Elo Rating System

[oneinam]

Is an ELO rating of 2000 against an ELO rating 1900 the same difference in terms of advantage as an ELO 1800 against an ELO 1700? I.e the differences are both 100 units but are they the same?

[Buenchico]

In both of your examples the stronger player would be expected to win 64% of games against the weaker one:
https://en.wikipedia.org/wiki/Elo_rating_system

[oneinam]

Hi Buenchico
Ok thank u 4 that answer. When u refer to 64% RU saying that a player with an ELO 2000 will win 64 out of 100 games against a player with ELO 1900? Is this a 14% advantage?

Further, from yr answer then the advantage is a linear one. Therefore a player with ELO 2000 will have a 28% advantage over a player with ELO 1800. (This seems to be a lot)

[Buenchico]

You've used the word 'advantage' before and, as a mathematics graduate, I don't like that term simply because it has no universally defined mathematical meaning.

So, with reference to your first paragraph, I firstly agree that a player with an ELO of 2000 should be expected to win 64% of games against a player with an ELO of 1900.

However, if was to try to assign a meaning to 'advantage', I could either get to a figure of 28% (not 14%), because 64% exceeds 36% by 28%, or to 77.77% because 64 exceeds 36 by 77.7% of 36. (The second definition would make far more sense to me but, as I've stated, mathematics simply doesn't recognise the word 'advantage' in the way that you've used it).

With reference to your second paragraph, the difference ISN'T linear. As stated in the third paragraph of my Wikipedia link, where their ELOs vary by 200, the stronger of two opponents would be expected to win 76% (not 78%) of games against the weaker opponent. Depending upon which of my two definitions (above) of 'advantage' that you choose to use, you either get to a figure of 52% or 216.67%.

[oneinam]

Let's touch base on language usage first. Tell me and define what word for "advantage" would u use. This would be very useful for me to use a mathematically universal term in this context. (Basically u know I am asking u to help me put together some sort of sense with the the ELO system and real world winning possibilities. I am very grateful for your time and input).

[oneinam]

Note I am trying to understand the relationship between a player with an ELO rating 2000 against a player with ELO 1900 first. Then I want to know this in relation to the said player ELO 2000 v another with ELO 1800.