I have recently been looking into the mathematics behind the Elo rating system and its application to areas other than chess. I can understand almost all of it but I'm having a problem finding out the meaning of one of the values, and how it is determined. The value I'm talking about is the
n value, which is supposed to be some number of rating points that a person
n rated points above their opponent is expected to win ten times as often (If my explanation is not clear enough, it is represented by the number 400 - the value used in chess - in the fomulae on the wikipedia page).
This all makes perfect sense so far, but I was wondering how you determine that value when setting up a new system. For example, in chess the value of n is 400 - why was this number chosen and not something more 'round' like 100 or 500? About the only effect I can see that this number has is the increase in precision (though not accuracy) of the rating for higher values of n, and if this is the case, does the value really matter so long as it remains consistent?