ELO

[Willie333b]

Is it possible to get lower than 0 ELO?

[Jest Phulin]

Looking at the math, I think it is theoretically possible. However, in practice, one would have to lose a *lot* of games, and generally against players who were considered weaker (which will be harder to find as Elo drops) to actually achieve it. This is also only true if there are several simultaneous games and Elo is only updated in batches.

The main part comes down to
New Elo = Old Elo + (k-factor x (actual score - expected score))

Since the expected score approaches zero as Elo drops, the adjustment factor also approaches zero.

Also realize that the sum of all Elo for a given pool is constant. So, if 100 people were initially in a pool, to drop one of them to 0 would require raising all the others by 15 (since they all start at 1500). However, at a difference of 1500 Elo, the expected score is only 0.01 (roughly), so again it goes back to losing a lot of games.

Interesting question, though.


Gah, and as I'm typing this out, I thought of another method to examine it. The expected score of two equally ranked players is 0.5. So, if a bracket were to be set up so that losers played only losers to lower the Elo, it would take (with a k-factor of 32) 93 games to get to zero. While that isn't that many games, it does require each successive game to be lost against an opponent who has also lost all of their games. Which means you would need 2^93 players in the pool, or way more people than are on BGA (or have ever lived, for that matter [or larger than the estimated number of atoms in the universe...])

[Nanaki404]

Which means you would need 2^93 players in the pool, or way more people than are on BGA (or have ever lived, for that matter [or larger than the estimated number of atoms in the universe...])

2^93 = (approximately) 8*10^27. This is 8 billions of billions of billions of players, but still far less than the number of atoms which is estimated around 10^80.


On the ELO note, leaving a game abruptly gives a ELO penalty in addition to the usual ELO loss from the "defeat". I don't know how this penalty is computed though, but maybe it does not depend on the ELO level that much, and means a player quitting a lot of games could drop faster to low ELO.

[Jest Phulin]

Huh. Yeah, I guess my reasoning was off when I looked at the number of atoms in the universe.

And, I forgot about the penalty for quitting. So, that means you can drop another 20 (I think) ELO per game by quitting, possibly more if you run out of time also, which means that you might be able to do it in about 50 games, with 2^50 accounts.