What's in a name? Names are important, if you ask me, as they lend meaning to pretty much everything. When I approached this game, I was struck by a few guiding points: it's a space-sim, the main character is referred to as "Adams," and no where on there did I find the jumpsuit-clad Samus (Evangelion spawned this thing for jumpsuits, you see). Regardless, it was pretty, there were ships turning into and out of robots, so I went ahead and hopped into it.
Going back to the names, Adams comes onto the fold as stuff really picks up. The storyline is that him and his nation or whatever are at war with the colonists (IN GLORIOUS 3D SPACE), and during his test to see if he's good enough to pilot, they're attacked in their own space by the colonists. The question is thrown around by how they've intercepted so close, but it isn't brought to the attention of the audience why they're called colonists, when we obviously hate them. Where did we go wrong?
Regardless, you kill them, save a freighter, and go on your lovely way.
I'd like to address my issues and concerns before I get into what I actually enjoy about the game, so I seem far less pessimistic.
For starters, comparing this to a space-sim is like comparing Ridge Racer to Gran Turismo. It's an arcade-game wrapped in a neat little bundle, and it does work, but it only works for so long before you start losing interest. The loss of interest stays because the weapon-unlocks are handled in the way to keep the player as far detached from their own customization as possible.
At the end of each mission, you're given points based off of how many things (and I say "things" because there's really no other class to set them in) you've destroyed, or at least got the assist on. Then, according to what seems like an absolutely arbitrary system, it just...rewards your performance with better gear that you can use retrofittedly or in future missions. To this point, I've unlocked three separate weapons, none of which are better than the gear you start out with. It makes me wish that there was an alternative that allowed us to use the points awarded to peruse the unlockables and pick our own, or at least gave us a point-amount until we get the next unlockable. I have very little incentive to actually focus on unlocking things because the new weapons so far provided are shorter range, far less damage, and aren't unlimited on ammunition.
The music is grating. Some people might like it, but I can't recall a crowd who'd really enjoy electric-sitars playing more groovalicious covers of EVE and Freespace. It might be that I've grown accustomed to very chill music while playing space-sims to emulate the feeling of weightlessness, and the songs in this game just so happen to make you feel very grounded.
To run down the controls really quick, you have accelerate as W, accelerate faster as shift, brake as S, and roll to the appropriate side with A and D. Unlike every space-sim you can think of, the obvious missing piece here is pitch, which, along with yaw, are all covered by the movement of the mouse. Yes. Your mouse covers yaw. It blew my mind. It feels like baby's first space-sim to me because of it, but then I realized what technical characteristics of a ship would actually allow it to achieve yaw, and suddenly, it all made sense. That being said, because of the inclusion of yaw in the game's mechanics, I've yet to figure out why roll is included, aside from people to yell, "DO A BARREL ROLL!"
To set the difficulty back even further, there really isn't much in way of having to dodge missiles (something that was ever-so-fun in Freespace); their tracking was a bit too tight and there wasn't any sort of way to track where the missile was coming from aside from paying enough attention to the beeps. Rather, what you did was wait until the beeps were screaming their asses off at you, then pressed Ctrl to send out an EMP and disrupt your signal. Woo.
The visuals, although originally very inspiring, fall off fast when you stare at the same static backdrop for about ten minutes, and notice that the explosions seem to be a nod at the games that it sought to emulate. The ship designs don't change, and the first ship is absolutely boring to look at. Every other ship's fine, but at the end of the day, I get tired of third-person just because my ship is so boring. It's not enough to break the game, but it is enough to mention it in a game review.
So, let's see, what did I critique? Visuals, music, gameplay, movement...that seems to about cover the elements, huh? So what DID I like about my experience with this game?
First up, I enjoyed how out-of-the-way (for the most part) the GUI was, even in first-person. It was very clean, with your ammo, shields and armor, and thrusters in various places along the top of the screen. It allowed the player to remain focused in the fight, even if every time you got hit, it looked like someone vomited destruction all over your screen (the destruction made you feel like you were in mortal danger until you noticed that THERE WAS NOT A DAMN THING HAPPENING TO YOU).
The pacing during battle was splendid: I was constantly trying to duck and weave, and the game even supplied cover for you to use if you're bad like me and kept crashing into surfaces to lower your shields. Of course, there were entire times where the game would tell you, "fly 10000 meters out, then 8000 meters again, then another 6000 meters before you can continue." I have no idea why it couldn't have been a cutscene, nor do I have any idea what they sought to accomplish; after that particular instance (beginning of the second stage, for anyone who cares), enemies warp in and attack you.
The story seems pretty generic, but the fact is, there's a story in a space-sim. Compared to the X-series and EVE, that's better than nothing, right? It's episodic, and there's no room for exploration, but each stage has a bonus requirement that will net you a passive-bonus, which is nice, if you're up to the challenge.
Overall, I'm hoping it gets better. The battle is exciting when not way too easy, and I'm sure that the weapons will be nicer once you get into the game, and I've yet to actually unlock the ability to turn into a giant mech with a shoulder-mounted laser-array (I'M HOLDING OUT FOR ZONE OF THE ENDERS), so I'm hoping that it gets much more exciting. I'll keep you guys posted.
Wednesday, January 23, 2013
Monday, January 7, 2013
A Meditation on Armor and Magic Resistance, or, "when are we ever going to use this?"
I'll start with some backstory, but if you'd rather not hear me rant about how much I hate non-math people, skip down to the bolded paragraph and keep reading.
So, college started back up for most of us today. My schedule's pretty math-intensive (senior math-major here), with (ahem) Introduction to Statistics, Introduction to Probability, and Linear Algebra (and a Shakespeare class, but whatever). If you're anything like me, when you hear, "probability," you're like, "there's no fucking way that there's a 4000-level class for probability." Evidently, there is. We start out studying Bernoulli's "Law of Large Numbers," and from there, I hear it goes batshit crazy.
As a math-major, there's nothing quite like hearing kids complain about their math courses. Today, I had the wonderful opportunity to talk to a sophomore Biochem-major who had just failed his Calculus I class last semester, who remarked that he'd "never need to use calculus in the future," and that he "doesn't know why [he] even has to take the stupid sequence (that's to say, Calculus I, II and III)." Now, as per usual, I immediately shot to my guns, and retorted, "probably when you'd never to find any sort of optimization of a system."
Later that day, I had a professor scoff at Calculus, saying that it's so utterly plebeian and Americans have a hard time with it because they're lazy and their society makes them even lazier. I couldn't find myself agreeing anymore, and it's kind of a funny aside, but he was my Calculus II professor--this big, fat Russian guy. Great guy.
So, when the shitfuck do we need Calculus? Most people just see it as this "scary topic" that they, thankfully, never have to touch. Others have to take it and absolutely hate it (methinks because they don't understand the beauty (be it in the concepts or the applications) of the math). Still, others, such as myself, find themselves absolutely enraptured in it.
Today's blog-post is the culmination of two lessons in one: first, I'll go over the concept of derivatives (a very basic topic in calculus), and then I'll go over how to apply it, by finding the efficiency of magic resistance and armor in League of Legends.
If we could take any graph of a function and throw a dart at it, where the dart ABSOLUTELY WITHOUT A DOUBT will land somewhere on the function, and then find the slope at that point, we have the derivative (which is to say, "the derivative on a point of a function is the slope at that point"). For instance, if we were to, say, take y=x^2 (which looks similar to a curved-at-the-bottom V) and find the slope of the line at x=0, then, it goes without saying that the slope will be 0. Now, the glory of this is that the actual x-derivative of y=x^2 is y'=2x, so the slope at x=1 will be 2. Go ahead and digest that really quickly. If you can't, it isn't the most important think you'll learn today.
Another example is the line, y=2x. Now, obviously, the function is in slope-intercept form: it's a line with slope 2, with the y-intercept at y=0. The derivative of this function is y=2, which is to say, regardless of where we put x (be it 0 or 1,000), the slope of the function will be 2. Make anymore sense?
So, let's talk the glory that is the application of this (aside from, you know, finding slopes, which is sort of a glory in itself).
The way that magic resist and armor works in League of Legends can be illustrated by two separate functions: y=100/(100+x), where y is the damage multiplier and x is the armor or magic resistance (they both work the same, so I'll just call it MR for the rest of the entry). So, essentially, If you have 20 MR, that means that you take damage at a factor of 100/120, or 5/6, so a 60 damage spell will only do 50 damage. If you have 100 MR, you take damage at a factor of 100/200, or 1/2, so a 60 damage spell will only do 30 damage. It's an important note that it isn't linear: if true damage would be 60 damage, and 20 MR would do 50 damage, then 120 MR would completely negate the damage IF MR was on a linear function (which is to say, the damage-reduction formula, y=100/(100+x), was a straight line with no curve).
Instead, however, the only way to get to 100% damage reduction is to get infinity MR. Yes, even at 10,000 MR, you'd still take damage (100/(100+10000) would equate out to ~.59 damage from a 60-damage spell, but that's STILL DAMAGE). This is known as an asymptote, because, mathematically (lest we're counting infinity), we can NEVER achieve immunity.
So, when does it become negligible to keep building MR? Conceptually, the more MR you get, the less of an effect it has. The different between getting hit with a 60-damage spell with 0 MR and 10 MR is ~6 damage, where the difference between getting hit with the same spell with 100 MR and 110 MR is ~1.5 damage.
We can find the rate at which MR will affect the damage we take by taking its derivative (which is a more complex process that I'll skip), which comes out to y' = -100/(100+x)^2. Here, we can take advantage of our human-curiosity by just plugging in numbers for x for the MR. At x=10, y' = ~-.00826, which means that the next MR will have, similarly, that much damage reduction (in which case, it does, with -~.00812). However, going closer to, say, 100 MR (x=100), y' = -.0025. 101 MR would equal -~.00248, which is significantly less than the difference between 10 and 11 (as we shown earlier). Because of this difference, it becomes much harder to see an established change when stacking past 100 MR. This equates out to you having to spend much more gold to see the same changes in damage-reduction after, say, 100 MR.
Stacking it, however, is more important whenever the other team begins to build magic penetration, because just as well as it stacks, it also comes apart. My favorite mpen item, and it has been for a long time, is the Void Staff, because of its 40% mpen property. What this entails is not +40% to THEIR magic penetration, but rather, their damage penetrates 40% of your magic resistance. If you have 100 MR, then, without a Void Staff, you'd only take 30 damage from a 60-damage spell, however, with one, you'd take 37.5 damage (albeit, seems silly, but when the enemy Anivia is doing 800 damage instead, that's a difference of 100 damage, not counting a difference in AP). In order for them to get 50% damage-reduction back, they'd have to get ~167 MR (which takes up more gold and another slot).
I want to go over the optimization-formula for damage between AP and mpen, but I'm just...so wiped out. SOME OTHER TIME.
So, college started back up for most of us today. My schedule's pretty math-intensive (senior math-major here), with (ahem) Introduction to Statistics, Introduction to Probability, and Linear Algebra (and a Shakespeare class, but whatever). If you're anything like me, when you hear, "probability," you're like, "there's no fucking way that there's a 4000-level class for probability." Evidently, there is. We start out studying Bernoulli's "Law of Large Numbers," and from there, I hear it goes batshit crazy.
As a math-major, there's nothing quite like hearing kids complain about their math courses. Today, I had the wonderful opportunity to talk to a sophomore Biochem-major who had just failed his Calculus I class last semester, who remarked that he'd "never need to use calculus in the future," and that he "doesn't know why [he] even has to take the stupid sequence (that's to say, Calculus I, II and III)." Now, as per usual, I immediately shot to my guns, and retorted, "probably when you'd never to find any sort of optimization of a system."
Later that day, I had a professor scoff at Calculus, saying that it's so utterly plebeian and Americans have a hard time with it because they're lazy and their society makes them even lazier. I couldn't find myself agreeing anymore, and it's kind of a funny aside, but he was my Calculus II professor--this big, fat Russian guy. Great guy.
So, when the shitfuck do we need Calculus? Most people just see it as this "scary topic" that they, thankfully, never have to touch. Others have to take it and absolutely hate it (methinks because they don't understand the beauty (be it in the concepts or the applications) of the math). Still, others, such as myself, find themselves absolutely enraptured in it.
Today's blog-post is the culmination of two lessons in one: first, I'll go over the concept of derivatives (a very basic topic in calculus), and then I'll go over how to apply it, by finding the efficiency of magic resistance and armor in League of Legends.
If we could take any graph of a function and throw a dart at it, where the dart ABSOLUTELY WITHOUT A DOUBT will land somewhere on the function, and then find the slope at that point, we have the derivative (which is to say, "the derivative on a point of a function is the slope at that point"). For instance, if we were to, say, take y=x^2 (which looks similar to a curved-at-the-bottom V) and find the slope of the line at x=0, then, it goes without saying that the slope will be 0. Now, the glory of this is that the actual x-derivative of y=x^2 is y'=2x, so the slope at x=1 will be 2. Go ahead and digest that really quickly. If you can't, it isn't the most important think you'll learn today.
Another example is the line, y=2x. Now, obviously, the function is in slope-intercept form: it's a line with slope 2, with the y-intercept at y=0. The derivative of this function is y=2, which is to say, regardless of where we put x (be it 0 or 1,000), the slope of the function will be 2. Make anymore sense?
So, let's talk the glory that is the application of this (aside from, you know, finding slopes, which is sort of a glory in itself).
The way that magic resist and armor works in League of Legends can be illustrated by two separate functions: y=100/(100+x), where y is the damage multiplier and x is the armor or magic resistance (they both work the same, so I'll just call it MR for the rest of the entry). So, essentially, If you have 20 MR, that means that you take damage at a factor of 100/120, or 5/6, so a 60 damage spell will only do 50 damage. If you have 100 MR, you take damage at a factor of 100/200, or 1/2, so a 60 damage spell will only do 30 damage. It's an important note that it isn't linear: if true damage would be 60 damage, and 20 MR would do 50 damage, then 120 MR would completely negate the damage IF MR was on a linear function (which is to say, the damage-reduction formula, y=100/(100+x), was a straight line with no curve).
Instead, however, the only way to get to 100% damage reduction is to get infinity MR. Yes, even at 10,000 MR, you'd still take damage (100/(100+10000) would equate out to ~.59 damage from a 60-damage spell, but that's STILL DAMAGE). This is known as an asymptote, because, mathematically (lest we're counting infinity), we can NEVER achieve immunity.
So, when does it become negligible to keep building MR? Conceptually, the more MR you get, the less of an effect it has. The different between getting hit with a 60-damage spell with 0 MR and 10 MR is ~6 damage, where the difference between getting hit with the same spell with 100 MR and 110 MR is ~1.5 damage.
We can find the rate at which MR will affect the damage we take by taking its derivative (which is a more complex process that I'll skip), which comes out to y' = -100/(100+x)^2. Here, we can take advantage of our human-curiosity by just plugging in numbers for x for the MR. At x=10, y' = ~-.00826, which means that the next MR will have, similarly, that much damage reduction (in which case, it does, with -~.00812). However, going closer to, say, 100 MR (x=100), y' = -.0025. 101 MR would equal -~.00248, which is significantly less than the difference between 10 and 11 (as we shown earlier). Because of this difference, it becomes much harder to see an established change when stacking past 100 MR. This equates out to you having to spend much more gold to see the same changes in damage-reduction after, say, 100 MR.
Stacking it, however, is more important whenever the other team begins to build magic penetration, because just as well as it stacks, it also comes apart. My favorite mpen item, and it has been for a long time, is the Void Staff, because of its 40% mpen property. What this entails is not +40% to THEIR magic penetration, but rather, their damage penetrates 40% of your magic resistance. If you have 100 MR, then, without a Void Staff, you'd only take 30 damage from a 60-damage spell, however, with one, you'd take 37.5 damage (albeit, seems silly, but when the enemy Anivia is doing 800 damage instead, that's a difference of 100 damage, not counting a difference in AP). In order for them to get 50% damage-reduction back, they'd have to get ~167 MR (which takes up more gold and another slot).
I want to go over the optimization-formula for damage between AP and mpen, but I'm just...so wiped out. SOME OTHER TIME.
Friday, January 4, 2013
Item Focus: Liandry's Torment
It's time for me to call to question the viability of this item on the grounds that it just doesn't seem that strong for the gold. Now, mind you, I don't actually KNOW the math behind this, but rather, this post is more of me calculating it out in a way that I hope you--the reader--will be able to understand and apply in future endeavors, if you so happen to get into mathcrafting in League of Legends.
First and foremost, let's examine the facts:
The logical step here would calculate the gold-worth of the passive by setting Liandry's AP:gold ratio to that of either (or both!), then calculating the total worth of the AP from the item, subtracting that from its cost over Haunting Guise, and that'll give us the "worth" of the passive (and its AP equivalent for the cost). If we take the Blasting Wand's ratio, we have 967.5 gold, so the remaining passive would cost 447.5 gold, or trade that with ~20.8 AP (for the other, it's 900 gold for the AP and 515 gold/~25.75 AP for the passive).
But what does that MEAN?! My dear readers, what this leads to is the question of if the passive is better than the AP that it'd provide otherwise, or if it's just more prudent to just buy something else after Haunting Guise (if you do decide to get it). Because of the several variables here (current health and magic resistances), we'll proceed empirically and expand out, hoping to find some pretty formula that we can make some snazzy general statements concerning the item. Asymptotes and such.
First, some assumptions.
First and foremost, let's examine the facts:
- Liandry's Torment
- Costs: Haunting Guise (Health Crystal (475), Amplifying Tome (435), recipe (575)), Amplifying Tome (435), recipe (980)
- Bases: +70 AP, +200 HP, +15 MPen
- Passive: Spell damage equal to 5% over 3 seconds of enemy's current health for single-target spells or 2.5% over 1.5 seconds otherwise (aoe, sustained damage, etc.). If movement is hindered in any way, it'll double the damage done.
- Note that this effect does not stack, so if you blow, say, 4 spells in 1 second, the total effect (if it ends in a single-target spell) will be 4 seconds, or 6 1/3% of their current health
- As this is spell-damage, it also factors in magic resistance
- Is not proc'd by the mastery, Spellsword, but it does proc Rylai's, which will apply the double-damage effect.
- Haunting Guise
- Costs: 1485 (1415 less than Liandry's Torment)
- Bases: +25 AP, +200 HP, +15 MPen
The logical step here would calculate the gold-worth of the passive by setting Liandry's AP:gold ratio to that of either (or both!), then calculating the total worth of the AP from the item, subtracting that from its cost over Haunting Guise, and that'll give us the "worth" of the passive (and its AP equivalent for the cost). If we take the Blasting Wand's ratio, we have 967.5 gold, so the remaining passive would cost 447.5 gold, or trade that with ~20.8 AP (for the other, it's 900 gold for the AP and 515 gold/~25.75 AP for the passive).
But what does that MEAN?! My dear readers, what this leads to is the question of if the passive is better than the AP that it'd provide otherwise, or if it's just more prudent to just buy something else after Haunting Guise (if you do decide to get it). Because of the several variables here (current health and magic resistances), we'll proceed empirically and expand out, hoping to find some pretty formula that we can make some snazzy general statements concerning the item. Asymptotes and such.
First, some assumptions.
- I feel like Annie is pretty much the most average champion in the game. Because of that, I use her kit to mathcraft to. If people have an issue with this, let me know and I'll do your champion next, I guess.
- We'll assume true damage. Magic resistance will alter the numbers, but it will just add effective health. If you really want to, you can alter the numbers, but I don't particularly see any reason to.
- The player's built a pro-as-fuck build: Liandry's first, questions later. In fact, very later: not only has (s)he bought it first, at the 50 minute mark, it's the only thing (s)he has. (S)He is level 18, though.
- Annie
- Q
- 245+.7*AP (single-target) => 245+.7*70 = 294
- W
- 280+.75*AP (aoe) => 280+.75*70 = 332.5
- E
- Irrelevant
- R
- 450+.75*AP (aoe), we'll ignore the consistent damage for the time being => 450+.75*70 = 502.5
So, let's say that you're against another Annie, with 15 MR (so true damage), with 3,000 health initially. The next picture will give you an idea of what I did and how by just plugging in the numbers into a spreadsheet:
The second column, mind you, is the current health after that instance's damage.
The damage from Liandry's alone did 203.23, the equivalent of ~92 AP (that's to say, it would do 203 damage if, instead of a Liandry's, you had an item that gave you 92 AP). Pretty substantial, because that's on top of the 70 base-AP given by the item, and effectively gave you a total of 162 AP. Alone, that means that you spent 17.9 gold per AP, which makes it more cost-efficient than a standard Rabadon's, who (alone) is at 21.33 gold per AP.
In order for a Needlessly Large Rod to be cost-efficient after the Haunting Guise, the current health at the start of this combo must be a little over 1900 (I'd say that I worked some voodoo math-magic, but really, I just kept plugging in numbers). It would do 99 damage from tick, which is the equivalent of 44.9 AP (with the +25 from Haunting Guise). Mind you, a NLD is 185 gold more than a Liandry's after Guise, and I guess, if you wanted me to, I could get really technical but by this point, my head is practically swimming from multiplication.
In conclusion, here's my final thoughts:
As with all AP items, you should really pick what you need: if you're doing fantastic, absolutely stomping everything and just wrecking shit and they're not building magic resistance and all that, there's less reason to build an expensive mpen item than to build something that'd more effectively increase your potential to continue to carry. Haunting Guise has always been one of those niche items; if your opponent in mid is building MR-boots, then Sorceror's Shoes are great. If they build a Chalice of Harmony for more MR, then, yes, build a Haunting Guise. However, don't feel obliged to build a Liandry's just because you have a Guise, especially early-game, where it just isn't cost-efficient. An alternative is to go Haunting Guise for the health and mpen, but switch over to a NLR because of its end-items being capable of being far more useful, then revisiting Liandry's if they get way too big. Because Rylai's procs it and the double-damage, people like Brand and Malzahar can definitely use it in some sort of Doran's opener (it's just one more step in the synergy).
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