More explanation on ELO

I just got a message from somebody who thought my ELO formula was unfair, so I explained it a bit more to them and thought I'd share:

"Feel free to suggest specific improvements to the formula. Currently I use:

myelo + 40 * (result - 1 - 1/(1+pow(10,(myelo-theirelo)/400)))

With a minimum gain for a win of 5 and a minimum loss for a loss of 5. So if two debaters with an ELO of 1500 each face each other, the winner has 1520 ELO points, and the loser has 1480. So it's completely fair.

Say you're ranked 1400 and you beat somebody ranked 1500. Then you go up more points than just 20 (in this case, you'd go up to 1426) because you won as the underdog, which is a lot more surprising than if you had lost. Conversely if you had lost, you would have lost less points than 20 (in this case you'd go to 1386) because your loss is not so surprising. The opposite relationships, of course, would also hold true for the 1500 ranked debater.

So it's actually no easier to go up in elo than it is to go down."

admin: That seems really fair. DDO's is more confusing.