Please explain the Elo ranking system

[fruktansvärt]

The formula K x (W - p(D)) makes no sense to me.
Especially p(D). p times D? (Then why is an x used after K?)

Example: Alex (Elo 224) loses to Ben (Elo 173)
Alex has K factor 60, and probability of win 57%
Alex total Elo variation -34.32

How does the formula produce -34.32? I don't get it. And wikipedia didn't help.
Probably this has been answered on this forum before, but you can't search for Elo or system here.

[Romain672]

K-factor start at 60 and decrease over games played. It multiply your elo gain and loss by 60 (compared to x20 when having lots of games) to make you reach your real level more fastly.


-34.32/60=-0.572, i find your 57%.

So it look like he needed to win 57.2% of games, but lost, so lose -0.572 (*60) elo.
If it was a 2 players games and if he won, it seem he would have won +0.428 (*60) elo.


I have no idea how it work exactly, but that would be a really weird coincidence.

[dschingis27]

The rhs of the following formula explains p(D) (from wikipedia in the Mathematical details section about Elo rating system :

Elo.png (8.6 KiB) Viewed 531 times

R_A is the Elo of Alex.
R_B is the Elo of Ben

If you fill in the numbers from you example, you'll get the result 0.57=57%, the win probability of Alex.

Now back to K x (W - p(D)) . W is always either 1 (Alex wins) or 0 (Alex loses). If he loses, then he loses the following Elo points:

60 x (0 - 0.57) = -34.32.

[fruktansvärt]

Ah, ok.
EA = p(D). It's one variable. I wish BGA would include that formula in their F.A.Q., or linked to it.
Thanks, dschingis27!