TITLE: Improving the Elo rating system to account for game results
QUESTION [8 upvotes]: I am looking for a ranking system for office table tennis. The popular option is the Elo rating system http://en.wikipedia.org/wiki/Elo_rating_system. This system is also popular in Chess I believe where the results are very binary (win or loss).
However in table tennis I'd like to take into account how much the player won by, if they won 21-9 this should be worth more than a 21-19 result. Similarly if they won by a greater margin against a higher ranking player it should be worth even more than the ELO system would normally grant. 
Has anyone encountered such a system? One that also takes into account the final score, not just the win.

REPLY [2 votes]: For this issue, I'd use the Margin to define a term between 0 and 1, here called $\mu$. The scores of Player A and Player B are A and B, respectively.
$$\mu_A=\frac{A}{A+B}$$ and $$\mu_B=\frac{B}{A+B}$$
however, for the final steps of this, we use the term $\mu_W$, which is the higher $\mu$ of the two.
In cases of a no-contest victory, the Winner would earn $\mu=1$, and the Loser would earn $\mu=0$.
In cases of ties, both players would earn $\mu=0.5$.
(In the following cases, A and B are interchangeable, depending on who is the Player in question)
In cases of smaller margins, the following limit holds true:
$$\mu_A=\lim_{A\to B}\frac{A}{A+B}=0.5$$
In cases of larger margins, the following limit holds true:
$$\mu_A=\lim_{(A-B)\to \infty}\frac{A}{A+B}=1$$
In reference to the scenario you provided $\mu_W=0.7$ in the case of 21-9, while $\mu_W=0.525$ in the case of 21-19. With these factors in mind, I posit that these factors should not be applied directly to the $S$ term in the following function, the recalculation in the Classical Elo: $$R'_A=K_A (S_A - E_A)$$
but, should be applied in this modification: $$R'_A=K_A^{\lambda^{\mu_W}} (S_A - E_A)$$ which, ultimately makes $K^\lambda$ a limit for the maximum movement, while keeping the movement at $K$ in cases of ties. I set $\lambda$ using the following: $$\lambda=1+\frac{\ln{y}}{\ln{K_A}}$$ with $y=2$ or $y=1.5$, although any $y$ could be used.