Formalizing the word "Advantage" (Warning: Abstract thinking ahead)

[Dragontamer]

One of the sucesses of Smogon IMO is the widespread formal definition of "counter". It is precise, and it is a very noteworthy concept to think about during team-building as well as during gameplay. Furthermore, the definition fits to the colliquial use, so even those who do not know the formal definition can have an idea of what a counter is.

I wish to build upon this tradition and formalize other ideas in the Pokemon game. I hope that this new definition can promote a deeper understanding of various teams and tactics...

Note: I don't think think that many definitions are needed to have a deep understanding of pokemon. Indeed, we can go very far with only the word "counter". So lets not have a sudden influx of definitions ehh?

Definition: Advantage
The probability of you winning on a given turn.

Definition: Starting Advantage
The probability of you winning based on information only in the first turn.

Definition: Advantage Gain
Any turn where you have a higher probability of winning than the previous turn.

Definition: Advantage Loss
Any turn where you opponent has an advantage gain, you have an advantage loss.

That are all the definitions I wish to propose. I hope that they are precise enough for Smogon.

Anyway, with these definitions, there are a good amount of implications here. First off, I explicitly mention probability. While you may lose a match because your 6x Dragon Danced Gyarados missed as he used Waterfall against a Froslass in the hail... you definitly held the advantage over the opponent.

Second, I defined everything based on the probability of winning. For example, if Gyarados has 5 dragon dances, it is unlikely that the 6th dragon dance will actually offer an advantage. That is, if you have a 100% chance of winning after 5 dragon dances, then the 6th dragon dance offers no advantage.

I should note that while it is theoretically possible to calculate the probability of winning, it is difficult to do so. So the concept of the advantage will remain abstract, as I doubt that we can ever calculate the actual numerical value of the advantage on any given turn, except in the most simple cases.

Also, note the duality of Advantage Loss vs Advantage Gain. If your opponent Dragon Dances, that is an advantage loss to you. If you rapid spin, that is an advantage gain to you. This appears to unfortunately contradict with the colloquial definition of advantage... but maybe not :-/

I feel that every good tactic can be described in these terms. For example, Stealth Rocks increases the probability that your pokemon can OHKO another pokemon, thus it increases the probability of winning. Stall teams can be described as simply having a simple and easily attainable advantage gain each turn. Sweeps can be described as having a total advantage, that is a 100% chance of winning, and obviously many teams would like to have that.

Just some thoughts. Night everyone!

 

[Deck Knight]

I submit that first you must formalize a definition of "winning" in this context.

For instance, I have a Magmortar out against Hippowdon. Most sets would be unable to do much to the Hippo, leaing him an advantage to Stealth Rock. However, were this LO Overheat weilding Magmar, the advantage goes to Magmortar.

If Hippowdon stays in, Magmortar "wins" the round, but could easily lose the game.

In such a case both players have achieved a strategic goal. Hippowdon's was to start Sandstorm, a wonderful unblockable starting advantage to have. Magmortar's job was to blow Hippowdon to kingdom come before it could SR. Had the set been inadequate to achieve that result Hippowdon would have attained two goals by likely setting up Stealth Rock.

However, Overheat lowers Magmortar's chance of winning if say, Gyarados then comes in and uses its one turn advantage to set up Dragon Dance. (75% is still a hefty price to pay though if they call your bluff and use Tbolt.)

 

[Dragontamer]

Win as in wins the game. As in, if you have a 1HP Scarf Weavile using Ice Punch against a 1HP Scarf Garchomp in a Sandstorm, you have a 80% chance of winning, and your opponent has a 20% chance of winning. (20% due to the chance of missing Garchomp)

Abstract, yeah, I know >_>

EDIT: In your Magmotar vs Hippowdon case, it is difficult to know who truely has the advantage. However, if it is late in the game, Hippowdon gained very little advantage. Stealth Rocks is a big advantage in the early game, but not so much in the late game. (Lets say the extreme case where Magmotar is the last pokemon alive, stealth rocks gave no advantage to the Hippowdon team)

 

[Deck Knight]

Win as in wins the game. As in, if you have a 1HP Scarf Weavile using Ice Punch against a 1HP Scarf Garchomp in a Sandstorm, you have a 80% chance of winning, and your opponent has a 20% chance of winning. (20% due to the chance of missing Garchomp)

Abstract, yeah, I know >_>

In your Magmotar vs Hippowdon case, it is difficult to know who truely has the advantage. Needless to say however, if it is late in the game, Hippowdon gained very little advantage. Stealth Rocks is a big advantage in the early game, but not so much in the late game.

The problem with taking such a micro-level calculation to the macro-level is the fact that skill and prediction is far more important than raw numbers. Making such calculations with 6 pokemon on each side is nearly impossible.

 

[Aeroblacktyl]

Um, I personally think you guys are putting too much thought into this. Sure it's nice to know what you're doing, but sometimes it's just better to play the game as a whole instead of a turn 1 by 1. You never know what could happen!!

 

[Dragontamer]

The problem with taking such a micro-level calculation to the macro-level is the fact that skill and prediction is far more important than raw numbers. Making such calculations with 6 pokemon on each side is nearly impossible.

Yes, I understand it is impossible. (well... probably O(2^n)... which is possible... with 10,000 years of computation...) However, I do not propose that we actually do these calculations. Instead, we hold the concept in our mind while thinking about team building and during gameplay execution.

EDIT: I should say this. These ideas are the primitives that we can build upon. Just as sets are the primitives to build mathematics upon, we need to have something at the bottom before we can start building up theories about whether one kind of team is good or not.

I have a feeling that these primitive can eventually be generalized to "counter", and possibly every other interesting aspect in the game-world of Pokemon. That is to say, before we can discuss strategy, we must build and understand some primitive representation of Pokemon

 

[StarmanXL]

Starting Advantage seems like it could be misleading...I mean, even after the first turn, each player is more than likely not going to know all the moves, spreads, items, and pokemon the other has. I mean, say you set up SR the first turn, but in that same turn the opponent sets something up, like a Nasty Plot or something. Who has the greater advantage? What if they pack a Rapid Spinner or something? Am I interpreting this wrong?

 

[majesty]

Advantage should have some inherant linking to probability of switching. For example:

If I see a Salamence, I bring out my Choice band mamoswine. This isn't necessarily a safe switch in, therefore it isn't necessarily a counter. However, once in, if the Mamoswine still stands there is a high probability that the opponent will switch since they don't want to take an ice shard in the mouth.

This would put you at an advantage immediately, having a high probability of a switch or otherwise predictable move by the opponent. For, if they try to get cute and fire blast with their mence, they will take the ice shard and can say goodbye to the salamence before it can touch the mamoswine. If they do the SMART thing, switch in a counter or the best counter they have at the time. This allows you to retain said advantage by unexpectedly switching to something else...for example, you could predict they'll bring in skarmory or a physical wall, so you could bring out a special wall...or you could just go for broke and smash the incoming pokemon with as free hit.

EITHER WAY your switch of mamoswine into salamence, which isn't a counter because mamo in no way is a for sure safe switch, has earned you an advantage in both the turn and potentially the match, if you either smash the salamence, dent heavily the incoming pokemon or outpredict with your own special sweeper.

keep in mind my example is just an example, but it is to illustrate my point. Also note that this example is based primarily around the notion of them switching and your reaction to it. If you react wrong, there is no advantage gain (unless they opponent gets lucky) and things return presumably to neutral.

 

[PypeHype]

I think Starting Advantage means that you are at an advantage within the information of the first round.

EX: You use nasty plot on the first turn while they use stealth rock, assume you can take out that pokemon. You have the advantage in this situation. You could very well sweep his team if he doesn't have a counter to your pokemon's set.

Starting Advantage doesn't (and can't) determine the remainder of the match. I think it shows who could win at that particular moment.

 

[StarmanXL]

I think Starting Advantage means that you are at an advantage within the information of the first round.

EX: You use nasty plot on the first turn while they use stealth rock, assume you can take out that pokemon. You have the advantage in this situation. You could very well sweep his team if he doesn't have a counter to your pokemon's set.

Starting Advantage doesn't (and can't) determine the remainder of the match. I think it shows who could win at that particular moment.

But if the opponent has a Focus Sash, you could go down the next turn when you attack. In that example, even though it seemed like you were gonna win, there was still unknown information (their having a focus sash) which was actually giving them the advantage.

Which makes me wonder, how can you recognize an advantage, and how can you use it to your benefit? I mean, one player could have the advantage, but it looks like they are at a disadvantage, so the other player could believe they have the advantage and get owned. And what if you don't have the advantage but your opponent doesn't know that? Isn't bluffing a good part of the game?

Advantage and stuff seems good, but it looks like it's real effectiveness comes in retrospect and not in the actual battle when information isn't readily available at a given time.

 

[Mekkah]

majesty,

The probability of you winning on a given turn.

You put a Mamoswine example. Mamoswine does indeed not counter Salamence, but it does hold an advantage over Salamence. Because it wins in all cases except when it switches in and gets KOed. Salamence is at a disadvantage because it cannot win. The next step is that Salamence switches out, but that is already beyond the area of where "advantage" went.

Definition: Advantage Gain
Any turn where you have a higher probability of winning than the previous turn.

Definition: Advantage Loss
Any turn where you opponent has an advantage gain, you have an advantage loss.

I'm going to bring in another practical case, despite the abstract nature. Swords Dancing Garchomp leads versus Stealth Rock, Ice Fangless Hippowdon. Hippowdon sets up Stealth Rock while Garchomp Swords Dances, for whatever reason they do so. Both would now have an advantage gain AND an advantage loss. Twice. Hippowdon's chances have been increased by Stealth Rock, then decreased by enemy Swords Dance. Garchomp's chances have been increased by Swords Dance, then decreased by Stealth Rock (though not really in this one on one case since it hasn't taken Stealth Rock damage). But they can't be both advantaged or disadvantaged. At least, the way it is now.

So, let's widen it a little bit. I think it should be something like "Any turn where the sum of the benefits of your advantages and disadvantages is lower than the opponent's is a advantage loss" and of course the opposite as well.

 

[Portugeez]

You should do a warstory using what advantage you thought you had (in that future battle) and maybe invite you opponent to say what the advantage is through the battle or at the warstory moment.

Sorry if I sound confusing.

 

[PypeHype]

But if the opponent has a Focus Sash, you could go down the next turn when you attack. In that example, even though it seemed like you were gonna win, there was still unknown information (their having a focus sash) which was actually giving them the advantage.

Which makes me wonder, how can you recognize an advantage, and how can you use it to your benefit? I mean, one player could have the advantage, but it looks like they are at a disadvantage, so the other player could believe they have the advantage and get owned. And what if you don't have the advantage but your opponent doesn't know that? Isn't bluffing a good part of the game?

Advantage and stuff seems good, but it looks like it's real effectiveness comes in retrospect and not in the actual battle when information isn't readily available at a given time.

Starting advantage is you have a higher chance of winning that the opponent, and is based on the the information you have. There are ton of things that could stop a nasty plot, but your opponent might not be able to stop it. You can never truly know if you have the advantage unless you know everything about the opponents team. We can only assume advantages based on your current information. I agree with you that these "advantages" don't really help you during the game.

 

[Mekkah]

Abstractly looking, you could just say "ok, all these possibilities exist, these possibilities are standard while these are novel or uncommon, therefore my chances look like this". Your opponent is likely facing the same dilemma anyway, too.

 

[Basics]

Attempting to formalize the definition of advantage is a little bit silly, as there are many different kinds of advantages in any game.

Take Chess, in the Danish Gambit Accepted Opening, White sacrifices not one, but two Pawns in return for an advantage in piece development. Black clearly has the material advantage (long-term, generally giving black a favourable end-game), but White has a positional advantage (short term, makes it very difficult for Black to safely develop pieces without falling into the countless traps this opening is famous for). Ultimately, it comes down to how each player uses this advantage, and converts it into a won game.

Although Pokemon is nowhere near as positionally deep or intricate, there are still many different kinds of strategical advantage. Maybe I sacrificed my Blissey (giving you a long-term advantage of "material") for the ability to safely bring in my SpecsMence against your team, and give me a good chance of decimating you completely (giving me a short-term, tactical advantage). Who truly has the advantage? It's hard to say.

 

[Bam]

I wrote up something that was somewhat similar to this on another forum to help explain the basics of battling to the less experience battlers there, but I used a number line instead of just saying that Player A has the advantage over Player B.

Pretend that there is an advantage scale in competitive battling. It looks like a horizontal number line, somewhat like this:

<<-5<-4<-3<-2<-1<0>1>2>3>4>5>>

You and your opponent's teams decide where each of you start on the line. If you lead with a Metagross, and your opponent leads with a Swampert, then you are at the disadvantage, because your only STAB attack on it is not very effective and Swampert can hit you with a STAB SE Earthquake. Thus, your starting position on that line is (theoretically) -1. Similarly, if your positions are reversed, then you (theoretically) start at 1. If you both have a Swampert out, or a similar situation, like a Forretress and Skarmory lead, then you both start at 0 (some may consider Hippowdon to have the advantage because its ability benefits the rest of its team members).

I took into account the rest of the game, though, instead of just going at a turn-by-turn basis:

Advantage should have some inherant linking to probability of switching. For example:

If I see a Salamence, I bring out my Choice band mamoswine. This isn't necessarily a safe switch in, therefore it isn't necessarily a counter. However, once in, if the Mamoswine still stands there is a high probability that the opponent will switch since they don't want to take an ice shard in the mouth.

This would put you at an advantage immediately, having a high probability of a switch or otherwise predictable move by the opponent. For, if they try to get cute and fire blast with their mence, they will take the ice shard and can say goodbye to the salamence before it can touch the mamoswine. If they do the SMART thing, switch in a counter or the best counter they have at the time. This allows you to retain said advantage by unexpectedly switching to something else...for example, you could predict they'll bring in skarmory or a physical wall, so you could bring out a special wall...or you could just go for broke and smash the incoming pokemon with as free hit.

EITHER WAY your switch of mamoswine into salamence, which isn't a counter because mamo in no way is a for sure safe switch, has earned you an advantage in both the turn and potentially the match, if you either smash the salamence, dent heavily the incoming pokemon or outpredict with your own special sweeper.

keep in mind my example is just an example, but it is to illustrate my point. Also note that this example is based primarily around the notion of them switching and your reaction to it. If you react wrong, there is no advantage gain (unless they opponent gets lucky) and things return presumably to neutral.

This is just a turn-by-turn example. Concerning the whole game, switching in Mamoswine and possibly being KOd is giving yourself a disadvantage. If you survive, you've accomplished nothing other than to make the opponent switch and bring down your Mamoswine's HP by a considerable ammount. By saying that your opponent may switch to something like a Skarmory, and that you can switch to something like Scarf Heatran, the fact that your opponent may call your bluff and hit hard whatever you switch in is not mentioned. Of course, that's where prediction is the main factor instead of just making a good choice of a switch in, and that's out of the realm of this discussion.

 

[majesty]

majesty,



You put a Mamoswine example. Mamoswine does indeed not counter Salamence, but it does hold an advantage over Salamence. Because it wins in all cases except when it switches in and gets KOed. Salamence is at a disadvantage because it cannot win. The next step is that Salamence switches out, but that is already beyond the area of where "advantage" went.

So, let's widen it a little bit. I think it should be something like "Any turn where the sum of the benefits of your advantages and disadvantages is lower than the opponent's is a advantage loss" and of course the opposite as well.

Mekkah: The reason I cited it in this case was because it provided a clear example of a simple advantage while at the same time not being a counter. I definately like how you expanded it and then defined it. Heh, at the time of writing I was running on 45 minutes of sleep and 5:45 of sleep over the last few days. I'm just surprised I made some sense!

 

[Dragontamer]

Attempting to formalize the definition of advantage is a little bit silly, as there are many different kinds of advantages in any game.

This is the common-use "advantage". The definition I offer here does not specify different kinds of advantages, nor does it need to. It is unfortunate that "advantage" has so many meanings (as you noted, material and so forth), which is why I attempt to formalize it into a single true definition.

The only thing as far as this topic is concerned... an advantage is the probability of winning on a given turn. That is all. Period. Yes, the attack pattern of you and your opponent must be taken into account, as well as the information avaliable to you and not avaliable to you, but it is a clear definition that can theoretically be calculated by a computer.

If I were to compare myself to say, the development of Logic... these definitions that I hope to settle in this topic are the most primitive form of formalized thinking. Much like ancient greeks and propositional logic. Maybe eventually a more powerful system of thought will be developed, but we have to start somewhere.

I'm going to bring in another practical case, despite the abstract nature. Swords Dancing Garchomp leads versus Stealth Rock, Ice Fangless Hippowdon. Hippowdon sets up Stealth Rock while Garchomp Swords Dances, for whatever reason they do so. Both would now have an advantage gain AND an advantage loss. Twice. Hippowdon's chances have been increased by Stealth Rock, then decreased by enemy Swords Dance. Garchomp's chances have been increased by Swords Dance, then decreased by Stealth Rock (though not really in this one on one case since it hasn't taken Stealth Rock damage). But they can't be both advantaged or disadvantaged. At least, the way it is now.

To make it a better example, lets assume Hippowdon doesn't have Roar >_>

So, let's widen it a little bit. I think it should be something like "Any turn where the sum of the benefits of your advantages and disadvantages is lower than the opponent's is a advantage loss" and of course the opposite as well.

Ah yes, but I did think of that already :-p You can note that the concept of "disadvantage" was not defined, only advantages.

You gain an advantage only when your move makes your probability of winning higher now than previously. In the case of stealth rocks vs swords dance, it would depend on how early it is in the match and stuff like that, but assuming all 6 pokemon still are alive, then the Stealth Rocks most likely will have a bigger advantage.

Thus, we would say the Stealth Rocks user has a bigger advantage than the swords dancer. Why? Because if it is early in the match, you don't know the opponent's team, and the opponent's team can easily contain a phazer / counter to Garchomp, or a Weavile. Stealth Rocks offers an advantage even if the opponent has a rapid spinner, as you can always switch to your ghost, or lay them down again.

You should do a warstory using what advantage you thought you had (in that future battle) and maybe invite you opponent to say what the advantage is through the battle or at the warstory moment.

Sorry if I sound confusing.

First, I'd like to understand the concept of the advantage, toss it around a bit, and maybe improve it :-) Thus, the point of this topic.

 

[obi]

Well, I think there is another piece to this.

First, there is the absolute advantage. If both players are of roughly equal skill, the player with the absolute advantage is the one that, all things about the players' teams considered, has the advantage.

Then there is the theoretical advantage. This differs from the above because it doesn't factor in everything, only what one player knows. Both sides have their own theoretical advantages, because neither player usually knows everything about the opposing team.

It is possible for both sides to believe they have won the advantage, but this is only based on their limited knowledge. For instance, if I explode my Gengar and OHKO your Togekiss, you may think "Oh, good, because my team doesn't have a reliable Gengar counter", and I may think, "Ah, now he has no more Ground resists, so I can start sweeping with CB Rhyperior."

 

[X-Act]

In my opinion, since Pokemon is not a complete-information game (unlike, say, chess), it's hard to know who has the advantage until both players reveal their entire team, together with its movesets and EV spreads.

 

[sa17dk]

So what exactly would be the point of formalizing the term advantage? To be more specific, when would you use the word "advantage" so that a formal term would be needed?

 

[Spaniard]

Advantage is something mental, it can't be expressed as a number nor can be exactly explained.

Also the battle is not won adding turns that benefit you (also because sometimes you can't say whether a certain turn was good for you). You win the battle as a whole, and this is a game about intuition, deceiving and strategy planning, where you don't have all the information and can use traits that you don't really have. As an example, i could switch my zapdos against your swampert and pretend that i have hp grass.

But as pokemon strategy and reasoning is lineal, I think that it isn't difficult to understand what advantage is, and that's what counts.