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More relevant than usual

novembro 24, 2011

Since we started speaking english, I believe that should keep it that way. No swedish, french, spanish or any other language are not globally known, so better safe than sorry. Really nice to meet all these people, that I’ll probably never see again in my life. Not that I care, but I should… Not relevant, moving right along, let’s make it interesting: Who was the best person I met?

Best way to resolve is comparing people. Like numbers, since they are mainly that to our perfect modern society <matrix>.  Anyway…  So I will compare two people we met. One play against the other, so we have a few players, listed later on this very same article, text, etc. I will use a very simple algorithm, previously used by someone who actually is the main reason that we are still connected.Just a basic explanation on the model, so you understand how it works.

Very simple. It can only be inferred from wins, losses, and draws against other players. A player’s rating depends on the ratings of his or her opponents, and the results scored against them. The relative difference in rating between two players determines an estimate for the expected score between them. Both the average and the spread of ratings can be arbitrarily chosen.

A player’s expected score is his probability of winning plus half his probability of drawing. Thus an expected score of 0.75 could represent a 75% chance of winning, 25% chance of losing, and 0% chance of drawing. On the other extreme it could represent a 50% chance of winning, 0% chance of losing, and 50% chance of drawing. The probability of drawing, as opposed to having a decisive result, will not be specified (yes, I’m lazy). Instead a draw is considered half a win and half a loss. <50% and 50% each, simple and faster>

If Player A has true strength Ra and Player B has true strength Rb, the exact formula for the expected score of Player A is: Ea = 1 / 1+10^(Rb-Ra)/400  

and so on for Player B: Eb= 1 / 1+10^(Ra-Rb)/400  

Also, Ea + Eb = 1, since the true strength of each player is unknown, the expected scores are calculated using the player’s current ratings. But the model also takes into consideration an expected score for each player. So girls are expected to score higher than guys. Argentineans are expected to score lower than everybody else and swedish are not expected to score at all. Sorry, had to make that joke… Couldn’t resist.

So when a player’s actual tournament scores exceed his expected scores, the system takes this as evidence that player’s rating is too low, and needs to be adjusted upward. Similarly when a player’s actual tournament scores fall short of his expected scores, that player’s rating is adjusted downward. The system’s original suggestion, which is still widely used, was a simple linear adjustment proportional to the amount by which a player overperformed or underperformed his expected score. The maximum possible adjustment per game (sometimes called theK-value) was set at K = 16 for masters and K = 32 for weaker players.

Supposing Player A was expected to score Ea points but actually scored Sa points. The formula for updating his rating is: R’a = Ra + K*(Sa – Ea).

An example to clarify things (only an EXAMPLE):

If Estefi Piacentini has a rating of 1613, and is compared 5 times. She loses to a player rated 1609 draws with a player rated 1477, defeats a player rated 1388, defeats a player rated 1586, and loses to a player rated 1720. Her actual score is (0 + 0.5 + 1 + 1 + 0) = 2.5. Her expected score, calculated according to the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) = 2.867. Therefore her new rating is (1613 + 32· (2.5 − 2.867)) = 1601, assuming that a K factor of 32 is used.

Note that while two wins, two losses, and one draw may seem like a par score, it is worse than expected for Estefi Piacentini because her opponents were lower rated on average. Therefore she is slightly penalized. If she had scored two wins, one loss, and two draws, for a total score of three points, that would have been slightly better than expected, and her new rating would have been (1613 + 32· (3 − 2.867)) = 1617. 

Makes sense? So, I came up with ratings for each and everyone of the people (players) we met in the trip and compared them all. Used the model above and got a few interesting results. But I don’t believe you want to know. If you do, I can forward it to you by email or inbox.

List of all players available when I share this on Facebook. And just to make this post interesting for most of you…

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