I'm sure you've heard hundreds upon thousands of threads discussing new scoring systems, so I don't want to waste too much of your time coming up with another random analytic. I just wanted to give some math as to how I think the Elo system can be improved for League of Legends.
The Elo system was designed for ranking Chess players. With this in mind, there are 3 major differences between Chess and League of Legends.
1. In Chess, your victory or defeat is based SOLELY on your own performance
2. In Chess, your Elo is based SOLELY on your own score (different than the above - explained below)
3. In Chess, you get to pick your opponents.
I dissected each of these mathematically to try and find a more appropriate scoring system for League of Legends, and I simply couldn't find anything better than the Elo system - however I feel the Elo system is being used incorrectly at the moment. So instead I've decided to point out hypothetical situations where these each become a problem and a solution which works to repair the Elo system so every player can be happier.
1. The problem here is one everyone complains about. "I went 24/2/19 as Tryndamere but the rest of my team went 5/40/6 and we ended up losing despite my own awesome performance".
This has led to people suggesting scoring systems based around total numbers of kills/deaths/CS. The problem with these systems (other than them not being zero-sum, so total Elo across all players will tend towards infinity) is that they can be abused. Through careful use of Flash and Teleport I can bounce between lanes guaranteeing 400 CS but never helping in team fights, and my Elo will just rise and rise despite being a worthless addition to the team.
A more appropriate solution to this is to weight Elo gain and loss according to participation. So if your team lost the match and everyone was going to lose 15 points, instead the people who participated the most lose 5 and those who participated the least lose 25. Using simple arithmetic means to calculate participation if everyone had similar numbers of kills/deaths/assists then you would expect to see everyone lose the same number of points. This means you are still guaranteed to lose points during a defeat, but if you had an afk team member you will not lose as many points (and they will lose more points)
2. The Elo system in a nutshell states that the more likely you are to lose, the more points you get if you win. Along the same lines the more likely you are to win, the more points you lose if defeated. The odds of winning are calculated by the difference in Elo (if one player had 1200 Elo and another had 1600 Elo, the 1600 Elo player has a 90% chance to win - ergo if he loses he'll lose WAY more points than he'd gain if he won).
The problem here is that Elo really isn't indicative of skill. Some people have played 500 ranked games, seen many wins and losses, and are sitting around 1100-1300 Elo. Some people just hit level 30 and wanted to try Ranked for the first time so they have 1200 Elo. These two players are considered "equally skilled" even though one has FAR less experience. To see where this is a problem, consider a 1000 Elo veteran who has been playing for a year paired with four 1200 Elo newbies. The average Elo for their team is 1160, so they may be matched against a team consisting of entirely 1150-Elo players. This is simply not a fair fight.
A more appropriate solution to this is to weight contribution to the team's average Elo according to the number of games played, perhaps with a certain cap. So if the 1000-Elo player has 36 games under their belt and the four 1200-Elo newbs join his team, the team's average Elo is considered to be (36*1000 + 4*1200) / 40 = 1020 (a better reflection of the team's skill).
3. This is the single biggest issue with the Elo system, the reason for the pseudo-myth of "Elo Hell", and the reason for so much grief revolving around this simple number. In League of Legends you are paired with people who have similar Elo to you. However as I mentioned above for point 2, the change in Elo is based on your difference in score. So if you win this match you'll only gain about 10 points, however if you won a match against people who had 400 more Elo than you then you would net a hefty 100 points.
In Chess, suppose I were a 600-Elo player and I decided that I needed to step up my game. I could practice outside of tournaments, read books, play with friends, and improve my game until I play with the same skill as 1700-Elo players. Now in Chess I would challenge these 1700-Elo players, and because we have the same skill I'd have a 50% chance to win. If I won I'd see a MASSIVE jump in Elo (+250-ish) and if I lost I'd see only the tiniest drop (-2-ish) simply because their score is so much higher than mine. After playing 10-20 of these games, and winning half of them, I'd have an Elo around 1400-1500. In League of Legends if I did the same (quit playing Ranked, practiced in Draft Normal, played with high-Elo friends, watched tournaments, read guides) then I returned to try and improve my score I would be paired against other 600-Elo players. In order to reach 1400-1500 Elo I would need to win AROUND 75 GAMES IN A ROW without a single loss.
Note that this is also the reason people believe in "Elo hell". You lose your first 10 games so you start out at 800 Elo, then you proceed to win 50% or more of your games but you simply can't escape. The reason I say Elo hell is a pseudo-myth is because while it's true that griefers, leavers, and feeders tend to lose and therefore tend to have low Elo - there are just as many good players as bad at low Elo and if you watch high-Elo games in spectator mode you'll see the gameplay is not much different.
The only appropriate solution to this is to completely remove the match-making system. Teams should be assigned completely randomly. This restores the dignity of the Elo system because if you do get unlucky and you're paired with four bad players against five professionals then you're not going to suffer a large hit to your Elo. With the match-making system removed the law of large numbers will take hold and people will begin to float towards values reflecting their own skill.
These are my three humble suggestions for bringing meaning to the ranking system in League of Legends. I believe that having an improved ranking system would cause people to rage less, cooperate more, and enjoy League of Legends more which would lead not only to an improved community but improved revenue for Riot Games as people are willing to pour more time and money into this game. I hope that people read through this and are willing to give me their thoughts on my suggestions.
I realize it's bad form to bump my own posts, but after 3 weeks and sinking back several pages I feel my wall of text may have frightened many people so I wanted to summarize and give my opinions a new chance to be considered:
1. Adjust ELO gain/loss at the end of each match according to participation. The losing team should lose the same total ELO, but each player loses a portion of this total according to their stats. This way the 20/2/18 player on a team with 4 players who all went 0/15/0 isn't punished for his poor team's performance
2. When calculating the amount of ELO that should be lost, produce a weighted average for the team's ELO based on the number of games they have played - possibly up to a cap (no further weight is gained after 100 games).
3. Eliminate the ELO-based match-making. Yes, this means that a team of 5 newbs may be paired against a team of 5 pros, but statistics states that more often than not teams will be equally balanced between good and bad players. More importantly: if a team of newbs is paired against a team of pros then they will only lose 1 or 2 ELO due to the difference in skill, and if they win they'll gain 100-200
If elo was calculated based on individual performance then people would just pad their stats rather then work as a team or continue trying to win the game. We want players to cooperate on a team, not compete.
and then of course there is always the fact that the support would get screwed by this every time and the ranged carry would end up with the first rank almost every time.
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