View Full Version : Elo rating question for SMS: what K-factor is used in match comparisons?

27-11-2017, 18:47
I've done a lot reading on Elo rating systems, and have even put some work into laying out the math in some online calculation tools (see link below).

Elo Rating Calculator (http://turo.io/#K-factor%3A%0AK%20%3D%2012%0AStarting%20ratings%20for%20player%20a%20and%20b%3A%0ARa%20%3D%201600%0ARb%20%3D%201200%0AMatch%20score%20(1%20win%3B%200%20loss)%3A%0ASRa%20%3D%201%0ASRb%20%3D%200%0ATransformed%20ratings%20(makes%20computation%20easier)%3A%0ATRa%20%3D%2010%5E(Ra%2F400)%0ATRb%20%3D%2010%5E(Rb%2F400)%0AExpected%20outcome%20(win%20probability)%3A%0AERa%20%3D%20TRa%20%2F%20(TRa%20%2B%20TRb)%0AERb%20%3D%20TRb%20%2F%20(TRa%20%2B%20TRb)%0AResulting%20rating%20(after%20match)%3A%0ARRa%20%3D%20Ra%20%2B%20K%20%20(SRa%20-%20ERa)%0ARRb%20%3D%20Rb%20%2B%20K%20%20(SRb%20-%20ERb)%0ANet%20rating%3A%0ANRa%20%3D%20RRa%20-%20Ra%0ANRb%20%3D%20RRb%20-%20Rb%0A)

One question that I constantly encounter has to do with the methodology used to accommodate the multiplayer nature of online racing. Traditional Elo rating systems compare player versus player, while pCARS 2 must compare player versus multiple-players. My question boils down to this:

What K-factor is used in each comparison?

I have attempted some retro-fitting of the math on a couple of occasions, and have had mixed results. Sometimes I find that using a flat K-factor of 12 works, while in other cases, each comparison must be made with a K-factor equivalent to 12/(N-1), where N is the number of race participants. The comparisons are performed with each racer's starting rating, and a "net rating effect" is computed for each, then simply summed up into a single net rating effect value.

Can you share any insight into whether this matches up well with the Elo implementation used in pCARS 2?

01-12-2017, 21:56

Roger Prynne
01-12-2017, 22:04
I'll see if I can chase up a DEV to shed some light on it for you.

01-12-2017, 23:31
Thanks, Roger. It's not super important, obviously. More of a curiosity, but I've been developing some materials that explain the rating system, and knowing the K-factor would make the demonstrations a little more accurate :)