Secret of facemash

Eduardo scribbling the Elo's formula!

What made Zuckerberg’s facemash.com run. The Math.

[ in the movie at least! ]

The formula that Eduardo Saverin wrote on Mark’s dorm room window( in the movie ) is known as Elo’s Formula. Its main benefit is that you don’t need a pyramidal structure to find out the best team [ like the ones used by the Euro league or the IPL ]

It is normally used to rank chess players, and in many more sports, but can be applied to any sample which has 2 outcomes [winning or losing, voted up or down]. Draws are considered half a win and half a loss.

Diving into the math of Elo’s formula –

Expected scores of two players A and B can be expressed as –

E_A = frac 1 {1 + 10^{(R_B - R_A)/400}}.

E_B = frac 1 {1 + 10^{(R_A - R_B)/400}}.

where RA and RB are known as base ratings. To provide a level field, you can take both of these to be same, initially, implying that everybody is equally likely to win in a one-on-one ‘battle’

What is expectancy?

It is the probability of a player winning in a battle. So if A scores then EA is=1 and EB=0 [ note that, EA+EB=1 ]
So now you can work out the players’ new ratings.

Extending it to all the players –

Now you simply have to apply the same formula for every one-on-one battle, using the latest ratings, and when your server crashes, you have ranked any number of players who took part in only one on ones.

Is that all?

No! This is a very basic outline of the much more complex Elo’s formula. If you feel interested in it, go google!

Other formulas used in similar situations [ further reading ] –

Pythagorean Expectation

Glicko Rating et cetera

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