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Dispelling Common Elo Myths

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MathMage

Senior Member

09-04-2011

The Elo system is not a complicated beast. In fact, as I point out later, it's one of the simpler rating systems. Despite that, you find all manner of fascinating misconceptions running about the forums. I hope to do something about that. So here's a list. I won't claim it's complete--humans are ingenious in their ability to misunderstand basic concepts in new and interesting ways. But these are by far the most common mistakes people make, and will maybe make less often after reading this thread.

Readers are welcome to make their own additions, of course. I will compile those in the second post.

"Riot doesn't use the Elo system, Zileas said they heavily modified it for use in team games."

He did. They did. It's still the Elo system. It's easy to see what sorts of modifications have been made (e.g. duo queue inflation, teamwide average Elo, lengthy probationary period of 80 games or so, newbie island), and they're mostly in the matchmaking side of the system. Elo remains largely the same, though there isn't quite the same zeal for maintaining an average Elo in chess as there is in LoL.

"I'm +20 W/L with worse Elo than XXX player with a -20 W/L, Elo is a broken system."

THINGS THAT ARE NOT THE SAME:
-W/L ratio
-Elo rating

For the most part, people who have higher Elo ratings with worse W/L records didn't just luck into it, they played against better players. Your ability to stomp all over 1000 Elo games does not prove that you're better than the guy who went 50/50 at 1500 Elo. Yes, there are exceptions like BigFatMissy getting carried by Chauster, but I'd still bet she's better than you.

"I hate how the system tries to keep me at a 50/50 W/L record, whenever I go on a streak I get uncarriable feeders on my team."

Elo does not try to give you a 50% win rate. It tries to give you a 50% chance of winning your next match, based on your current Elo. Obviously, this gives you a 50% win rate only if your current Elo is your true Elo. There is no mechanism in the Elo system that says "okay, this guy's been winning too much, let's hit him with a double troll whammy!"

But what about those 10-win streaks where you get paired with a double leaver duo queue or whatever? Well, look at what you just said. You just got 10 games without getting trolled. In Ranked solo queue. I'd say you're about due. Have some perspective.

"Even Hotshot couldn't carry four feeders all the time at 1200 Elo, therefore Elo Hell exists!"

To rise in Elo, you don't have to carry every game including the ones in which you get four feeders or two leavers or whatever. You just have to win more than you lose. Contra your perception, you're not always the one getting bad teammates. If you are more skilled, it will show.

"The Law of Large Numbers says you'll get closer to your true Elo over time, so Elo Hell doesn't exist!"

The Law of Large Numbers doesn't say any such thing. If Elo were based on that, the system would be broken. Elo functions precisely because the likelihood of your winning the next match is based on your performance in previous matches (translation: lower Elo = higher chance of winning and vice versa). LLN addresses a series of independent events (like coin flips) where the probability of your next heads does not depend on how many heads you've gotten so far.

Now, that doesn't mean the Law of Large Numbers teaches us nothing about the Elo system at all. For example, if you look at how good your teammates are compared to your opponents, LLN implies that over time you'll find that your teammates are about as good as your opponents. You won't consistently get the worse team or the better team.

To put it another way: Over time, the only wild card is you. Only you can change your Elo in the long run. The question that spurs the Elo Hell debate is how long the 'long run' takes.

"All the problems with Elo are caused by newbies starting at 1200 and ruining games for the rest of us. They should work their way up from zero."

It's always amusing to see established 1200 players groaning that they're obviously so much better than new players because they're 1200 Elo after 1000 games played or whatever. That said, starting new players off at the average Elo provides the best experience for the new players. The large initial Elo changes minimize new players' impact on the 1200 introduction point and surrounding brackets, because it takes so few games to get out of those brackets.

"These large Elo adjustments at the beginning make it too **** easy to luck into Elo Hell because you get leavers/feeders/trolls in your placement matches."

Small Elo adjustments in the beginning would make everyone's experience miserable because everyone would be crammed together even closer to 1200. The large adjustments persist (to a degree) through your first 80 matches or so--at least, that was my experience--so you have plenty of opportunity to make up a few early troll games. And let's be honest--the most common reason for this complaint is that people started playing Ranked before they were ready, tanked their Elo, and now that they finally know how to play the game they're trying to grind their way up. Garbage in, garbage out--tell the Elo system you suck, and the Elo system will agree.

"1200 Elo is better than 75% of Ranked players, Zileas said so. Deflation has thrown the average Elo way out of whack, and that's the problem with the system."

Zileas said that 1200 Elo is better than 75% of all players, Ranked and Unranked. The reason is that people who play Ranked tend to be better than people who don't. Is the average exactly 1200? No, but it's not 1000 either. Probably closer to 1150. Also remember that a massive part of that deflation comes from inactive accounts falling to 1400 from whatever Elo they were at--and that's false deflation, because it comes from accounts that aren't being used, so the deflation is isolated to those accounts, and doesn't affect the general population.

EDIT: Zileas' statement is months old. More recently, the adjustment to bronze/silver/gold was accompanied by statements that bronze (1249+) represented the top 25% of Ranked; silver (1400+) represented top 10%; gold (1520+) represented top 3%; and plat (1900+) represented top 0.2%. Using bronze as a baseline, one can extrapolate that 1200 represents the top 32% of the community. Silver implies that 1200 is top 40%. Gold implies that 1200 is top 29%. And plat implies that 1200 represents the top 24%. The real conclusion I draw from this is that Riot didn't bother to actually calculate where the top 25-10-3-0.2% marks were, but a second conclusion is that 1200 actually is somewhere around 70th percentile. And the average Elo is likely around 1050 (calculating from Bronze, 1200-1249 Elo is 7% of the ladder, it shouldn't get any less dense as we approach the average, and we have about 18% to go).

I'll preserve this as a myth, because it was initially born from erroneous readings of Zileas' statement about the entire playerbase. However, the myth has become reality, and I hope Riot does something about it.

"Elo was created for 1v1 games like chess, therefore it's unsuitable for a 5v5 game like LoL"

I'll tell you what's unsuitable for a 5v5 game: solo queue. One man queuing with four randoms against 5 randoms, and you want the system to tell you how skilled you are? Elo makes the best of a bad situation, and it's no less suitable in this case than in the 1v1 case. It won't sort people as quickly in solo queue as it does in 1v1 situations, but no system can do that.

"Elo is used in team games like football and baseball, so it's suitable for LoL."

There's an important difference: Elo is used in team games...to rate teams. In this way the system is reduced to a bunch of 1v1s even though there are 20 people on the field. In LoL, however, Elo is used to rate individuals. This is fraught with randomness and peril, and leads to much higher variance in Elo after any given number of games. It still works--the above argument still applies--but not nearly as well. This is one reason why I advocate for the premade ladders to rate teams, rather than players.

"Elo is the best system there is, and I challenge you to find a better one."

Bayesian rating systems are one example of a superior system. They track both your rating and the uncertainty in your rating; this allows them to more carefully adjust your post-game Elo. The TrueSkill rating Microsoft uses for games like Halo is a Bayesian system.

Another system, much more pie-in-the-sky but potentially even better, would be a Win Probability Added system. This is a sabermetric technique baseball analysts use to attempt to quantify how each individual play changed the team's chance of success. People talk about simplistic ways to weight Elo changes like KDA or towers downed or gold earned--well, this system would actually be able to measure personal performance in a team game.

So why do we have Elo if it's not the best system available? Simplicity. Elo is easy to implement, maintain, and understand. It's reasonably effective with minimal time investment. Bayesian systems are moderately more effective for much more effort and statistical know-how. And WPA is an infinite time sink that can be constantly worked on for marginal improvements--at the low end we have those simple KDA/gold/towers weighting systems, and at the high end we could track every ability used, every step taken, every last little detail of the match...if someone invested the time to quantify all that. LoL is much more complicated to analyze than baseball because there are no at-bats, and thus no real way to conduct turn-by-turn 'state' analysis.

Even the current system can be improved in some simple ways, however. For example, one small but useful innovation would be to temporarily increase Elo adjustments following a long period not playing Ranked. This accurately models the increased uncertainty about your skill level--you might have not played at all and become terribly rusty, or you might have practiced your ass off and gotten much better. It allows people who tanked their Elo initially, because they started when they weren't ready, or got trolled in their placement matches, to get a jump start moving up the ladder. The same for people who let inactive accounts slide to 1400. And it removes the incentive for such players to smurf another account to 30 and try for better luck in their early matches--by the time they do that, their old account will have just as volatile an Elo.

-----------------------------------------------------------------------------------------

If you made it down here, congrats. This was a bit longer than I'd anticipated--after all, it was initially only going to be about one of these myths, rather than all of them. My fingers just wouldn't stop typing.

So, how many of these have you heard before? Got any new ones for me? I'm happy to add 'em.


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MathMage

Senior Member

09-04-2011

Reserved for additional myths and ideas to improve the Elo system.

"Bigfatjiji has X smurfs in top 25, therefore Elo Hell doesn't exist!"

Quote:
die4769:
I have another myth for you: "This 2000 ranked player made a smurf and carried himself up to 2000 elo again, elo hell doesn't exist"

A 2000 ranked player is a lot better than a player who belongs in, say 1400 elo, they have skills that a 1400 elo player wouldn't be able to use, like being able to get his team to follow him in an effective manner. That's a poor, poor argument.


Nobody questions that the best players can carry up the ladder. If you belong at the top, you'll get there. The issue is the difficulty of climbing when you only belong a couple rungs higher. The farther you are from your true Elo, the more influence you have on the game--but how close do you get before your influence becomes negligible? Bigfatjiji can't answer that.

"Elo would be so much better if it measured stats like KDA, CS, Towers, Gold Earned, and the like. It would reward people for their individual performance."
Quote:
UnicornFan91:
singed splitpushes bot.
he manages to get 3 people to go stop him.
team gets baron and pushes 2 top turrets.
singed dies from 3 people.
singed played a major part of allowing his team to secure 2 towers and baron, yet he gets nothing out of your proposed fix.

in a game like league, there are too many factors to apply such a system


Stats only tell a small part of the story behind any game. They vary from champion to champion, from build to build, from role to role; and many of the key elements that lead to victory have no statistical recognition whatever. The clamor for personal stats as an element of Elo is a symptom of the "Me first" mentality in solo queue, and nothing more.

"1000-win players shouldn't be paired with 10-win idiots. The newbs are always noobs who lucked into their Elo, and I can't carry their asses."

New players have to be paired with established players at some point, or they'll never receive an accurate rating relative to those players. Large Elo adjustments minimize their individual impact on established players prior to finding their approximate Elo bracket, but it also means their luck can put them a few hundred points away from their true Elo, at least for a little while. We all know someone who initially got up to 1400 Elo, then "got a string of bad teams" and fell all the way to 1k before grinding back up. Yeah, that's how those new players see it, and your seeing it differently is as much because you're looking for someone to blame as because of anything real.

----------------------------------------------------------

Here I compile a list of changes that I think would improve the Elo system.

-Increase post-game Elo adjustment for inactive accounts. The reasoning behind this is explained in the first post; briefly, it reflects the system's increased uncertainty about the inactive player's skill level on returning to Ranked, and disincentivizes smurfing for people who got trolled in their placement matches.

-Reduce duo queue post-game Elo adjustments. Right now, the system acts to bring the two players' Elos closer together. It rewards the lower-ranked player more for a win, and punishes him less for a loss. But this is not a sound response from an information theory standpoint. The system should instead recognize that duo queue lessens its ability to judge which player is doing the work, because the system never gets to analyze the players separately. So the Elo adjustments of both players should be reduced, win or lose, because duo queue games do not represent as large an update in information as solo queue games. This would essentially remove every possible duo queue exploit.

-Temporary Ranked bans for leavers and AFKers. This is one problem that simply should not exist in Ranked. There should be no way anyone can get away with repeatedly leaving in a competitive environment. 3 day ban for first offense, 1 week for second, 2 weeks for 3rd, 1 month for 4th. Include a forgiveness mechanism for people who stay on their best behavior for a while. Let them play normals, bots, customs--anything that isn't going to screw up others' competitive games.


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LordSocky

Senior Member

09-04-2011

Posting in a MathMage thread. I wish I was half the Mathemagician that you are.

I also love how you play devil's advocate repeatedly in the post. It shows that you aren't blind to one side.


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imidorifeed

Member

09-04-2011

how many digits of PI can you name?


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MathMage

Senior Member

09-04-2011

Quote:
imidorifeed:
how many digits of PI can you name?


Ironically, I can remember the digits, but not how many I remember. Um.
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798...

103 digits, I guess.


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Texas Snyper

Senior Member

09-04-2011

/applaud

Another awesome MathMage thread.

+1

EDIT: @"No, but it's not 1000 either. Probably closer to 1150."
I think you may be underestimating where its at. You are accounting for Elo decay from inactivity and state that its localized to those accounts. But that is only until they get active again and rise up the ladder, passing their decay to others. You also did not mention Elo deflation due to que dodges. This would most likely be the major component to the average Elo decay. The average only 'goes up' with every new account to ranked games and only once per but is always going down due to que dodges.


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Grunghole

Senior Member

09-04-2011

I read this without noticing that it was MathMage.

But now that I see that, I'm not at all surprised by the succinct and lucid posts that seem to be your hallmark. This is a great thread, and should be stickied.


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SHOE788

Senior Member

09-04-2011

Quote:
It's always amusing to see established 1200 players groaning that they're obviously so much better than new players because they're 1200 Elo after 1000 games played or whatever. That said, starting new players off at the average Elo provides the best experience for the new players. The large initial Elo changes minimize new players' impact on the 1200 introduction point and surrounding brackets, because it takes so few games to get out of those brackets.


First of all "average elo" is relative. Riot could seed new players at 2000 and the "average elo" would rise to around 2000.

Secondly, the reason the elo system exists is to separate players of different skill levels, correct? Then why is every single player, whether they are a 500 elo or 2300 elo player, seeded into 1200. This causes the 1200 bracket (Around 1000-1400) to be the bracket with the MOST skill diversity, thus you can end up with team mates that are 500 elo, or 2300 elo.

Debunk this


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Aristodemis

Senior Member

09-04-2011

A thread which everyone who has ever posted in an Elo Hell thread should read.


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Texas Snyper

Senior Member

09-04-2011

Quote:
SHOE788:
First of all "average elo" is relative. Riot could seed new players at 2000 and the "average elo" would rise to around 2000.

Secondly, the reason the elo system exists is to separate players of different skill levels, correct? Then why is every single player, whether they are a 500 elo or 2300 elo player, seeded into 1200. This causes the 1200 bracket (Around 1000-1400) to be the bracket with the MOST skill diversity, thus you can end up with team mates that are 500 elo, or 2300 elo.

Debunk this


His usage of "average Elo" is referring to the 50% mark where half the players are above it and the other half are below it. By definition, it would be at 1200 since the Elo system only adds new pts to the total pool with new accounts. However, with Elo decay, the 'average Elo' has actually dropped below 1200.

The reason everybody is seeded into the 1200 bracket is because that is the arbitrary point in which Riot chose. It doesn't matter what number they picked, but that number they do pick will become the middle of the road. That is how the system works. It will only remain the most diverse in skill as long as you have a flood of new people to ranked. Once the influx slows down, everybody will get filtered into their proper spots and the diversity will dilute itself.

/debunked