Welcome to the Forum Archive!

Years of conversation fill a tonne of digital pages, and we've kept all of it accessible to browse or copy over. Whether you're looking for reveal articles for older champions, or the first time that Rammus rolled into an "OK" thread, or anything in between, you can find it here. When you're finished, check out Boards to join in the latest League of Legends discussions.


How to gain elo - the mathematical approach

Comment below rating threshold, click here to show it.

Father Tunde

Senior Member


From what I have seen there are three possible reasons why people play solo queue::
- To raise your elo.
- To practice to become a more skilled player.
- To play just to have fun.

If the first option applies to you, then this read is for you. This post is designed to explain what the absolute theoretical best strategy is to gain elo. If you adopt this strategy then you can raise your elo so high that the only limitations to your elo become your skill and the amount of games you play.
If you are only interested in the second option, then this post is still relevant because it is easier to improve your play at higher elo levels.

Some of you believe that you are below the elo you deserve. If this is your case then please read this post. It will describe exactly how to get to the elo you deserve.

Introduction (You don’t need to read this part if you are already sure you want to read the strategy. Only read this if you are trying to decide whether you are interested enough to to read the whole strategy or not. If you are already sure you want to read the whole strategy, just skip to the next chapter.)

I used to hate solo queue and love premade. Almost every solo queue game I got so incredibly frustrated I considered quitting LoL.
When I played my first 5v5 ranked premade with 4 friends on skype it was like heaven. No flame, no rage, everyone calls ss, the jungler comes to gank, the whole team comes when baron spawns, in teamfights focussing is brilliant, etc. Whereas in solo queue everything is disastrous.

But now I’ve changed. Now I love solo queue. And what has changed is that now I understand solo queue. I understand its shortcomings but also its beauty.
The thing about premade is that even though everything is smoother and seems to go better, you still depend on your team. Even if you play really well, you’re always stuck with the same team. In solo queue you still get to interact and play with other players but at the end of the day you get rated individually.
At first sight solo queue seems to have too much luck involved with it, destroying the whole individual rating idea, but after time I have learned to see through this luck. What I understand now is that Elo is a mathematical system, and to play a mathematical system, you need a mathematical approach, in order to eliminate the luck factor. And once you understand it, you will see it for the beauty that it really is.

You might have seen the movie 21. For those who haven’t, here is a short summary: A bunch of college math students work out a strategy to make money of the blackjack table in the casino. Instead of going to the casino to bet and hope the standard way, they use a system called ‘card counting’ to consistently win money from the house. They go to Vegas to apply this and are instantly successful. Hundreds of thousands of dollars start rolling in and very quickly they start living the good life. This is based on a true story of the MIT blackjack team. This happened in real life: people took what was supposed to be a gambling game and using maths they beat the system and turned it into an income.

This can be done in solo queue as well. Solo queue might seems like a gamble at first. People often call it the elo lottery: you just start a game, hope you have a good team, and if you do, you win, otherwise you lose. This is gambling. This is what you would do if you were to play a game of blackjack without card counting. And as we all know: if you gamble the house always wins. If the MIT blackjack team just went to the casino and gambled they would’ve never secured a penny. But instead of gambling they calculated, and they got rich. If you wouldn’t gamble in a casino out of fear of losing, why do it in League of Legends? Instead of gambling you can calculate, and then, just like in 21, you will start winning uncontrollably. We’ll go into detail later. But first, in case you’re still not convinced, let’s look at another example.

Moneyball is a movie about baseball. In baseball, new players for the team are normally scouted for and chosen by a huge group of experienced, trained professionals. But, in Moneyball, the manager of the Oakland Athletics does something revolutionary. He throws away this age old tradition of using instinct and experience to scout the best players and instead moves over to an entirely mathematical based approach. He looks at all the statistics of all the baseball players in the database and looks almost exclusively at their on-base percentage (which means how often they ‘score’-from my limited baseball knowledge). At first they go through a few hiccups while adjusting to the system, but eventually the team goes on to a new world record win streak of 20 in a row and soon after that the manager gets offered a job at the Boston Red Sox as the highest paid general manager in baseball history.

This, again, is based on a true story. And again, this applies to solo queue as well. Instead of relying on experience and instinct to determine whether you will win a game or not use a controlled mathematical approach to win and you will find your odds drastically improving.



In order to be able to understand this ideal strategy you will need a basic understanding of probability and in order to be able to apply this strategy you will need strong willpower and emotional control. If you think you have these two then read on.

Very well, let us begin.

Luck (everything that is outside your control) is a large factor in deciding the outcome of a game.

In a game of Summoner’s Rift there is you and then there are nine other players. Immediately it is quite obvious that the outcome of the game does not depend solely on you. From a mathematical perspective you are only one of ten variables and so what you do will only have a small impact on whether you win or lose. What the other nine players do will have a much greater effect on whether you win or lose. Most of what these other nine players do is out of your control and so luck will play a major factor in the outcome of any particular game.

But luck evens out

You see, you don’t just play one game, you play many. And over a large number of games, luck always evens out. What I mean by this is that you might have an afk on your team this game but a few games down the line the enemy team will have an afk too. For the slightly superstitious amongst you this might be hard to believe. But a good way of displaying this is using dice: Play against a friend. You each get a die. Every turn you each throw your die. The person who rolls the highest number wins that round. At the start, one of you might be rather lucky and end up winning the majority of the rounds. But if you keep playing for a long time I guarantee you that you will each end up with roughly the same amount of wins. Try this as many times as you want, this will happen every time. This is because the dice game is based solely on luck and luck always evens out. This is a basic law of probability. The same applies to solo queue, your luck WILL even out.

Though sometimes it is hard to notice this.

Take the afk example. If someone one your team leaves or goes afk for a few minutes, you will notice it immediately. It will annoy you, frustrate you, etc. But if the enemy team has an afk, you might not even notice until the announcement lady says they reconnected.

Say you die because of lag or high ping. Again, it will annoy you to the ends of days. But if it happens to an enemy, you might not realize it was lag and put it down to skill from your side.
There are many nuisances in solo queue such as dcs, afks, lags, freezes, flamers, etc. that kill you a little bit inside when it happens to you but you might barely notice if they happen to the opposing team. This could give you the illusion that you have more of these nuisances or ‘bad luck’ than others. So in order to accept that luck really evens out you have to remember to look at it objectively.

From now on we will assume luck always even outs (eventually).

I hope that you agree with me on this. The rest of the post only makes sense if you agree that luck always evens out. If you don’t believe this I still hope you’ll read on further but many of the concepts might not make sense to you.

Short-term elo, long-term elo and true elo

First, lets get some definitions out of the way. Not just for the sake of it, but because we need those definitions in order to understand the concepts that follow.

Short term-elo is the elo you get after you have only played a few games. This will mostly be determined by luck. For example: Say you are a really good player thats 2k+ elo on NA. You’ve just made a new lvl 30 account on EUW and have now started playing ranked. It is possible that due to sheer bad luck you lose your first three games (say it was 4v5, or 3v5 or something). This would put your current elo at around 1050. But clearly this is not where you belong because you are a much better player. This is your short-term elo. After you play many more games, your luck will start to even out, you will start to win loads and your elo will go up very fast.

Say after another 100 games you end up at 2k elo - the same you had on NA. This is your long-term elo. This is the elo you end up with after your luck has evened out. After how many games exactly your luck will even out is hard to say, just like how in the dice game you can’t precisely predict when you will each have an equal number of wins. All you can know is that the more games you play the higher your chance of your luck evening out and so the closer you will be to your long-term elo.

Your true elo is the elo where you belong, i.e. the elo at which your skill level is the same as all the other players at that elo. At that elo you should win half your games and lose half your games over a long period of time because you are no better and no worse than the rest at that elo. The only way you can raise your true elo is by becoming a more skilled player.
Sometimes, however, your long-term elo and your true elo are not the same. I.e.Your elo does not reflect your skill level. This could be because you never get your role. For example you could be a really good mid and top player but somehow always end up playing other roles.
Or it could be because you often get mad at your teammates and then start playing worse.
Or it could be because you always instalock your favourite champion and dont communicate with your team so they get really mad and play worse.
There are many possible reasons as to why your long-term elo is not as high as your true elo.

The purpose of this post, of this mathematical approach, is to get your long-term elo as high as possible. Up to your true elo, or even higher (this is possible, but we’ll get to that later). .

Control the things you can control, ignore the things you cant control

In a game there are two types of events that will affect the outcome of the game:
-Those within your control
- Those outside of your control.

Those outside of your control
Everything you cannot control falls under luck. You can't change these events and they do affect the outcome of your game. But that's ok, because luck will eventually even out anyway. So no worries, just ignore it and forget about it.
If luck evens out, then the only thing remaining which affects the outcome of the game is everything that you CAN control.

Those within your control
Anything you do will either have a positive effect (increase your chances of winning that game) or a negative effect (decrease your chances of winning the game).The amount of positive actions you do compared to the amount of negative actions you do will determine your general ‘chance of winning a game’. And this in turn will determine the long-term elo that you will end up at after playing loads of games. Of course it’s s not just the quantity of actions you take, but also their quality. Missing a last hit, for example, will only have a small negative effect, whereas making a good baron call will have a massive positive effect.

In short, the mathematical approach goes as follows: completely ignore everything you cannot control and for everything you can control do as many positive actions as you can and as few negative actions as you can. Now let us see how we apply this strategy, with some examples:

Examples of how to apply this:

A Gangplank on your team dies top in a 1v1 situation. First blood. Here you might start flaming him for being noob and feeding, and then lose focus and start playing worse. This attitude is obviously wrong.

Gangplank’s death was not your fault, it was due to bad luck, and so you should just ignore this tragedy and continue playing your best in your own lane. This seems like a good mentalilty at first. But the mathematical approach says this attitude is also wrong. You see, Gangplank’s death was not entirely out of your hands. There are some possible actions within your control that could have prevented Gp’s death.
For example: If you saw that he was losing his lane hard and getting low on health, if you were mid or jungler, you could have ganked him to help him out and prevent that death. Whoever you are, you could have seen that he was low, told him to play really safe and maybe he would have listened and then not died. Or maybe, in champ select, he was last pick and you forced him into that role, whereas if he played a role that he was better at, then he would have not died so easily.
Depending on the situation, some of these things that YOU could have done could have prevented his death and so increase your chances of winning. Of course you cant watch all four teammates all the time and tell them constantly what to do in chat as you have to watch your own champ as well. But my point is that at any time in the game, there are many things that you can do that can increase your chances of winning.

Example Noc

You are bot lane, and your Nocturne comes to gank. You manage to get a kill, but because you miss a skillshot you miss the second kill. Usually people think like this: this is a one for nothing exchange, so that was good. This attitude is WRONG. That kill you got purely because of Nocturnes amazing ganking (i.e. luck), not your own skill. But the second kill you missed because of your bad play. And so not getting that second kill was a negative action which reduces your chance of winning the game.

Example Amumu

The laning phase is over and you are all roaming the map in team. Your Amumu sees the enemy team and engages them. It turns out that was a bad engage that causes your team to lose the teamfight. The traditional approach might see it this way: You lost the game because of Amumu’s bad engage, there was nothing you could do about it, so just ignore it, it was bad luck.
But as in the previous example, the mathematical approach explains this is the wrong attitude, and again, there are many actions you could have taken to prevent this. You could have pinged back (the retreat ping) loads of times so he doesn’t engage, or just tell him in chat that he shouldn’t engage.
Of course, in order to do this you had to analyze the situation beforehand and then conclude that it would be bad to engage. Pretty much before every big fight, you should decide whether it would be good to fight or whether it would be a bad idea. If it’s a bad idea then tell your team not to do it. If you should engage, then tell your team to do so. One late game ace has such a massive effect on the outcome of the game that this is possibly the single most important skill in solo queue. Of course you can’t always be sure whether you should engage or retreat. And this is what separates the good from the bad players. And this is why the Elo system IS an indicator of skill. You see, in the Amumu example, a good player would ping back and make sure the team doesn’t engage there. A bad player would tell Amumu to engage and so lose the fight and consequently maybe lose the game.

But then there are also those who don’t say anything. When you do this; when you keep quiet while an important decision is being made, then you let other people in the team make the decisions for you, and so you are letting luck decide. If you are a bad player, or at least worse than average, then you would be better off letting your team make these decisions. Because if you get involved it is more likely that you have a negative impact than a positive impact. But if you are a good player, better than the average on your team, then it is important that you are involved in every decision, or at least in as many as possible. Because then you can turn a neutral action (not saying anything and letting your team decide) into a positive action (i.e. one that increases your chances of winning and so increases you long-term elo).

In solo queue, people often forget that you have some control over your teammates and so you actually have control over the entire game, not just your own champion.
The mathematical approach will not tell you whether to engage or not to engage. It will not make you more skilled. But it will make you more involved in the game so that if you are more skilled, this skill actually helps you win the game.

The game starts in champ select

Even during champ select, there are so many actions you can take that will increase or decrease your chances to win.
Before the game starts, you could look up every player on your team on lolking. Check their stats with the champion they selected. Then, overall, decide whether you have a good chance of winning this game or not. If it doesn’t look to good, just leave the queue. You used to lose 10 elo everytime you leave a ranked champ select. But because they removed this penalty, this now allows for many queue dodging strategies to increase your elo. You could for example dodge everytime you dont get your best champ, everytime you have a troll, or just everytime the enemy has a strong team comp etc.

The troll situation is an interesting example. Remember how luck evens out: If you have a troll this game that will make you lose the game then a few games down the line, the enemy team will have a troll that will make them lose as well. This scenario would make your wins to losses due to trolls 1-1. But if you leave the queue when you get that troll, then you can prevent that troll loss, making your overall wins to losses due to trolls: 1-0. And so, this way, you can use ‘luck’ to your advantage!
Remember that luck is only really luck if you have absolutely no control over it. As soon as you can have some influence on something you must make sure to use it to your advantage!
Of course leaving queues is really annoying as it means you have to wait and it takes forever for others to find a game. So, I would personally not advise that you dodge too much as it is really annoying for the rest of us.
But the mathematical approach is purely about gaining elo, and so it had to be mentioned, because dodging strategically can seriously reduce your losses and so significantly increase your long-term elo.
Another out-of-game trick is duo queuing. Of course you can go duo bot, or mid and jungler, to help the co-ordination in your team, which should increase your chances of winning. But you could also purposely only duo with people that are really good, and thereby increase your chances of winning.
While on the subject of duoing: remember that it is really bad to duo with a player who feeds. If your duo partner does really bad and loses the game for you then that is NOT out of your hands. That is not bad luck. You chose to duo with that friend and so you caused that loss.
Another thing worth remembering is this: if you duo with someone who is higher elo than you then you will gain more elo for winning and lose less elo for losing. So if you duo 10 games with someone of a higher elo and you lose 5 and win 5, then overall you would have gained elo.
Its the other way round for when you duo with a lower elo friend. So if you can duo with a higher elo person thats usually a good idea.
These are clear examples of how you can raise your long-term elo above your true elo. Duoing with a strong friend or looking up people on lolking wont actually make you a better player, but will still raise your elo.

How this differs from premade.

In a 5v5 premade, if an ally plays bad, you can't just ignore it, because you will be playing with them again and again. You have to tell them what to improve so your team can become better overall. Or if they are beyond hope you might have to consider kicking them from the team.
In solo queue you can't chose your teammates like that and the only way you can improve the teammates you get is by raising your elo. So the best thing to do is to apply the mathematical approach and focus on your individual play.
However, you must not play solo. It is a team game and so you must still play as a team. In solo queue you will be tested on your INDIVIDUAL ability to play as a TEAM.

When the mathematical approach does not apply

There are some cases where the game is already lost, or that the game is already won i.e. the outcome of the game is already determined, regardless of what you do. For example: Say all the enemy buildings are destroyed, their entire team has just died and half your team is hacking away at the enemy nexus. In that scenario you will win the game anyway. What you do no longer matters. Even if you do something really stupid like flash into the enemy fountain and die, you will still win the game. In this case, how well or bad you play wont alter your chances of winning anymore and so will not change your long term elo. No amount of negative actions could turn this game into a loss. In this scenario the mathematical approach does not help anymore.

So if a game is already won or already lost, according to the mathematical approach, it doesn’t matter what you do. This causes some players to troll or to stop caring when they think a game has been decided. I, however, would recommend against this. Here’s why: Most players are fairly bad at judging whether a game is a certain loss or a certain win. Even at higher elos I have seen 4v5 wins or massive comebacks (from having all inhibs down). Most games that look bad can still be won. Doing your best and being able to turn would-be losses into wins has a massive effect on your long-term elo. Additionally, having tried your absolutely best when the game was already lost will not cost you anything.
Secondly, if you slack off, and stop playing serious because of such a situation, then that attitude might carry over a bit to the next game and decrease your chances of winning there.
So imho, you should ALWAYS try hard.

A special note on elo hell

Be especially careful in the infamous ‘elo hell’. There is a range of Elo between 1200 and 1300 and probably a bit above and below where there are so many leavers, afks and trolls that skill is much less a factor in determining who wins than luck. Luck plays such a big role that sometimes you feel powerless to change the outcome of the game. Even if you play really well you could go on a losing streak. Because of this it might sometimes feel like the mathematical approach isn’t working. But it is exactly here that is is very important that you stay true to your approach and continually apply the mathematical approach. Otherwise you will never get out.

Stay consistently true to your approach

It is important to NEVER let your emotions take control and always 100% apply the right attitude. Say you lose 5 in a row due to sheer bad luck, but you applied the mathematical approach, then its not a problem, luck will eventually balance out, and you will get a 5 win streak later. BUT if you lose 5 in a row, and then get so upset and frustrated and stop believing in the mathematical approach that you start trolling or blaming your teammates, basically stop applying the mathematical approach, then you have lost it. Then you ****ed everything up, and the maths will work against you.
Its like in the movie 21, where one night they get upset and start drinking: they stop counting and just play on feeling. As Professor Micky Rosa says: “you’re not counting, you’re gambling”. Once you stop playing according to the mathematical approach you stop playing to gain elo and you start gambling at the elo casino.

When I first started applying this mathematical approach I actually lost 6 games in a row. 6 games in a row! I was extremely demotivated and was very tempted to throw my mathematical theory into the water, but I was sure it should work, because the logic was so sound, and so I persevered. Soon enough my bad luck ended, and since then I have only been gaining Elo. The only time I now lose Elo is when I let my emotions get the better of me and forget the mathematical approach for a second, or if I play when I’m tired, sick, or just playing bad for whatever reason.


In solo queue, over the long term, you are only judged on your individual ability. And so it is very important to act accordingly and only focus on the things that you do and how they affect your chances of winning.
Make sure that at all times you are doing everything you can to increase your chances of winning and as little as possible that decreases your chances of winning and just let the maths do the rest.


It is important to remember that there is a factor of randomness or luck involved in every game. This does not mean that the mathematical approach wont work if you have bad luck, all it means is that the mathematical approach is only guaranteed to work over the long term.

Even if you apply the mathematical approach perfectly you will not win every game. For a 2.7k elo player it might be fairly easy to carry 1400elo games. But say your true elo is 1500. If you are now at 1400elo, you might find it hard to make a significant difference. You won’t win every game until you reach 1500, or even win a large majority of the games. Instead you will win maybe 11 out of 20 games.

Please note that this technique will not instantly make you a more skilled player. I am not telling you what champ to pick, how to last hit, or when to do baron. All this technique will do is ensure if you are more skilled, then it will show. And so you are using the elo system to your advantage and not to your disadvantage. This means that over the long term you will gain elo and get closer to your true elo.

Now, since I’ve written a post on how to gain elo I’m sure the first thing many of you did was look me up and check out my elo. This is understandable. "Check your sources" my history teacher always told us. Now when you look me up, you’ll see I’m only 13xx elo. Not exactly the elo of someone you wanna take advice from you might say. You might want a decent explanation as to why I’m not 2.7k elo. The reason, very simply, is because I’m not good enough. The mathematical approach allows you to take your elo as high as your skill allows (and sometimes a bit higher). But my skill isn’t that of a 2k elo player, its that of a 13xx elo player. I actually used to be much lower for a long time. But this approach has allowed me to get to where I deserve. Another reason is because sometimes I don’t apply the mathematical approach perfectly. I do my best to keep calm and focus on winning the game, but sometimes even I can’t help it and the rage gets the better of me and I start flaming, or losing focus.

You don’t need to take my word for it though. I am not asking you to trust me on this. I hope that the mathematical approach speaks for itself and that if you understand the theory you will agree that this mathematical approach is the best and you dont need to take my word for it or check my elo.

Even if you agree that the mathematical theory is sound, understanding it is not enough, it takes a long time to develop the kind of restraint to apply it perfectly.

That concludes the end of my post.

Good luck with your future Elo endeavours.

May the maths be with you.

TL;DR: In solo queue the things you cannot control (luck) will always even out so they don’t matter. You should just ignore them and you should constantly focus on doing as many positive actions as possible to increase your chances of winning and as few negative actions as possible.

EDIT1: I meant 'mathematical' more in the sense of logical rather than to with numbers. 'Probability' approach' or 'logical' approach just didn't sound right ^^ I didn't mean to mislead.

EDIT2: You don't have to wait until your luck evens out to start seeing results. If you are far below your true elo then your superior skill will help you to start winning games already, even with bad luck. I did say that luck will eventually even out. However, it might not exactly even out. It is highly unlikely that your luck will have exactly evened out at any point during your LoL career. However, after a couple dozen games, it is very likely that it will have roughly evened out, and this is already good enough, because one or two wins more wont have a huge difference on your elo and your skill over those hundreds of games will have a much larger affect than that little bit of extra bad or good luck.

EDIT3: Of course retreat pings and instructions and stuff will only have an affect on winning if your teammates actually listened to those calls, which isn't always the case.

Comment below rating threshold, click here to show it.


Senior Member


TL;DR - try to play as well as you can, rebuke yourself when you make a bad play.

This genuinely is the only content of your post when you take out the personal anecdotes.

Comment below rating threshold, click here to show it.




Father Tunde:

You are bot lane, and your Nocturne comes to gank. You manage to get a kill, but because you miss a skillshot you miss the second kill. Usually people think like this: this is a one for nothing exchange, so that was good. This attitude is WRONG. That kill you got purely because of Nocturnes amazing ganking (i.e. luck), not your own skill. But the second kill you missed because of your bad play. And so not getting that second kill was a negative action which reduces your chance of winning the game.

Really good post especially this part, this is something most people miss when they're playing and think they did so good.

Comment below rating threshold, click here to show it.


Senior Member


I read the complete wall. I tended to play only 1 or 2 rankeds a day but I guess I will increase that amount now.
Good post, nice work.

Comment below rating threshold, click here to show it.


Senior Member


One of the only advice posts I'm giving a + too.

I'm a cynical ******* usually so be proud.

Comment below rating threshold, click here to show it.




Pure and simple..thread is wrong..
"And over a large number of games, luck always evens out. What I mean by this is that you might have an afk on your team this game but a few games down the line the enemy team will have an afk too."
Its not true, i get 3 somethimes even 3 afk in my team a day..enemy team does gets maybe one, or somethimes not even one..there are lines you just cant carry, you cant help them even if you gank that line for 5-6 times..those lines are allways in my team, they just keep feeding..thats my ranked exp..pure luck involved, which i lack..

Comment below rating threshold, click here to show it.


Senior Member


Pure and simple..thread is wrong..
"And over a large number of games, luck always evens out. What I mean by this is that you might have an afk on your team this game but a few games down the line the enemy team will have an afk too."
Its not true, i get 3 somethimes even 3 afk in my team a day..enemy team does gets maybe one, or somethimes not even one..there are lines you just cant carry, you cant help them even if you gank that line for 5-6 times..those lines are allways in my team, they just keep feeding..thats my ranked exp..pure luck involved, which i lack..

Well you didnt get it at all.
You are a victim of selective perception

Comment below rating threshold, click here to show it.

Rex Novus

Senior Member


Pure and simple..thread is wrong..
"And over a large number of games, luck always evens out. What I mean by this is that you might have an afk on your team this game but a few games down the line the enemy team will have an afk too."
Its not true, i get 3 somethimes even 3 afk in my team a day..enemy team does gets maybe one, or somethimes not even one..there are lines you just cant carry, you cant help them even if you gank that line for 5-6 times..those lines are allways in my team, they just keep feeding..thats my ranked exp..pure luck involved, which i lack..

What you lack is skill, not luck.

Comment below rating threshold, click here to show it.


Senior Member


Where's the math?

Comment below rating threshold, click here to show it.




So much text Oo.