An Elo score is a measure of power-ranking different parties in games or other activities and estimating the probability of victory if those parties were to face off against each other. It has an update procedure so that the scores change depending on who wins the match. Naturally, the winner gains points upon victory while the loser loses points. However, the size of the update varies based on the probability of victory. A heavy favorite defeating a major underdog will gain few points (and, correspondingly, the underdog will lose few points). Conversely, a major upset will result in a large point gain for the winner and a large point loss for the loser. The Elo score is most famously used in the chess world.
The Elo formula is intimidating at first but is easily understood upon examination. Formally it is:
RA,New=RA,Old+K(SA-EA)
The first term RA,Newrefers to the new rating for Player A after the outcome is determined. The second term RA,Old refers to Player A’s old rating. K is just a positive constant. SA is the outcome for player A (1 if they won, 0 if they lost). EAis the Elo updating value and is defined by the formula below:
EA = (1+10(1/400)(RB,old-RA,old))-1
As you can see in the formula, the key to the updating procedure is the difference between player B and player A. If Player B has a much higher rating than A, then the exponent on 10 will be much larger. Due to the -1 exponent on the whole (1+ 10…) term, the larger the exponent on 10, the smaller the value of EA. As a result, if SAis 1 (meaning player A won), then SA-EAis large and positive, and thus the update is large and positive. Conversely, if SAis 0 (meaning player A lost), then SA-EA is small and negative, meaning the update is small and negative.
Elo scores can thus be an effective measure of skill or accuracy.