For those of you who have seen The Social Network, you may remember Mark inviting his friend Eduardo to give him his chess algorithm at the beginning of the movie when Mark Zuckerberg creates Facemash.com. You may also remember the scribbles on the window:

and

As this equation seemed strangely familiar and a few minutes after absolutely not following the movie and only thinking about this equation boom! Epiphany, the Elo Rating System [4]. An algorithm/method used predominantly in chess but also in many other areas. The FIFA world ranking for instance, uses the Elo Rating system to rate the teams, same for tennis and many other games.

Facemash Harvard’s HotOrNot

Before we continue any further, let us define the words hot and ugly associated to girls. A hot girl is a girl with a higher ranking, and an ugly girl is a girl with a lower ranking. Following that logic, a normal girl is a girl at the top of a bell curve or in other words, a girl that is averagely ranked. No disrespect is meant to women in this article, I am simply outlining and trying to describe in concise, simple and understandable ways what the idea behind Facemash [1] was.

As explained in the movie, Facemash was quite simple. Not unlike hotornot.com, students went to a page and 2 random images of girls were picked and presented to them. The students then had to click on the hottest girl presented to them and then another set of two girls would be presented asking the students to repeat the same actions they had done.

The difference with hotornot was that the girls presented were all Harvard students. In other words, the students were rating girls of Harvard based on their looks (You can imagine why Mark got into trouble).

The algorithm used — The Elo Rating system briefly described further — insured a fair rating and ranking of the girls. A hot girl A winning over hot girl B girl would gain more points than winning (or being picked) against ugly girl C. Same goes for the following: ugly girl C wins over ugly girl D. ugly girl C gains “x” points in her general ranking. If ugly girl C wins over hot girl A then ugly girl C gains more points because the ranking of hot girl A is much higher than ugly girl D. The previous scenario is roughly what the algorithm implemented by Mark was doing. It was somewhat insuring a level of fairness despite the misogynistic nature of the product.

In today’s society, the Elo Rating system is used by many rating and ranking system to predict the outcome of matches but also insure a level of fairness between teams of different levels playing against each others.

The Fédération International de Football Association (FIFA) uses the Elo rating system to rank their teams. For instance, the payoff for Spain winning over Russia would be much smaller than the payoff if the United States were to win against the Netherlands (A bit of humour is always appreciated). Again, if you are interested, you could visit http://www.eloratings.net/ which shows the exchange of points in World Football.

Another example of this algorithm is a little game I like to play on miniclip.com called discpool. The goal is to win the most games against strong players to take their place in the global ranking. When you are registered you can amass points when winning over other players. If you are a strong player — Just like the hot girl, a strong player is a player with a high ranking — and you loose against a weak player —ugly girl — you loose more points than loosing against another strong player.

Following this logic, the weak player also gains more points winning against you, the stronger player, than winning against another weak player. If the simple rules of this algorithm weren’t followed, weak players could easily propulse themselves at the top of the ranking tables without being able to beat the stronger players.

Elo Rating

As per wikipedia says [3]:

The Elo rating system is a method for calculating the relative skill levels of players in two-player games.

Investigated a bit further, the Elo Rating system conceptually gives you the ability to execute two main operations. The first one is to calculate how strong a player is. By knowing how strong Player A is, it is fairly simple to deduce who is stronger between Player A and Player B and who has the greater chance of winning. However even if Player A is likely to be stronger in a two-player game against Player B, sometimes the latter will cause an outrage and beat stronger Player A. Moreover, Player A winning against Player B , who has a lower ranking than Player C doesn’t have the same repercussion on the final ranking of Player A. Winning against a stronger player will bring the total ranking of a player x higher. Same goes for loosing against a player who has a lower ranking than said player.

Remember, the rating of a player is inherently dependent of the ratings of the other opponents or other players in a tournament — The other members of the set.

Furthermore, using the Elo Rating system [4], one can establish a system to calculate the results of games, events, championships, etc. This calculation is known as the numerical Elo results.

The Elo rating system is quite simple yet elaborate. There are a few more variables than only the equation that Eduardo drew in the window however the Elo rating system is still accessible to almost everyone. There are numerous articles, papers, websites, research and writings online. If you are remotely interested in statistical analysis I would encourage you to read “The Rating of Chessplayers, past and present” ISBN 0-668-04721-6” [6] and trying out http://elo.divergentinformatics.com/ [5] which is an online Elo Rating calculator.

Links

[1] http://en.wikipedia.org/wiki/Facebook
[2] http://www.chesselo.com/
[3] http://en.wikipedia.org/wiki/FIFA_World_Rankings
[4] http://en.wikipedia.org/wiki/Elo_rating_system
[5] http://elo.divergentinformatics.com/
[6] http://www.ibookdb.net/isbn/0668047216