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First, I'd like to introduce myself, what this guide is, and what this guide isn't.
My name is aBlindKitten, and I fancy myself a bit of a theorycrafter. My summoner's name is W7ngless, if you feel like griefing me in-game for whatever. In real life, I'm a Math and Physics double-major at a not-entirely-reputed university, and as such, I tend to think in a very math-oriented manner--numbers, systems, all that good stuff, it intrigues me. That has led me to make this guide, as there is a number of details to the League of Legends system that some of my friends don't recognize, so I figured I'd share.
This guide is meant not specifically for one champion or champion-type, but rather, mentioned as generalizations for most players. As you'll be able to tell by some of the later material, it's not for beginners to try and pick up the game initially, but rather, those who want to get better. I borrow much from my experiences with the ancient Chinese game of Go, which I'm familiar with, but by no means fantastic at, as well as some vector geometry, and a dab of Starcraft. I won't get too deep into any of it for the time being, but be warned: if you don't like to see things overthought, this guide probably isn't for you. :D
This guide isn't the end-all-be-all of LoL guides. It doesn't take the place of hours of practice, nor does it try; it shouldn't be lived-or-died by, nor should you take everything within it to heart. I'm not a professional, thus, it's up to you to what you take lightly and with a grain of salt. It will not go over build-orders, it won't show you the secret to Treasure Planet, it won't tell you my innermost opinions on champions and summoner spells or anything, and most importantly, it should be noted that this is more for my benefit moreso than anyone else's (however, I do believe that there is AT LEAST one person out there like me, so it'll benefit them, too!).
Without further ado, let's dive right in!
General Concepts of LoL - Snowballing
Obviously, if you're reading this guide, you know the idea behind League. Destroy turrets, kill enemies, get money, fuc--you get the idea.
One of the hardest parts of the game that I've found, especially for new players, is that they don't understand the seriousness of a single kill. In any given game, you start out with 475 gold, and have a set gold/second rate in which you accrue more, which is then compounded by minion kills, turret kills and champion kills, obviously.
So, let's say you're solo-laning against an Annie. She has her Amplifying Tome, she's laning you hard, driving you away from last-hits, keeping you at your turret, unable to do much besides /d. You finally get fed up, overextend, and she winds up killing you. Damn, try harder next time, right?
Oh wait, with that 400 gold that she just got from killing you, she bought another Amplifying Tome (hypothetically, of course).
Now, you're looking at an Annie who has twice her original AP (due to items) who has kept you out of your lane, and has grossly outlevelled you. Purveyors of economics probably have a word for this. I, personally, refer to it as the "snowballing" aspect of LoL.
You have to catch up somehow. Do you risk asking for help? Doing so would force her out of lane, but would leave another lane underhanded, and even more disadvantaged as you are solo-laning alone against Annie. Do you tough it out and try to do better? With her already more powerful than you, it'd be hard to accomplish successfully (should be noted that this is hypothetical--I'm exaggerating to make a point).
These questions remain answered only by the player (obviously), based solely upon how his or her judgment of the matter at hand proves. It should be noted that, handled incorrectly, Annie could continue to become more powerful, keeping you at bay, thus, costing you the game. All from that first kill.
This is the pressure of "first blood."
Go Concepts - Territory and Influence
The champions selected for the team in this build were selected for a reason: they're the typical champion who relies on movement domination more than others--Kassadin has Riftwalk to escape and gank, Katarina has Shunpo, Trist has her Rocket Jump, and Anivia and Lux have CC. In terms of escaping, this typically means that the goal of these skills are to place an obstacle between yourself and your enemy, be it a jungle-wall, a turret, minions, an slow-orby-thingy, or a wall of ice.
What about the other champions, though?
Before I get into hypotheticals, let's take a more in-depth look at Summoner's Rift.Top and bottom are both, for the most part, symmetrical (the "less parts" that they aren't will be covered later), and the middle lane is, obviously, in the middle. No ****, right? Now, let's take into consideration, influence.
"Influence," in Go, is typically conceptualized as where you have threat presence. In LoL, it could be seen as the range to which your champion could do damage to another champion. Typically, influence spawns from you extending from an area that's already under your control--or, your territory. In Go, the first moves you make is to try and make a bit of territory, then extend your influence into your opponent's territory, thus, trying to outplay them and take over their territory. That being said, in LoL, your territory is your turret, and your influence can be seen as your champion's skill-range and damage-output as opposed to the influence of your opponent (a level 18 Kassadin with 6 Deathcaps will have more influence than a level 1 Kassadin with 6 Sight Wards, but more on this later).
The fantastic thing about both of these games is the lack of requirement of luck, for the most part. The system that LoL has is typically bent solely around the skill and playstyle of the player itself moreso than trying to roll dice and see who does more damage. Everything can be calculated, and because of this, that level 1 Kassadin, if played with godlike precision, can still kill that level 18 Kassadin theoretically (Physics has taught me to realize the difference between "impossibility" and "statistically improbable"). The reason this is, is because "influence" does not equate out to "profit--" it's pliable, and can be undone, just as territory can be.
This (long) introduction leads into my point: There are ways to maximize your influence while minimizing your opponent's influence.
Taking a close look at top (for sake of ease, I'll be concluding that we spawn from bottom-left), we have a T-shaped intersection between the two turrets, with the brush and all that. Because of the brush, however, it allows us or our opponent to advance on our position without the other party being able to see them in most cases, meaning that, if one team pushes out past the middle of the lane, the other team can lie in wait in the brush and cut them off from their turret, thus, minimizing their ability to make it back to their territory, and cutting off their influence. After the gank, the gankers have free-realm to go about extending their influence almost freely, and possibly taking over the other territory.
To tie in vector-geometry, let's say that you're some champion, and you extend along the wall to the brush. To your right, about 5 paces out, there's an enemy champion. He starts heading 45 degrees southwest, cutting off your ability to make it to the turret. In Go, this could be seen as what's known as a cut, and, if he so plays it right, could destroy your influence.
That's not to say that you couldn't make it back--implying that you're both moving the same speed, and you're only attacking using melee attacks, the Pythagorean Theorem would show that you have a shorter distance to travel. However, if he does move in to intercept you, and you react conversely by moving southeast at about 30-degrees, he'd be between you and your turret, extremely close to your territory and your influence, thus, making his influence VERY small, and he's in quite a bind, as you can push him downwards into your turret (****ing Trist). That's all assumption, though. Just something to get you thinking like a math-geek.
Mid has a larger issue--the introduction of influence can come from three ways. To combat this, with the right angle, you can ensure that you can cover distance without allowing the opponents to get within range to debilitate you. I've seen many a person run straight back, allowing me to close the gap and deal the damage I need to deal, without realizing that, in ideal settings, they could've easily escaped to their territory. Here comes the math!
Assuming your opponents were trying to set up a gank and your allies were incompetent and didn't realize the mia. You're pushing mid, you're about halfway through the lane, and your opponent's about 10% out from his turret, when suddenly, another opponent comes from the top lane, about 50% as well. For simplicity's sake, I'm ignoring collision with the walls that contain the mid-lane's brush. He comes running at approximately 45-degrees southeast, while the turreting opponent comes 45-degrees southwest. As you run backwards, if you were to run 45-degrees southwest as well, the top opponent would turn with you, and, whereas he wouldn't be able to catch you assuming ideal conditions (no skills, same movement speed), had he been a more mobile champion, he would be more able to catch you. To counteract this, a bit of math that I'm too tired to do would show that, if you were to sharpen the angle between south and your movement vector to (I'd approximate without actually doing any math) 20-degrees west of south, you'd not only keep a fair distance from both, but had the top-opponent been just tagging along, pathfinding to you, he'd be at risk of being in-range of your turret. If only gameplay was as empirical as math, huh?
More General Concepts - Openings
A lot of newer players I see will push out before minions spawn, or before their partners, get there, in hopes of scoring a kill before they dip back to safety. I recall a forum thread about this, how, to counteract such play, the opposing team would grab a clairvoyance, place it at golem, then lie in waiting along the brush on the inside of the joint on top or bottom. This allowed them to make sure that the other team wouldn't all be grouped around golem waiting for it to spawn, and if they weren't, there'd be a chance that one or two of the opponents would push out, looking for trouble, to find two champions in the brush already, and a cc-champion waiting to stun them. Such an opening, I'd imagine, would require a great amount of communication, but, as any Zerg player would attest to, is a great method of map control on such small amounts of resources. Also, something to think about: what the hell is your mid-laner doing before the match starts, anyway? Important thing to take into consideration: the mid-laner shouldn't give away his position, so it's important to pay attention which side the brush is on--have the mid-laner go through the jungle into that small patch on YOUR side, as to not give sight to the enemy where he is.
Conversely, another method I see a lot is a cc-champion in the brush, and a dps-champion outside of it, both advancing, with the dps-champion close enough that the cc-champion can stun enemies within his range. It's general human nature to see something they want, get greedy, and chase it down--in this nature, if the other two champions are lying in wait on the other side of the brush, they come out, attempt to gank, get stunned, and during that time, can get counter-ganked before they can do anything to prevent it. Off the top of my head, one of the best teams I can think of for this would be, say, Lux and Yi, with Lux going her stun before her slow. Mmm, Ignite.
In a pro-match, one of the more common openings is a group of three (usually the two from the lane closest and the mid-laner) focusing down the golem buff. If you've never seen it, I can't think of any examples of it, but clairvoyance on a support character would be fantastic to use here to ensure that, if they go for it, send your entire team to gank the three, steal golem, then spread out to your lanes. Just make sure whoever needs it, takes it! :D Conversely, ******** NO ONE I've played with has ever started a match out with getting mid to help them with golem.
Starcraft General Concepts - Map Awareness
Let's talk Starcraft really quick.
In Starcraft, Zerg has to know when it's safe to expand, when to make units, when it's safe to make workers, etc. The map also affects this, as you can have an expansion right by your main base, allowing for an easier time defending it than, say, across the map in some ninja-corner.
Just like in Starcraft, in League of Legends, it's important to have awareness of your surroundings. A close inspection of the map will show that the bottom lane is extremely close to Dragon, while the top is extremely close to Baron. Early- to mid-game, Baron's too hard to get anyway, whereas Dragon can be solo'd. It may not be best, but strive to keep strong laning partners down there, just in case you feel like they're trying to pull some sneaky ****.
More close inspection of the map will show that, for the blue team, blue will spawn top, while red spawns bottom. As red is typically a more physical-buff, try to keep the characters who need it, down there, with the characters who need blue buff up top (vice-versa for the purple team).
Beyond placement of units, though, it should also be mentioned that awareness of what's going on elsewhere is also a big deal, moreso for characters like Twisted Fate or Soraka, who can affect various parts of the field. Who just failed a gank?, who has low health?, who needs Wish, and who needs whatever Karthus' ult is called? Who just ducked into the bushes and can Flash out for a gank? Mia-calls are an obvious map-awareness tool, and it is an integral one, but it should also be mentioned that, if you see someone in trouble and you can assist in some way that'd turn the tides in your favor, sure, there are reasons not to, but don't rule it out. Just saying, Lux's ult can shoot REALLY ****ING FAR
I've played with a guy who typically mids, who would call mias for other lanes, along with the players from the other lane. Such a practice not only allowed others to know that he was paying attention (meta-game confidence boost?) but also that, even if they missed the call, he'd be ready. Let it be known that not everyone is expected to do this (OH GOD 5 MIA CALLS FOR ONE CHAMPION) but it's another exaggeration to make a point--you have limited vision over the entire map. Make the best of it.