### Are ratings commutative? General forum

8 replies. Last post: 2020-09-01

Are ratings commutative?

I don’t know whether a standard ELO or some other formula is used here, but in any case... let’s say I’m on track to win one game and lose one game against another (single) player, with a higher rating.  Will our final ratings be affected by the order in which these two games wrap up?

Let me say that this question is asked in a bemused, rather than competitive, spirit.

equally well, I could ask a similar question about the timing of, say, losing two games against two different players of different ratings...

• _syLph_ at 2020-09-01

If your goal is to have the higher elo at the end then i’m pretty sure it is better to lose first and win second.

Like lets say they both have 1k elo and its +50 for the one who wins and -50 for the one who loses. One of them will end up at 950 and the other at 1050. Then for the second game obviously it will be a rating change over 50 if the underdog wins for example 60 or whatever, then it would be like 950+60 and 1050-60 or something so in the end it’s 1010 and 990.

• David J Bush ★ at 2020-09-01

An explanation of the ratings here, and lots of other Little Golem stuff, are at the unofficial LG FAQ page.

• metzgerism at 2020-09-01

I intend to exhaust every possible method to beat you in our second game.

If that helps at all... :)

• Lip smacking talkers at 2020-09-01

http://www.edcollins.com/golem/
http://fatphil.org/lg/faq_full.html
https://en.wikipedia.org/wiki/Elo_rating_system

NewRating1 = Rating1 + K * { Result [ 1 + 10 (Rating2 – Rating1)/ 400 ] 1 }             K=32, Result=(0=loss,0.5=draw,1=win)

1500,1600 +win+loss 1529.17,1629.17 both gain 29.17 with rounding at both stages this is 30
1500,1600 +loss+win 1529.455,1629.455 both gain 29.455 with rounding at both stages this is 29 !

so will depend on exact ratings

• MisterCat at 2020-09-01

I say commutative; no plan to justify with computations here, or argue against point differences due to rounding, as above.

We use ELO in Chess tournaments, and your rating change is computed at the end of the tournament, including THE AVERAGE rating of the opponents you faced (and other stuff, such as points for win/loss, rating difference, etc.).  We all know how to find an average, do we not?  Since addition is commutative, so is ELO.

mc

• _syLph_ at 2020-09-01

i think its actually trivial to recognize that it isnt commutative if you exaggerate to like 10000 games in a row with either 5000 wins first or 5000 losses first. doesnt matter what my rating is after the first 5000 games, if i win 5000 games in a row at the end my rating will be high at the end and if i lose 5000 games in a row at the end my rating will be low at the end.