Metroid series quantification
Posted: 2006-04-07 02:46am
You might want to get a snack, this is going to take a while.
It was mentioned in earlier threads that no one had really tried to quantify the technology used in the Metroid series. This is understandable, considering there is very little to go on. There are no technical manuals. There are no creatures whose response to attacks can be easily compared to any creatures we are familiar with. There are no weapons that can really be directly compared to any human weapon, no armor that can easily be compared to armor we have available. This all makes quantification very difficult. However, I am going to give it a shot nonetheless simply because the Metroid series seems to come up in vs. battles that don’t seem to go anywhere because no one can make any real comparisons. It is also a fun exercise since this is my first sci-fi tech quantification. I expect to make some mistakes, so be thorough when reading this. Please check the math in particular since that is the key to the analysis.
First I have to establish something to base my quantification on. There are currently 7 real Metroid games: Metroid, Metroid II, Super Metroid, Metroid Fusion, Metroid Zero Mission, Metroid Prime, and Metroid Prime 2. Of these, Prime and Prime 2 are 3D first-person games. This makes it very difficult to quantify them relative to the other series due to the perspective issue, lack of a uniform distance metric, inability to directly see Samus, splash damage issues, non-constant frame rate, and the fact that I don’t have either of these games handy at the moment. Additionally, the weapons in the Prime games are completely different than the weapons in any other Metroid game. Although some of the names may be similar, the weapon behavior is completely different. This would limit the applicability to the other Metroid games.
Metroid can be excluded right away because it is a rather low-resolution 8-bit game and only has a handful of the weapons. Samus is also pretty deformed relative to later incarnations. Additionally, Zero Mission supersedes Metroid in the story arc so Metroid is really redundant now. Metroid II is more similar in terms of the resolution and Samus’s proportions, but lacks most of the more powerful weapons present in later games.
This leaves Super Metroid, a 16-bit game, and Fusion and Zero Mission, 32-bit games. Fusion can be ruled out because Samus’s armor and several weapons had to be completely changed due to her X-parasite infection, all the enemies have been significantly modified due to X-parasite infection, and she never actually kills anything using her weapons (she simply causes the X-parasites to revert to their true form then she consumes them). In the end I think Super Metroid is the best option, for a variety of reasons. First, Samus has a much larger variety of weapons and abilities available to her in Super Metroid than in the Zero Mission. Second, I am far more intimately familiar with Super Metroid, having beaten it dozens of times. Third, I already have a relative quantification of weapon damage levels and enemy responses to weapons for Super Metroid. Fourth, the weapon I am using as a basis for this quantification, by some coincidence, happens to both be used by Samus and against her in this game, giving my a basis for quantifying both offensive and defensive abilities (more on this later). Finally, Super Metroid gives Samus the unique ability to activate and de-activate weapons and abilities as desired, allowing me to analyze weapons and abilities in isolation from one another and in locations or against enemies ideally suited for this analysis. No other Metroid game has this option. I should note that some things that can be expected to be constant will be used from other games (I will notify you when I do this). Also note I am not including the images I used for the analysis, but I can submit one or all of them if anyone requests it (although it may take a little time to get it into a form that is presentable).
It should be noted that overall weapon behavior among the 2D games is relatively consistent. It can probably be safely assumed that the quantifications of the weapons here can be applied to all the 2D Metroid games within a reasonable margin. The same could be said of defensive abilities if you exclude Fusion, where Samus does not have the same suit of armor as in the other games. The 3D Metroid games are another matter entirely. Defensive information is probably applicable, since it is known that Samus’s power suit from Zero Mission is the same as the one from Prime, and Prime 2 is very similar. Additionally, the normal power beam, charge beam, missiles, bombs, and power bombs in Prime and Prime 2 are likely at least similar to those in Super Metroid. However, comparison between the other weapons and abilities is futile since they bear no resemblance to the weapons and abilities from the 2D games.
Now that I have established that I am going to be basing this mostly on Super Metroid, the first and most basic thing is to establish a distance metric I can use to analyze lengths. This is central to all my other analyses. From the Metroid II instruction manual, Samus’s height is 1m 90cm = 6ft 2.8in and her weight is 90kg = 198.4 lb. It is unlikely that she grew or shrank significantly in the very short time between Metroid II and Super Metroid (Super Metroid takes place almost immediately after Metroid II). However, this is her outside of her Power Suit. In the games she is wearing a suit of armor that adds significantly to her height. By using an image from the Zero Mission ending animation, I was able to determine that her helmet added (23-20)/20=15% to the distance between her eye and the top of her head, including her hair (note that raw data from images is expressed in pixels in this analysis). An image from the Super Metroid official Nintendo Player’s Guide shows distance between her eye and the top of her head is 38/692=5.5% of her total height (taking into account the angle of her leg in the image). This would make the added height 0.055*0.15=0.83% of her total height. For a 1.9m height, adding 1cm for hair (1.91m, a rather insignificant change due to the size of the pixels in the game), this would be 1.91m*0.0083=1.58cm=0.624in. Using the picture from the Super Metroid manual, the soles of her shoes are 33/692=4.77% of her height total height, or 1.91m*0.0477=9.11cm=3.59in. So this would add approximately 6.4in to her total height in-game, making it about 1.91m+0.0156cm+0.911cm=2.017m=6ft 7.4in. Note that there are some minor perspective issues in the Super Metroid Player’s Guide image, but considering my precision is limited to the in-game pixel size I don’t think they will matter significantly.
Now, going by a screenshot from the game I can try to compare this height to her height in-game to get a size for each pixel in the game. This is complicated by the fact that Samus doesn’t stand up straight. She keeps her knees bent and her heels well off the ground. This requires using the Pythagorean theorem to get an actual height. The end result is Samus is (12^+11^2)^(1/2)+29=45 pixels tall, approximately. This would make each pixel 2.017m/45=4.48cm=1.76in. I will round to 1.75in/pixel=4.45cm/pixel for simplicity.
I mentioned before that I had found a weapon that I could use as a basis for quantification. Although it is not a perfect option, it is the best I have been able to find. The weapon is the super missile. For those not familiar with the series, the super missile is an unguided rocket weapon used primarily as an anti-armor weapon. It has limited ammunition, although Samus can get ammunition refills by killing enemies. What makes the super missile best suited for this role is that it is the only weapon that creates a noticeable, measurable effect that can be directly compared to something that is well-known on Earth. Upon detonation, the super missile generates a significant earthquake (or zebes-quake, technically) that shakes the entire room. Using the Richter scale I can determine the rough energy dissipated by the earthquake, and thus get a lower limit on the destructive power of the super missile.
The Richter scale is based on mean horizontal motion amplitude during the earthquake. In the case of the super missile, this is a 2 pixels or 3.5in=88.9mm displacement (the displacement is in mm for the Richter scale). The Richter magnitude is computed using the formula M=log(A)-log(A0)+d, where A is the amplitude of the measurement on a seismograph, A0 is the measurement of the seismograph amplitude in response to an magnitude 1 earthquake, and d is a fudge factor for the seismograph in question. Solving for 1=log(A0) we find that log(A0) should be 1, since d is not an issue because we are measuring actual ground movement at the epicenter so there is no distance and no seismograph to take into consideration. Another issue is that the seismographs do not measure actual movement, they are calibrated with a gain of 2800. So a real movement of 1mm would lead to a measurement of 2800mm. So this leaves us with M=log(2800*88.9)-1+0=4.40 earthquake. This is equivalent to the energy in 1.244 kilotons of TNT, or about the energy of a small fission bomb. With 50 available, this weapons gives her about 62 kilotons of destructive ability from this weapon alone.
Not all energy from the explosion would necessarily be converted directly into the earthquake, there are additionally forms of energy such as heat and radiation that may harm a target but not cause ground displacement, but it does put a lower limit on the energy coupled to a target. It should be noted that at most half the energy from the super missile could be coupled to the wall of the cavern you are in, since half of it radiates away from the wall. However, unless you are shooting it into an small, enclosed space (such as when you shoot the super missile into the mouths of the giant monsters Kraid and Crocomire), half the energy would be directed away from the target anyway so this would be likely give a pretty valid idea about the energy coupling to a target. Now some people might argue that there is no noticeable effect on the walls resulting from this blast. Keep in mind this is a 2D, 16-bit game. There is no mechanism in place for editing the room tiles in such a way to make such an effect obvious. There are inherent technological limitations in the presentation of the effect of this weapon. However, no matter what the case the energy dissipated by the room as a result of having a super missile detonate against it is in this range, so the energy must be there somehow. If you want to take it absolutely literally you could say that the rocks are just really tough, but the energy needed to cause the earthquake seen must be in the super missile in some form.
Another important factor to keep in mind is the blast radius of the super missile, or lack thereof. There is absolutely no splash damage from the super missile, even one pixel. That means the radius of the damaging part of the super missile explosion must be less than or equal to the radius of the missile itself. This radius is 3 pixels = 5.25in. There is a ball of light from the explosion that is several times that radius, but it does not cause any damage to even the weakest foes so it must be a relatively harmless side-effect of the real damage-causing mechanism.
As I mentioned earlier, the super missile is also unique in that it is the only one of yours weapons in the game that an enemy uses against you. Towards the end of the game you encounter a tall, humanoid mini-boss called Gold Torizo. If you fire a super missile at Gold Torizo, the creature will catch it in mid-air and throw it back at you, at which point it detonates in the normal manner. When you are hit by your own super missile you are dealt 50 units of damage. This is out of a maximum possible of 1400 units of energy plus 400 reserve units (1800 units total). So it would take 36 super missiles to destroy Samus. This also gives a measure of her damage resistance. Assuming a linear relationship between weapon yield and damage to Samus, we are talking about 24 tons of TNT per unit of energy or about 44 kilotons to kill Samus entirely.
The final factors regarding the super missile are its velocity and rate of fire. It travels 25 pixels = 43.75in in one frame. The frame rate of Super Metroid is fixed at 60 fps. This means the super missile has a velocity of 43.75in/(1/60s) = 150mph =240kph= 66.675m/s. So no where near as fast as a bullet but fast enough that it would be difficult or impossible to dodge at close range. There is also little warning of the firing, since the sound the super missile makes when fired is pretty quiet and there is no muzzle flash from the firing or flame from the sustainer motor. There is an intermittent smoke trail, but it dissipates after only a fraction of a second and is not particularly dense to begin with, with several feet between each small puff of smoke. The super missile can be fired at 180 rounds per minute, or about 224 kilotons per minute. Samus will go through her maximum supply of 50 super missiles in about 17 sec if she fires them as fast as she can.
If this analysis stands up to your scrutiny, it will give me a basis by which to gather information for the other weapons and technology found in the game. Based on Darth Wong’s recommendations, I think it would be logical to get feedback on these results before I begin applying them to other weapons and technology. That way I am not doing calculations that are flawed or irrelevant. Once you all are satisfied with these results I will begin analyzing the rest of the technology in the game. Hopefully I will be able to get enough detail that the results will be of use to the forum.
It was mentioned in earlier threads that no one had really tried to quantify the technology used in the Metroid series. This is understandable, considering there is very little to go on. There are no technical manuals. There are no creatures whose response to attacks can be easily compared to any creatures we are familiar with. There are no weapons that can really be directly compared to any human weapon, no armor that can easily be compared to armor we have available. This all makes quantification very difficult. However, I am going to give it a shot nonetheless simply because the Metroid series seems to come up in vs. battles that don’t seem to go anywhere because no one can make any real comparisons. It is also a fun exercise since this is my first sci-fi tech quantification. I expect to make some mistakes, so be thorough when reading this. Please check the math in particular since that is the key to the analysis.
First I have to establish something to base my quantification on. There are currently 7 real Metroid games: Metroid, Metroid II, Super Metroid, Metroid Fusion, Metroid Zero Mission, Metroid Prime, and Metroid Prime 2. Of these, Prime and Prime 2 are 3D first-person games. This makes it very difficult to quantify them relative to the other series due to the perspective issue, lack of a uniform distance metric, inability to directly see Samus, splash damage issues, non-constant frame rate, and the fact that I don’t have either of these games handy at the moment. Additionally, the weapons in the Prime games are completely different than the weapons in any other Metroid game. Although some of the names may be similar, the weapon behavior is completely different. This would limit the applicability to the other Metroid games.
Metroid can be excluded right away because it is a rather low-resolution 8-bit game and only has a handful of the weapons. Samus is also pretty deformed relative to later incarnations. Additionally, Zero Mission supersedes Metroid in the story arc so Metroid is really redundant now. Metroid II is more similar in terms of the resolution and Samus’s proportions, but lacks most of the more powerful weapons present in later games.
This leaves Super Metroid, a 16-bit game, and Fusion and Zero Mission, 32-bit games. Fusion can be ruled out because Samus’s armor and several weapons had to be completely changed due to her X-parasite infection, all the enemies have been significantly modified due to X-parasite infection, and she never actually kills anything using her weapons (she simply causes the X-parasites to revert to their true form then she consumes them). In the end I think Super Metroid is the best option, for a variety of reasons. First, Samus has a much larger variety of weapons and abilities available to her in Super Metroid than in the Zero Mission. Second, I am far more intimately familiar with Super Metroid, having beaten it dozens of times. Third, I already have a relative quantification of weapon damage levels and enemy responses to weapons for Super Metroid. Fourth, the weapon I am using as a basis for this quantification, by some coincidence, happens to both be used by Samus and against her in this game, giving my a basis for quantifying both offensive and defensive abilities (more on this later). Finally, Super Metroid gives Samus the unique ability to activate and de-activate weapons and abilities as desired, allowing me to analyze weapons and abilities in isolation from one another and in locations or against enemies ideally suited for this analysis. No other Metroid game has this option. I should note that some things that can be expected to be constant will be used from other games (I will notify you when I do this). Also note I am not including the images I used for the analysis, but I can submit one or all of them if anyone requests it (although it may take a little time to get it into a form that is presentable).
It should be noted that overall weapon behavior among the 2D games is relatively consistent. It can probably be safely assumed that the quantifications of the weapons here can be applied to all the 2D Metroid games within a reasonable margin. The same could be said of defensive abilities if you exclude Fusion, where Samus does not have the same suit of armor as in the other games. The 3D Metroid games are another matter entirely. Defensive information is probably applicable, since it is known that Samus’s power suit from Zero Mission is the same as the one from Prime, and Prime 2 is very similar. Additionally, the normal power beam, charge beam, missiles, bombs, and power bombs in Prime and Prime 2 are likely at least similar to those in Super Metroid. However, comparison between the other weapons and abilities is futile since they bear no resemblance to the weapons and abilities from the 2D games.
Now that I have established that I am going to be basing this mostly on Super Metroid, the first and most basic thing is to establish a distance metric I can use to analyze lengths. This is central to all my other analyses. From the Metroid II instruction manual, Samus’s height is 1m 90cm = 6ft 2.8in and her weight is 90kg = 198.4 lb. It is unlikely that she grew or shrank significantly in the very short time between Metroid II and Super Metroid (Super Metroid takes place almost immediately after Metroid II). However, this is her outside of her Power Suit. In the games she is wearing a suit of armor that adds significantly to her height. By using an image from the Zero Mission ending animation, I was able to determine that her helmet added (23-20)/20=15% to the distance between her eye and the top of her head, including her hair (note that raw data from images is expressed in pixels in this analysis). An image from the Super Metroid official Nintendo Player’s Guide shows distance between her eye and the top of her head is 38/692=5.5% of her total height (taking into account the angle of her leg in the image). This would make the added height 0.055*0.15=0.83% of her total height. For a 1.9m height, adding 1cm for hair (1.91m, a rather insignificant change due to the size of the pixels in the game), this would be 1.91m*0.0083=1.58cm=0.624in. Using the picture from the Super Metroid manual, the soles of her shoes are 33/692=4.77% of her height total height, or 1.91m*0.0477=9.11cm=3.59in. So this would add approximately 6.4in to her total height in-game, making it about 1.91m+0.0156cm+0.911cm=2.017m=6ft 7.4in. Note that there are some minor perspective issues in the Super Metroid Player’s Guide image, but considering my precision is limited to the in-game pixel size I don’t think they will matter significantly.
Now, going by a screenshot from the game I can try to compare this height to her height in-game to get a size for each pixel in the game. This is complicated by the fact that Samus doesn’t stand up straight. She keeps her knees bent and her heels well off the ground. This requires using the Pythagorean theorem to get an actual height. The end result is Samus is (12^+11^2)^(1/2)+29=45 pixels tall, approximately. This would make each pixel 2.017m/45=4.48cm=1.76in. I will round to 1.75in/pixel=4.45cm/pixel for simplicity.
I mentioned before that I had found a weapon that I could use as a basis for quantification. Although it is not a perfect option, it is the best I have been able to find. The weapon is the super missile. For those not familiar with the series, the super missile is an unguided rocket weapon used primarily as an anti-armor weapon. It has limited ammunition, although Samus can get ammunition refills by killing enemies. What makes the super missile best suited for this role is that it is the only weapon that creates a noticeable, measurable effect that can be directly compared to something that is well-known on Earth. Upon detonation, the super missile generates a significant earthquake (or zebes-quake, technically) that shakes the entire room. Using the Richter scale I can determine the rough energy dissipated by the earthquake, and thus get a lower limit on the destructive power of the super missile.
The Richter scale is based on mean horizontal motion amplitude during the earthquake. In the case of the super missile, this is a 2 pixels or 3.5in=88.9mm displacement (the displacement is in mm for the Richter scale). The Richter magnitude is computed using the formula M=log(A)-log(A0)+d, where A is the amplitude of the measurement on a seismograph, A0 is the measurement of the seismograph amplitude in response to an magnitude 1 earthquake, and d is a fudge factor for the seismograph in question. Solving for 1=log(A0) we find that log(A0) should be 1, since d is not an issue because we are measuring actual ground movement at the epicenter so there is no distance and no seismograph to take into consideration. Another issue is that the seismographs do not measure actual movement, they are calibrated with a gain of 2800. So a real movement of 1mm would lead to a measurement of 2800mm. So this leaves us with M=log(2800*88.9)-1+0=4.40 earthquake. This is equivalent to the energy in 1.244 kilotons of TNT, or about the energy of a small fission bomb. With 50 available, this weapons gives her about 62 kilotons of destructive ability from this weapon alone.
Not all energy from the explosion would necessarily be converted directly into the earthquake, there are additionally forms of energy such as heat and radiation that may harm a target but not cause ground displacement, but it does put a lower limit on the energy coupled to a target. It should be noted that at most half the energy from the super missile could be coupled to the wall of the cavern you are in, since half of it radiates away from the wall. However, unless you are shooting it into an small, enclosed space (such as when you shoot the super missile into the mouths of the giant monsters Kraid and Crocomire), half the energy would be directed away from the target anyway so this would be likely give a pretty valid idea about the energy coupling to a target. Now some people might argue that there is no noticeable effect on the walls resulting from this blast. Keep in mind this is a 2D, 16-bit game. There is no mechanism in place for editing the room tiles in such a way to make such an effect obvious. There are inherent technological limitations in the presentation of the effect of this weapon. However, no matter what the case the energy dissipated by the room as a result of having a super missile detonate against it is in this range, so the energy must be there somehow. If you want to take it absolutely literally you could say that the rocks are just really tough, but the energy needed to cause the earthquake seen must be in the super missile in some form.
Another important factor to keep in mind is the blast radius of the super missile, or lack thereof. There is absolutely no splash damage from the super missile, even one pixel. That means the radius of the damaging part of the super missile explosion must be less than or equal to the radius of the missile itself. This radius is 3 pixels = 5.25in. There is a ball of light from the explosion that is several times that radius, but it does not cause any damage to even the weakest foes so it must be a relatively harmless side-effect of the real damage-causing mechanism.
As I mentioned earlier, the super missile is also unique in that it is the only one of yours weapons in the game that an enemy uses against you. Towards the end of the game you encounter a tall, humanoid mini-boss called Gold Torizo. If you fire a super missile at Gold Torizo, the creature will catch it in mid-air and throw it back at you, at which point it detonates in the normal manner. When you are hit by your own super missile you are dealt 50 units of damage. This is out of a maximum possible of 1400 units of energy plus 400 reserve units (1800 units total). So it would take 36 super missiles to destroy Samus. This also gives a measure of her damage resistance. Assuming a linear relationship between weapon yield and damage to Samus, we are talking about 24 tons of TNT per unit of energy or about 44 kilotons to kill Samus entirely.
The final factors regarding the super missile are its velocity and rate of fire. It travels 25 pixels = 43.75in in one frame. The frame rate of Super Metroid is fixed at 60 fps. This means the super missile has a velocity of 43.75in/(1/60s) = 150mph =240kph= 66.675m/s. So no where near as fast as a bullet but fast enough that it would be difficult or impossible to dodge at close range. There is also little warning of the firing, since the sound the super missile makes when fired is pretty quiet and there is no muzzle flash from the firing or flame from the sustainer motor. There is an intermittent smoke trail, but it dissipates after only a fraction of a second and is not particularly dense to begin with, with several feet between each small puff of smoke. The super missile can be fired at 180 rounds per minute, or about 224 kilotons per minute. Samus will go through her maximum supply of 50 super missiles in about 17 sec if she fires them as fast as she can.
If this analysis stands up to your scrutiny, it will give me a basis by which to gather information for the other weapons and technology found in the game. Based on Darth Wong’s recommendations, I think it would be logical to get feedback on these results before I begin applying them to other weapons and technology. That way I am not doing calculations that are flawed or irrelevant. Once you all are satisfied with these results I will begin analyzing the rest of the technology in the game. Hopefully I will be able to get enough detail that the results will be of use to the forum.