# Forum for Rating Histogram Comparisons

The inclusion of chess data in particular makes this table senseless. It would appear that the lower possible rated chess player, is stronger than experienced Go players. But all beginners start out equal; ll the graphs should start from the same point to reflect this. Chess will top out lower than Go, but that's the reality, there are more levels of difficulty.

Let's remember that this chart does not represent Go playing strength: it represents the respective ways that system measure playing strength. Having chess in there at all is weird.

BTW it's not a histogram (otherwise known as a bar chart.)

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yoyoma: Re: Misleading (2008-02-15 03:32) [#4318]

What is the proper word instead of "histogram"?

tderz: Re: Misleading? Histo-/Nomogram (2008-02-15 16:31) [#4320]

actually I don't care what it is called - it's looks nice!

## Histogram

A graphical description of individual measured values in a data set that is organized according to the frequency or relative frequency of occurrence. A histogram illustrates the shape of the distribution of individual values in a data set along with information regarding the average and variation. (source: http://sqa.fyicenter.com/sqa/Glossary_17.html )

### Histogram:

A graphical display representing continuous data in different categories or groups. (source: http://mdk12.org/instruction/curriculum/mathematics/glossary.shtml)

## Nomogram

(Or alignment chart; also called nomograph, nomographic chart.) The graphical representation of an equation of three variables f(u, v, w) = 0, by means of three graphical scales (not necessarily straight), arranged in such a manner that any straight line, called an index line, cuts the scales in ... amsglossary.allenpress.com/glossary/browse

A mathematical device or model that shows relationships between things. For example, a nomogram of height and weight measurements can be used to find the surface area of a person, without doing the math, to determine the right dose of chemotherapy. ... www.stjude.org/glossary

Graphical assessment tool consisting of a three coplanar curves, each graduated for a different variable so that a straight line cutting all three curves intersects the related values of each variable. www.archlighting.com/industry-news.asp

A graph that enables one by the aid of a straight-edge to read off the value of a dependent variable when the value of two or more independent variables are given. www.sfsa.org/sfsa/glossary/deftrmnn.html

A graphical means of solving an equation. The 2 dimensional drawing allows for quick approximations. Nomograms are often used in stereology to make predictions about how much sampling is required to obtain a given CE. ... www.stereology.info/glossary/

Chart of scaled lines for facilitating calculations. A simple nomogram consists of three straight lines arranged in such a way that, when a straight-edge is placed so as to join values of two of the variables, the corresponding value of the third variable can be read off at the intersection of ... www.quarrying.org/dictionary/n.html

a graphic representation of numerical relations wordnet.princeton.edu/perl/webwn

A nomogram or nomograph is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a function. ... en.wikipedia.org/wiki/Nomogram

HermanHiddema: Re: Misleading (2008-02-15 11:54) [#4321]

Line chart/graph would be fine, I guess.

The name is beside the point however, nobody's claiming that it is a histogram.

AndyPierce: ((no subject)) (2008-02-13 16:41) [#4306]

Chess will top out lower than Go, but that's the reality, there are more levels of difficulty.

This is wrong. The x-axis is percentile, so it's perfectly reasonable to plot chess, or checkers or whatever on this graph.

The chess data is just there for reference, to see what kind of chess rating matches what kind of go strength

Furthermore, all the graphs top out at exactly the same point, which is the right side of the graph, at "top", just to the right of 99.9%

Also, all the graphs start out at exactly the same point, which is the left side of the graph, at 10%.

Also, saying that "the lower possible rated chess player, is stronger than experienced Go players" is meaningless in this context, stronger has no meaning when comparing players of different games, only when comparing players of the same game.

I have written a lot of text explaining the graph at Wikipedia's rank & ratings talk page, so read that for more on this.

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209.208.239.250: Re: reply (2008-02-13 20:32) [#4308]

Yes, in fact on 1/30 you wrote that the graph is "too complicated" and "qualifies for deletion or replacement." I agree, the same applies here.

HermanHiddema: Re: reply (2008-02-14 11:33) [#4310]

I disagree. This page is very specifically about the comparison between different rating histograms, it shows the raw data and the sources for that data. This graph exactly plots that data. In this context I think the image should stay.

209.208.239.250: Re: reply (2008-02-14 20:04) [#4315]

It is your privilege to disagree with your own writings, but the graph has been removed from Wikipedia.

HermanHiddema: Re: reply (2008-02-15 12:37) [#4323]

I just explained why I thought the graph should be on this page despite the fact that I agreed it caused confusion on the wikipedia page, how is that "disagreeing with my own writings"?

Also, I strongly suspect that although you are anonymous here, you are in fact wikipedia user kibiusa. If you are please say so, ok?

209.208.239.250: Re: reply (2008-02-15 14:46) [#4324]

yes

HermanHiddema: Re: reply (2008-02-15 16:23) [#4325]

Thanks, this way I won't have to repeat anything I have already written on wikipedia.

LukeNine45: ((no subject)) (2008-02-13 23:27) [#4309]

For what it's worth, I do not find the chart confusing. I think it's very useful.

LukeNine45: ((no subject)) (2008-02-14 18:55) [#4313]

One just needs to understand what it's saying; it's answering the question, "What do you call someone in the Xth percentile in the different systems?" Since the USCF and EGF give answers in the same "units" it seems perfectly fine to match them up even though the units mean different things in the different scales.

If anything, the part about it that's misleading is that the 5%, 95%, and following columns are spaced the same as the columns that are 10% apart. This gives the shape of the tails of the graph an unnatural shape.

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Unkx80: Re: ((no subject)) (2008-02-14 19:46) [#4314]

I agree with LukeNine45: I am okay with the rather interesting Go-chess comparison, and that the X-axis has a somewhat funny scale.

Interestingly, even when the X-axis is spaced at 10% apart, all three lines look almost linear and hardly have the S-shape that is the signature of most cumulative distribution curves, for most part of the curve anyway. Probably this is an artifact of such ratings?

velobici: Herman, is it meant to be a nomogram ? (2008-02-14 23:17) [#4316]

The graph clearly shows the distribution of ratings as percentile. A useful way of presenting the data. Perhaps there would not be a discussion if there were four graphs, one of AGA, one for EGF, one for KGS and one for USCF.

What appears confusing to me is that 100 points EGF and 100 point USCF (which now uses Glicko rating in place of Elo rating system) appear to be equivalent to 20k because they are at the same location vertically on the graph...people may be mislead to think that its a nomogram they are viewing.

Herman, is it meant to be a nomogram ?

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HermanHiddema: Re: Herman, is it meant to be a nomogram ? (2008-02-15 12:13) [#4322]

No its not meant to be a nomogram.

The reason 20k and EGF 100 are at the same height in the graph, is because the EGF defines 20k as Elo 100.

Basically, these are four graphs, put into one image. In principle, therefore, it should have 4 y-axis scales, one for USCF, one for EGF, one for AGA and one for KGS. I have made a choice to use only two y-axis scales, because both EGF and USCF have ratings in the range 100-2900, and both the AGA and KGS use kyu/dan grades in the range 30k-9d (roughly). Furthermore, I have chosen to line up the left and right y-axis scales with the EGF standard 100 = 20k, 2000 = 1k, 2100 = 1d, etc.

As already discussed at wikipedia, points in different graphs that are in the same place vertically are not related. Points that are in the same place horizontally are related.

Example: You have rating 2000 USCF, and are curious what that is equivalent to in go. Find the point where the USCF graph crosses 2000, which is at about 90%. Then move straight up to see where the other graphs cross that percentile, which is (roughly) 2200 EGF (2 dan), 3 dan KGS and 5 dan AGA.

velobici: Limitations and Arpad Elo on rating systems (2008-02-14 23:09) [#4317]

Please recognize that the graph presents a distribution of ratings in four systems, each of which tries to assign a numeric value to a changing characteristic of an individual based upon a very sparse sampling of that individuals performance against a small number of other individuals. As such, it is quite hard not to read too much into the data. But Arpad Elo is a good bit more eloquent that I

Often people who are not familiar with the nature and limitations of statistical methods tend to expect too much of the rating system. Ratings provide merely a comparison of performances, no more and no less. The measurement of the performance of an individual is always made relative to the performance of his competitors and both the performance of the player and of his opponents are subject to much the same random fluctutations. The measurement of the rating of an individual might well be compared with the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind.

yoyoma: ((no subject)) (2008-02-15 03:45) [#4319]

I originally put together this page with the table only. My main goal was to enable someone to say such things as: I am 1950 USCF and 1d KGS. What percentile of the relevant population am I for these? Am I in a higher percentile in one or the other? Or approximately the same?

The graph is pretty, but it is not immediately obvious how to make these judgments from the graph. The first thought would be to look at the Y-axis and make them equivalent, but this is wrong.

Finally if the graph is kept, I think the X-axis must be fixed to be linear instead of distorted at the <10% and >90% edges.

I would also prefer that the EGF ratings be given in kyu/dan instead of the Elo numbers, because the Elo numbers use a very different formula than USCF numbers.

81.204.223.161: Switching the axes in the diagram? (2008-11-19 20:49) [#5302]

I think it would be clearer if the diagram would have the percentile axis oriented vertically. Because after all, the percentile is supposed to be the "real" measure of skill level (the word "level" itself suggests a vertical orientation).

Then I can look up the skill level associated with a 2700 AGA rating or a 2200 USCF rating.