Is the Elo rating system accurate?

Is the Elo system rating accurate?

Given an absence of inspiration and interesting topics to talk about, I thought that for today's article it would be nice to revisit every whiner's favorite topic: Elo Hell!  No matter what skill rating you're at, you will find that you are still in what players call 'Elo Hell' due to dependence on your team's collective effort to win, rather than being able to singlehandedly influence the outcome of a game.  Today's post will look at Elo Hell as a statistical whole, rather than looking at an individual's contribution to winning.  We'll be investigating what it takes to fall into Elo Hell, the chances of winning a given game, and why you should stop whining about feeders and trolls.

How does the Elo rating system actually work?

We've heard a lot of talk about the Elo and what it suggests, but I'm sure many of you readers are uninformed as to how it actually works.  The Elo system originated as a simplistic method to compare the relative skill between different chess players, and is used today in dozens of games.  While there are more complex ways to compute the chances of winning a given game, the Elo system is prized because it is both simple and accurate.  Assuming that Riot's Elo system accurately reflects upon the Elo system used in chess, the chance that your team will win is:

 Percentage of winning a given game = 1 ÷ [1 + 10^(ΔElo/400)]

...And your chances of winning a game given your true skill rating are as follows:


But VVinrar, only people with a Ph.D. in Elo Hell Studies can read that table!  Help!

Luckily for you, "Elo Hell Studies" is a degree that only pretentious theorycrafters use as a joke.  It's not that hard to read at all!  The row variable is the difference between your true rating and the enemy team's average true rating, while the column variable is the difference between the rest of your team and the enemy team.  For example, if the average rating of the enemy team is 1200, your true Elo is 1300 (+100), and the average Elo of the rest of your team is 1225 (+25), then your team should statistically have a 57.1% chance of winning the game.

What does this suggest?  Even if you are more skilled than your enemy and you win your lane, you are still at the mercy of 9 other players, and in the grand scheme of things you have only slightly increased than chances of your team to win.  Conversely, if your entire team is dramatically less skilled than the enemy team, you have a much lower chance of winning.  If your team is an average of 400 true Elo lower than the enemy team, you have approximately a 9.9% chance of winning a given game.

If it wasn't already obvious, this implies that if your team's Elo is higher than the enemy team, you have a better-than-average chance of winning a game against them.

Elo Hell and You

But VVinrar... I used to be be 1400 and now I'm 1100, and it's all because of the trolls!

This may be true, but you have to remember, Riot's matchmaking system involves thousands of players who are at your exact skill level, and millions of players in its entire database.  Your Elo may not be precise for yourself as a player, but on a statistical whole, most players are exactly where they should be.  The system is very accurate, but it also has a pretty wide standard deviation (~200) which makes it hard to pinpoint player skill, especially for any given game where they are playing a role or champion that overstates/understates their predicted skill level.  There are trolls on each team, and I highly doubt your rating is low because of a few factors.  Remember, in all of the games you have ever lost, there has only been one common factor.

Using binomial probability, if you play 20 games where you are consistently 100 Elo higher than every other player in the game, you have approximately a 16% chance of dropping 12 games or more against your enemies.  Over the long term, this may average out and you will rise back to your true Elo; however, with a small sample size, you are basically at the whim of the matchmaking gods.  Especially if you have inconsistent play, it may take several dozen games to reach your true Elo; however, if you reached the triple digit mark of games, you've likely found your true skill level.  I hate to be the person who breaks the big news to you, but if you've been at a certain skill level for a few hundred games, you might actually belong there.

Common Complaints (Warning: Numbers)

But VVinrar, I fell 300 whole Elo.  It must be the trolls!

Believe it or not, a lot of players can luck into their top Elo.  For a fresh player jumping into ranked, you only need to go 6-4 to achieve a rating of 1300.  If you're a true 1100 Elo player, you have a 29% chance of getting 6 or more wins in your first 10 games against 1200 players, a 22% chance of getting 6+ wins against 1300 players, and a 15.6% chance of winning 6+ times against 1400 players.  Combine these numbers together, and what do you get?

The average 1100 player has a 6.4% chance of reaching 1400 and a 1% chance of hitting gold.

Well, these are the same 6.4% of players who are complaining about falling 300 Elo.  This means that in any given 1100 Elo game, there is a 10% chance that at least one out of the ten players has been at 1500 at one point and a 48% chance that at least one player has been at 1400.  And then guess who are the players complaining about the trolls? "Unlucky" bastards.

Note: Going 6-4 will only gain you 90 Elo instead of 100, but pretending it gets you 100 Elo is more convenient for these calculations. Also, these are approximate values only;  my math skills are too sucky for continuous calculations. 

Final Thoughts

Remember, no matter how good you are at League of Legends, you still have a chance of losing a game because of your teammates; however, if your own personal skill level should be enough to influence the odds of winning towards your favor if you are good enough, especially if you bring a 1-2 punch of a viable champion and solid gameplay.  If you don't win many games right away, don't be afraid!  The law of large numbers is on your side: eventually, you'll get back to your true skill level regardless of the feeders and trolls.  From a statistical perspective, you are only one player in a game controlled by dozens of internal and external factors, and you can't always singlehandedly determine the outcome of a game.  Given enough time, your rating should accurately reflect your true skill, but you need to give the system enough games to get you there.

TL;DR: The Elo system is accurate, but it has very high variance.  Don't worry about your Elo.  If you are actually below your true skill rating after a few games, you'll get there sooner or later.  If you've played more than a hundred games and you're still below your true Elo, you should introduce yourself to my friends Dunning and Kruger.

Quote from VVinrar

I hope you enjoyed reading today's post! I have a special request for the readers today: I would really appreciate it if you could take the simple time to visit and read my interview with Forbes @ If the article has a 'successful' amount of views, the author will publish the second part of my interview (which is much more interesting than this one) and it means a lot to me both personally and professionally if this happens.

For more of my work:

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  • #84 Cerbereth

    My take away from this is that "Elo hell doesn't exist" is inaccurate, and should be "elo hell ceases to be a factor once one plays over a 100 games." The problem is there is no way to make that slogan catchy I guess.

  • #85 ranigad

    Elo hell doesn't exist, period. Most people think of elo hell as an elo range (oftentimes the one they're currently in) where they cannot rise as a direct result of poor play from other individuals. They claim that because of bad play from their teammates, it is impossible to gain elo. This is statistically inaccurate. 

    Sometimes, even after over 100 games, you'll be at a low elo. The idea of "elo hell" would still exist with individuals who are stuck are lower elos but believe themselves to be deserving of higher ones despite the fact that they may be at their true elo already. They will do what I stated above and constantly blame teammates for their inability to move up. Elo hell is, in my opinion, more psychological than anything. It is a state of mind where one refuses to believe that one own's lack of ability is preventing oneself from gaining elo. 

    In fact, my friend who's a platinum player claims that anything below 1800 is elo hell. -shrugs-

  • #86 Cerbereth

    I like your Raichu icon. Anyway the way it was explained to me is let's say everyone on your team contributes 2 units to winning the game, because they are 2.0 players. Your better than them though and your a 2.2 player. So the matchup ends up being 10.2 vs 10.  Having the extra .2 definently makes a difference, but the difference is so small that in many games it will have little effect, but over the long term it will eventually bring you to a higher elo.

    Support players also have a very hard time trying to carry themselves to a higher elo, and generally need to duo que with a carry to be successful. It's why there are so many good supports below 1200 elo.

  • #87 GentlemanGustaf

    words like 'good support' have no meaning. Are they better supports than those found at, say, 1500? That's what matters.

  • #88 Cerbereth

    Let me rephrase that I am more impressed with the supports I get below 1200 elo in ranked than the ones I get when I play normal draft. On the flip side I am less impressed with the teammates I have in other roles below 1200 elo than I am with the teammates I have for those roles in normal draft.

    It is therefore my opinion based on experiences I have had that the supports I get below 1200 elo are probably better players than their elo would indicate.

    Above 1400 elo it seems like no one wants to support at all.

    I am also very excited for the new league system as I have had good experiences with the league system that bloodline champions uses and it appears that lol is adopting a similar system.

    Last edited by Cerbereth: 1/16/2013 9:52:15 PM
  • #89 ranigad

    There are always people who are above or below what their elos would indicate because that's the nature of elos. You could be playing with a person who lost their first two games and just happened to drop (I lost my first 3 and ended at 1100 before making it back up to 1500 at the end of the season), you could be getting smurfs, individuals who have a single good game, or even the possibility that draft mode supports are just less skilled because they don't play the role often. In addition, I dare to venture that you haven't had experience with a higher elo support (because you're comparing sub 1200 with normal drafts rather than above 1200 - higher elo as in 1800s). There's a substantial difference in their play. 

    Even if you are impressed by supports below 1200 doesn't make them great, they're just better than supports that you've had in normals. The pool in which you're comparing is limited and so it's somewhat biased xD (not saying that you're wrong, maybe 1200- elo supports are below their true elo, but perhaps there are other reasons than just "elo hell").

    Again, I'm getting side tracked xD Anyways, the new league system seems interesting for sure. I will miss the ability to straight up compare myself to my friends with the elo system, especially with the tangible ability to see progress (i.e. my elo is rising so I must be playing better). The new system seems more about your individual progression than your progression relative to others. Although I think this should be the attitude ranked inspires, I will definitely miss elos.

    (Sorry, I tend to ramble and get side tracked >_>)

  • #80 inb4jelly

    honestly if you cant get past 1100 then it isnt your teammates. all players at that elo are extremely bad. you should completely roflstomp them

  • #74 PeregrineBF

    There are two definitions of Elo Hell that I feel are important.

    Definition 1: Elo Hell is a situation where you are stuck at an Elo lower than your true skill, and will never escape due to your team members at this Elo being bad.

    Definition 2: Elo Hell is a situation where you are at an Elo lower than you believe your true skill to be, and will have to fight your way through trolling team members to get to a point where you feel you can have fun again. The game has ceased to be fun, and you could work your way out but it doesn't seem worth the effort.

    The first kind doesn't exist, it has been disproved many times by simple statistics. The second kind is purely a psychological effect, can happen at any Elo average, and is quite real. It can be fixed by an attitude change, but such a change is very hard for most people. It might be better to call the second kind Elo Purgatory, since it is escapable unlike the concept of Elo Hell.

  • #73 CptObviousSWE

    I really didn't get that table, I guess I have get my Ph. D. in Elo hell first.

    Or someone can explain it like I'm a retard : )

  • #81 ranigad

    Each side represents the difference of the label from the average elo of your opponent's team. On the left side, you would subtract the opposing team's average elo from your true elo (where you should be based on your skill). On the top side, you would subtract the opposing team's average elo from your average elo. Then you find where the column and row intersect and that's the probability of you winning.

    Let's take his example. The enemy team's average elo is 1200, your elo is 1300, and your team's average elo is 1225.

    On the left, you would take your elo and subtract the enemy team's average from it. 1300 - 1200 = 100. Find the row that's +100.

    On the top, take your team's average elo and subtract the enemy team's average from it. 1225 - 1200 = +25. 

    Now find where they intersect and that would be the chance of your team winning, in this case it would be 57.1%

  • #82 CptObviousSWE

    Now that I see it it seems pretty obvious and pretty basic math, but, as I said, I really didn't get it. 

    Thanks a lot!

  • #68 Wiltsee

    i can't argue against numbers. but there's one thing worth mentioning:

    what if you main support? it's the role with the least dramatic impact on the game. sure, the wards and clutch reactions are of help to the team, but the carries and jungler have a far greater impact on the tide of the games (As they are the only ones capable of literally carrying a team to victory). 

    this means that when you play support, you aid the efforts of what you hope are competent carries. but you can't actually carry. it's really a matter of faith. sure, it makes sense that at some point you'll hit your proper elo, but if you main a role that is entirely dependent on others (as opposed to a role that is fairly dependent), you're a bit fucked, no?

    Last edited by Wiltsee: 1/4/2013 6:03:13 PM
  • #69 sgtcolon

    I have never subscribed to this, even in season 2, it is even less true for season 3 (you can now become a competent tank or mage, if you are playing well, even by mid game). Supports can carry. Yes, you heard me right. Just make sure when you play support that you have a huge impact on the game. Securing kills, saving team mates, maintaining map vision and having awareness for your whole team, timing buffs, calling plays, getting auras! Carrying doesn't mean killing everything, it means having a very positive impact on the game and winning! Instead of thinking that you are entirely dependant on your team, start playing as if they are entirely dependant on you!

    Last edited by sgtcolon: 1/4/2013 6:48:46 PM
  • #71 Wiltsee

    but carrying does mean killing everything. it means making efficient use of your time and abilities to accrue gold (killing minions and people), and making efficient use of that gold to buy the proper items needed to win teamfights (kill people) and push lanes (kill minions). all while avoiding being killed.

    i suppose i was a little understated in it, but i never said the support made no impact. simply that the support's impact is dependent on your team's competence. after all, what's the use of map awareness if your carries don't notice it themselves? these are bonuses that have to be taken advantage of, and if they're not, they're ineffective.  a well-timed sona ult can win the fight, good wards are helpful, but carries who don't understand how to lane/teamfight can undo all of that, all despite a support's stellar performance.

    whereas if an ADC's performance is stellar, his team may just (or already will) win the game. this is pretty undeniable, no?

    tl;dr: ask yourself this question; when was the last game you ever looked at the support and went "yeah, he's the reason why we won"?

    Last edited by Wiltsee: 1/5/2013 10:09:26 AM
  • #75 RoflSayNo

    there are only few who main support so the most supports are really crappy xD

    i main support in low elo (top elo 1500) and i am very pleased with my elo because 1500 elo is too much compared to my skills x) anyway even though i am worse then a lot other players i am a better support then the most other players at my elo. so imagine ur 4 team mates and 4 enemys have the same skill BUT u are the supporter and u are better then the enemys supporter. if u rly main support its most likely that u are far better then the enemys supporter xD ur entire team will have an huge advantage. 

    (sry for my bad english >_>)

  • #76 sgtcolon

    I can honestly say countless time I have carried or been carried as/by supports. Just because the AD got the last hit on a champion kill doesn't mean the AD is carrying the game. Alos, I have met AD players that are slow to react, but never have they ignored a double ping when I have warded well enough to give them decent warning. So, yers, you can not rely on having truly capable team mates, but support is arguably the best role in the game to make up for your team mates drawbacks.

    Further to this, you actually can build as a tank or mage on support now since your gold revenue is hugely increased. I have seen Taric's leaving bot lane with Runic Bulwark and Mikaels Crucible beating the shit out of the enemy mid laners etc etc. The list goes on. It's probably even more potent having a 2nd AP carry!

    TL;DR: Kills are not everything. Carrying does not mean being 12 0 0. Securing objectives and advantages is what wins games and all roles are capable of influencing this.

  • #77 BossPikachu

    If you get into some bad teams, there is not much you can do as a support. The lower elo you get, the worse people play, and the less they pay attention to the mini-map and other players. Therefore, the less influence you have as a support player. I realised this a little bit too late as I dropped from 1450 back to 1250 past weekend. I will try and ad carry myself back to 1450 again.

  • #78 Wiltsee

    Quote from BossPikachu »

    If you get into some bad teams, there is not much you can do as a support. The lower elo you get, the worse people play, and the less they pay attention to the mini-map and other players. Therefore, the less influence you have as a support player. I realised this a little bit too late as I dropped from 1450 back to 1250 past weekend. I will try and ad carry myself back to 1450 again.


    the issue, colon, is that the benefits the support provides (the benefits you've mentioned) are benefits that have to be noticed and utilized. the buffs, the wards, the harass, the cc; all of this have to be taken advantage of successfully to be of any use. if they can't, it's worthless. and if your team, particularly your ad carry, has little awareness about what to do in any given situation, your support will not cover this.

    you'll end up with a 0/3/4 kda and telling yourself "i seriously should've been a carry."

  • #79 BossPikachu

    Exactly. Though it is always smart to point things out, extra clear if necessary  Retreat-ping someone if you see the jungler heading towards them, or camping in a bush. Ping on roaming enemies that you see at unusual places. Time enemied wards that are placed in tri-bush, at dragon etc (time when placed +3 minutes). If they don't know theirselves, tell the ad carry to be more passive and farm, or to be a little bit more aggressive if you see the possibilities. If there is a misunderstanding, or if a mistake was made, tell them it was 'your bad' even though it was not.. And never surrender too early.

  • #70 monkyyy

    if u main support ur true elo would be when u manage to have a 50% chance of winning the game; even if that means 100% of games u never feed; if u could only have a negative effect on the game; the elo system is designed for the propose of making all factors besides weather u win or lose; irrelivent

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