Quote:

**Colred**:

The truth is, for most players, it is extremely difficult to reach the “escape velocity” necessary to travel past the masses in an ELO system. The nature of any ELO system is to pull most players back to the middle, while propelling the few truly exceptional players (whether good or bad) toward the ends.

Consider an example game: Team Derp plays at 1200 ELO. If all the competitors are equal in skill (accurate ratings), Team Derp has a 50% chance of winning the match. If Derp wins, the Derp players will gain ELO and play a tougher team the next time out, making Team Derp more likely to lose its next game. Although there will be small rises and falls in the short term, the long term outcome should be that Team Derp will return to 1200 again and again (unless the players improve).

Now, consider the same game, with ONE player who is inaccurately rated. Say 1 of the Derp players is actually a 1400 ELO player. That should increase Derp's chances of winning against an accurately ranked 1200 ELO opponent. But how much do their chances improve? While a 1400 player may be markedly better than a 1200 player, he still only represents 20% of his team's players. And a 200 point ELO advantage can be mitigated by laning role, bad team communication, team composition, etc. The truth is, that 1400 player will have to work very hard, and maybe get a little lucky, to earn his 1400 rating, simply because 1400 is too close to the masses at the average ELO.

However, the more exceptional a player is, the less true this is. A 2000 ELO player should be strong enough to overcome most obstacles presented by games at 1200. And the further a player rises in ELO, the more accurately players will be rated and the more consistent the team play will become, making skill increasingly influential in the outcome of the game. This is how ELO systems propel exceptionally good, or exceptionally bad, players toward the ends of the spectrum.

But, for the rest of us, the natural gravity well created by ELO will tend to pull us back toward the mean.

Protip: it's the Elo system, no allcaps. It doesn't stand for anything. The guy who came up with it was called Elo. Other than that, I enjoyed reading your guide, agreed with most stuff.

Statistically, can you explain why there is a gravity well pulling people towards the mean? If you truly belong at 1400 Elo, and your current Elo was 1300, every time you play a game there is a higher chance for you to win than lose. There doesn't appear to be a "gravity" at all - rather, whenever you play, you will always tend to gravitate towards your "true" Elo.

Imagine a card game where two players each get 5 cards at random. The player with the higher sum of all his cards wins. The average value of the cards, out of 10, is 5. Now imagine that one player instead always receives a 6, and four random cards.

**On average**, that player is more likely to win. If that player always received a 10 instead, he is

**even more** likely to win.

Similarly, a 2400 smurf might end up with 4 afks, and lose. But then again, the other team might end up with 4 afks and lose even harder.

**Statistically**, the smurf is more likely to win. His odds of playing a game at 1200 Elo and winning might be 80 to 20. The same applies to a 1400 player at 1300, but his odds of winning might be 52 to 48.

You gave an example of a 1400 Elo player playing 1200 Elo games. Your question "but how much do their chances improve?" is not rhetorical. The answer is that it improves. Even if by a very small amount, it improves to the point that it's not a 50/50 coin flip anymore - rather, you have a higher chance of winning than losing. There is no gravity towards the mean, there's only gravity towards your "true" Elo.