Elo rating system (my thoughts)

[ELO Evangelist]

The fact that you have entered this thread means you probably know what an ELO rating system is but in case you do not here is a brief explanation. Arpad Elo a physics professor and chess master realised that chess needed an accurate ranking system and in the 1970 devised a system based on statistical estimation over a natural distribution curve. This system of statistical estimation is widely regarded as the most accurate mathematical model for predicting probabilistic outcomes. It is used today by many sports but has been improved many times along the way, and herein lies the problem, not all ELO rating systems are created equal. Different organisations use different ELO rating systems with differing degrees of accuracy. You would think that an organisation would want it's rating to be accurate but as we know this is not the case. Take FIFA's 3 points for a win and 1 point for a draw regardless of oppositions strength or whether the match was home or away. We know this system can at best only be described as moderately accurate. The same goes for many ELO systems used at the moment. Ease of use overrides mathematical complexity and as a consequence accuracy suffers also. Of the 3 most widely used natural distribution curves

Gaussian (normal), Logistic and Poisson, Arpad chose the normal curve to model chess but this turned out to be not the most accurate and the Logistic is now used by some chess federations and the normal is used by others. Another shortcoming of Arpad's original ELO system was the K factor it was found that early in a ranking estimation the value should be large and then as the team or player's rating (μ [pronounced miu] value) is known then this factor should be reduced. The answer to this problem became ELO systems with clumsy stepped K factors as the rating became higher or constant K factors. Whilst at university reading computer science I found myself helping one of my maths professors code a custom ELO algorithm. The work was being done by the university for a major Internet IT company for the primary purpose of page ranking. The System the maths team created was mind numbingly complicated but featured algorithms that create it's own custom distribution curve and a variable K factor. One more thing that this system could do that most ELO algorithms can not is take into account draws and the affect they have on the win loss distribution variance accurately. Since being exposed to this algorithm and writing most of the code for it I have become an evangelist for ELO based systems ever since and have been using them to my advantage for a few years. You would not believe the number of punters I know that think the existing soccer league tables are accurate. I regularly search for ELO based research papers to see if the system that my university devised and is in daily use by millions of Internet users has been surpassed but it seems still to be the best. It is a strange fact that organisations not not require their ELO systems to be as accurate as possible. Take the FIFA world rankings or most domestic ELO systems you will come across. They average together home and away performance to give and average ELO rating because they think your average soccer fan can not understand a system more complicated than a single figure. So keep up the good work guys because I think in a few years time everyone will know about ELO based ranking systems because the computing power needed to use them is now on every one's desktop. You can guarantee that the pro syndicates and the bookmakers have been using ELO systems for years.

[carlos50]

Re: Elo rating system (my thoughts) Is there a research paper about the algorithm you helped build? Other main research papers you can recommend?