ACF 3118316
FIDE 3201457
https://aus2020.chesschamp.net/
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Money is the cause of all evil!
Wrong
Lack of money is the cause of all evil!
That just shows how long it has been up for!
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According to my computations, his true performance rating is 2800.000263
I think it can be safely rounded to 2800.
I am assuming a normal distribution with standard deviation 200*sqrt(2) to calculate the expected score for each game, just like Elo originally proposed.
Yes to 6 decimals places. Using a normal distribution it is 2800.00026342 to 8 decimal places.
True.
Elo switched to a logistic function and introduced it years ago in the USCF calculations.
Using the logistic function it is 2800.21939096 to 8 decimal places.
Interestingly the FIDE rating regulations totally mess this all up.
The published tables which are what they actually use for calculations are based on the normal distribution.
However the approximating formula they list is the logistic formula.
Why they stick with the inferior normal distribution is anyone's guess.
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Mos Eisley spaceportThe toolbox. You will never find a more wretched hive of scum and villainy.
I suspect it has something to do with the bureaucratic nature of changing anything in FIDE.
BTW Do you have some reference to the argument Elo had at the time that the USCF switched? I believe it happened and in fact other people have said the same thing as you just adding that the USCF looked at a lot of data and determined the logistic distribution was better. But generally the logistic and normal distributions are difficult to distinguish without a very big dataset. A reference to the dataset or a graph of the data demonstrating the logistic distribution would be great.
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Mark Glickman's paper suggests (page 6) that the results are basically identical with either distribution, and it's just easier to calculate using the logistic - that was certainly my experience in implementing the Elo formula. (I tried to copy the relevant section, but Adobe Reader doesn't seem to like the format of the paper!)
Thanks Patrick I have the paper and can check it out. There are some figures in that paper but mostly they are generic although Figure 6 is constructed from a large dataset of actual games I don't think it is demonstrating that a particular distribution is better.
I also had problems with the paper that seems to totally mess with Adobe's search function as well.
So einfach wie möglich, aber nicht einfacher - Albert Einstein
I think the difference of normal vs logistic is a very minor issue for FIDE ratings.
There are far bigger problems with the Elo system as implemented by FIDE:
1. Between two rated players, the expected score is checked up from a table that provides very low precision (with modern computers, it is easy to compute it).
2. The "conversion from fractional score into rating differences" is also provided by a table: the fractional score is first rounded to two decimals(!), and then the table is consulted. Again, modern computers can provide a very precise answer in a very short time.
3. For unrated players, the ratings of the opponents are averaged. Again, using modern technology, it is easy to compute a "true performance rating". I understand that FIDE does not want anything like that for new players that score more than 50%, I think this issue can be (artificially) addressed.
4. The 400-point rule is artificial. Computing the expected score for each game individually, there is no need for it.
5. In complete round-robin tournaments, all the results of the unrated players count towards the rating of their opponents; but even if one game is missing they do not (they also do not count in other type of competitions, like Swiss system). In an extreme case, this is quite unfair. It is possible to rate all the games solving a non-linear optimization problem (the only requirement is that the unrated player does not lose all the games, and does not win all the games). The procedure described by FIDE is based on assumptions that rely heavily on all the games being played, just drop those assumptions.
I've made a webpage that takes a Vega cross table of a Swiss event and adds a (logistic) true-performance-rating column, with an option to replace ratings of zero with some other figure.
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It can be easily done in Excel, as long as the score is neither 0% or 100% (I am thinking of Elo system).
First, define a constant
sigma=200*sqrt(2)
Put the ratings of the opponents in a column (nothing else should be here), lets say A
Define
n=count(A:A)
Now, you might have the score of your player for each game, or the total score.
If you have the individual score, just add them up and compute the total score.
I am assuming 0 < TotalScore < n
You need now an initial guess. The average rating of the opponents should work well.
Lets call this TruePR
Now, take another column, lets say column B.
In cell B1 put
=norm.dist(TruePR, A1, sigma, TRUE)
Copy this to the lower cells.
Add this column B. Lets call this result ExpectedScore
What we want to achieve is ExpectedScore = TotalScore, by modifying the TruePR
In another cell, write
(ExpectedScore - TotalScore)^2
Now open the Solver.
The Objective is to Minimise the cell with (ExpectedScore - TotalScore)^2, by changing the TruePR.
No extra restrictions are needed.
You might need to repeat this a few times.
This can be generalised if you have two (or more) players with an unreliable rating (or even unrated), they have played among them, and need a TruePr.
Note: Pax uses a logistic distribution, while the Elo system is actually based on the normal distribution.
Greetings,
José.
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