - unhealthy/paralyzed mons have less control of what to hit and when to hit it - often you just hope to hit "something" before being killed

    2. Speed - being able to go first is often vital in getting the explosion to hit at the mon of choice at the right time

    3. The alternative threats of the self-KO mon which must be addressed, which a) causes the exact timing of the explosion to be less predictable, and b) influences which mons are likely to switch/stay in to take the explosion.

    I believe part b) of the third point is the crucial point. Below is a table of the mons which are likely to switch/stay in for at least one turn verses the following five major self-KO mons.

    Pokemon explosion control.png

    1. Friendlymie (Psychic Starmie)
    2. Standard Mie (Blizzbolt Starmie)

    The above table can be used as a rough guide to which targets each of the self-KO mons are likely to succeed in hitting. The more frequently a mon stays in against a given self-KO mon, the more likely it is that it will be a potential target of that self-KO mon. I believe the usefulness of the realistic targets combined with the likelihood to take them out is the key component of the benefit of exploding on a particular turn. The opportunity cost will be the mon sacrificed during the explosion. Of course it must be realised that explosion doesn't harm Gengar and Goldon, and sometimes explosion would not be the best move against the mons shown e.g. Gengar should use tbolt instead of explosion on Starmie.

    It should be mentioned here that Starmie is a unique mon in the sense that it will be difficult to take out with explosion and/or revenge kill since it has access to recover, and outspeeds Tauros. A paralyzed Starmie will be much easier to take down however, though the value in doing so would not be as high.

    Analysis of each self-KO mon

    [​IMG]
    Gengar is high in control being a fast pokemon which is difficult to predict. It's able to quite easily hit a few important mons. However, the range of targets aren't that many, and hitting them often involve risks, especially Alakazam. Moreover Gengar's explosion is quite weak. Even though it's possible to supplement explosion by firing a few shots of nightshade/tbolt there is a trade-off in 'control' - during the process you may be KO-ed by crit hits, paralyzed, or that it gives the opponent a chance to put Reflect up. The big plus to Gengar's explosion is the low opportunity cost of blowing up at all stages of the game, especially once the sleep clause has been activated.

    [​IMG]
    Cloyster in my opinion is the most useful bomb in RBY. The table above shows that it has one of the largest number of potential targets, second only to Exeggutor and it's strong explosion power ensure that most of them can be taken out successfully or revenge-killed with little difficulty. Cloyster also outspeeds anything slower than Lapras which helps the control element. The most important feature is the relatively low opportunity cost of sacrificing it - if you blow up say Chansey or Alakazam then it's an advantageous trade. Cloyster is the closest thing to 'being able to take out any pokemon at any time of your choice' - it can be used as a bomb at any stage of the game with little or no strings attached.

    [​IMG]
    Exeggutor's explosion is almost as good as Cloyster's and the range of the targets they can feasibly hit overlaps quite a bit. Exeggutor also outspeeds Chansey, though not Lapras. What really lets down Exeggutor's explosion is the opportunity cost because Exeggutor is a very valuable pokemon - you need it to spread status and absorb Psychic. Both Exeggutor and Cloyster can quite easily take out Chansey and Alakazam when given the chance, but the later is by far the more 'cost-effective' way to do it.

    [​IMG]
    Powerful bomb, can potentially kill Starmie on full health. However, the low speed can be a problem, as it may allow Chansey the time to set up reflect. Also if the opponent posseses Zapdos, Golem is not free to explode due to the high opportunity cost.

    [​IMG]
    Some bonus for being the most powerful bomb in RBY in terms of raw power - can guarantee a kill on Starmie, and may even take out Tauros, Zapdos and Exeggutor on full health. However, because of it being a beast Snorlax will drive out many things and so it's range of targets are limited. Quite often it's just Snorlax blowing up on another Snorlax. Snorlax also ranks low on control being the slowest mon in the game, and having a high opportunity cost for blowing up.

     
    Last edited: Dec 28, 2017
  2. Ortheore

    Ortheore Leader

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    I just want to point out that the raw damage inflicted by explosion should be considered a minor criterion at best. This is due primarily to Tauros being around to revenge kill virtually anything- the only thing that complicates things is Starmie, since it's fast, has access to recovery and might not die from an explosion whereas something like Zam will. Even Gengar, which has a fairly pathetic explosion can compensate for this by outpacing most of its targets with Night Shade before blowing up, which compensates for its weakness a lot.

    Also it's worth considering the nature of the thing that's blocking you- being blocked by sleeping Zam is not the same as being blocked by GolDon, as sleeping Zam is imo more common and also leaving it in is a high risk play because it's an obvious opportunity for physical attackers

    I also want to point out that in the option value section you only really note that leaving it until later makes it more predictable, but there's more to controlling the target than that imo- how can a pokemon get around Gar/GolDon/Sleeping pokemon?
     
    Disaster Area and P5726 like this.
  3. P5726

    P5726 Member

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    Hi Ortheore, thanks very much for the comments and very well pointed out. All the points were spot on and I've incorporated them into the update. Some of my logics etc were flawed or ambiguous I corrected them. I think especially the concept of 'control' needs addressing and I believe a key part of it i.e. the target each self-ko mon is likely to hit are shown by the table. Would appreciate your thoughts on it, as the positions of things in the table are quite subjective based on my personal observation.
     

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