Interesting work.

This method makes implicit assumptions about the relative strengths of #100 ranked players across time, that will artificially inflate the ratings of players from times when the playing pool was smaller, e.g., Fischer. Today, the Earth's population is almost double what it was in 1970, and rapidly growing regions such as India and China have started to partake in elite chess only relatively recently. Just look at how the number of Soviet or Russian/Former-Soviet players has reduced from 15/19 on your 1971 list, to 7/14 in 2009.

Sonas' chessmetrics system makes a similar (bad) assumption, in fixing the average rating of the players ranked 3-20 (although that doesn't seem to check out if you crunch the chessmetrics numbers). I can sympathize with the problem - there's no really good way to normalize the ratings without having some measure of just how many players were active at any one time.

Well, I think this is debatable. The number of top-level tournaments is also greater today. Show me a top 100 list today and I will have heard of nearly all the players. I doubt I could do the same in 1970, and I certainly couldn't if we went even further back.

<That's what the list is based on. The population doubled, but nobody perceives #20 of today as "elitaire" as #10 of 1970. Also note, the list isn't intended to measure <strength>, it is intended to measure <domination> on the elite level. On the elite level and only there.>

Okay, I see what you're trying to do, and I agree that this is not a measure of objective strength. After all, a rating (be it Elo, chessmetrics or whatever) doesn't compare strength between eras, it only compares relative playing strengths in the same era. But I still have a problem with the argument - let me show you why:

Let us suppose for the sake of argument, that the strengths of chess players worldwide follow a bell curve with Elo rating. Now the point is, that if the playing pool becomes larger, the top 100 becomes a smaller slice of the tail of the distribution.

For example, suppose the total number of players is n = 10^5 (in reality there are many more than this), the mean rating is 2000, and the standard deviation is 150. Running a simulation of this, I find:

#1 - 2691
#2 - 2619
#3 - 2616
...
#100 - 2468

So the Delo rating of #1 is 2823. Running this simulation 10 times, I found an average Delo rating for the #1 player of <2817>.

Now, let's increase the total number of players to n = 10^6. Running a simulation of this, I find:

#1 - 2733
#2 - 2703
#3 - 2691
...
#100 - 2553

So now the Delo rating of #1 is 2781. Running this simulation 10 times, I found an average Delo rating for the #1 player of <2768>.

Now suppose I increase n to 10^7. Now the average Delo rating for the #1 player is <2754>.

You see what's happening - the larger the playing pool, the smaller the #1 Delo rating (all else being equal). So in practice, Fischer is being given a significant advantage by this approach.

Alex, Sonas observation is just a specific case of rating distance being kept over time between two absolute ranking positions. This doesn't hold for the vast majority of the ranking positions. I wrote about this here: zarg chessforum (empty ignore list needed, and it starts from the " Jeff showed a diagram where.." paragraph).

The whole idea of trying to conclude something from rating change over time of absolute ranks, when the pool size seriously increases, is completely wrong. Did you ever see anyone referring to IQ change over time of person ranked #X on the list? Absolute rank can only be relevant when the pool size doesn't change over time.

<whatthefat: After all, a rating (be it Elo, chessmetrics or whatever) doesn't compare strength between eras, it only compares relative playing strengths in the same era>

That's not very accurate, Fide desires that rating values will be kept over time, and they are currently studying the issue of rating inflation in order to try making this happen. Rating inflation would have been a none-issue for fide if rating was just supposed to measure temporal relative strength of each specific time.

I know that alex, that's why I don't understand why all of the sudden u decided that rectifying rating lists to #100 = 2500-rating was a good idea.

By doing that you are actually saying the opposite, namely that the #100 ranked player's rating has been unjustifiably increasing since 1985, and hence you need to "re-adjust" it to 2500 in order to compare dominance level from different periods.

You posted lists showing how wrong such an idea would be, and then for reason I didn't understand, you decided it was a good idea after all.

<but do you really think that the number of professionals grew like 15-fold in the last 40 years? Isn't it more so that in the modern world one can come further as an amateur?>

I don't think one comes on the expense of the other: That we have much more amateurs today thanks to a much handier accessibility and a lower rating floor, doesn't mean that we don't have more professionals as well. Having more amateurs increases the chance more of them can advance further (as you said), but that also mean that more of them would become professionals, or at least professionals to some period of time.

As I see it, the main reason the rating of #100 position has been constantly increasing, is because the number of players in the pool is constantly increasing, and the average chess level is increasing as well. Hence I see no reason to rectify the top 100 ratings like that in order to make such comparison, and surely not in such brutal way, reducing the modern players rating by 130 points..

<You talk about ranks being close to 2400 and say about possible influence of the change of K-factors at this level. But note: the gap to #100 remains constant, while #100 itself is moving, i.e. the rating of those ranks has moved too and is no longer around 2400...>

That's not very accurate, Fide desires that rating values will be kept over time, and they are currently studying the issue of rating inflation in order to try making this happen. Rating inflation would have been a none-issue for fide if rating was just supposed to measure temporal relative strength of each specific time.>

Consider this thought experiment:

Tomorrow, all chess players become objectively 400 Elo points stronger. So somebody who is rated 2100 today, will tomorrow play at the level that a 2500 player today plays at. Will anybody's ratings change as a result? No, of course not. All it means to be 400 rating points better than someone else is that on average you score 10/11 against them. If everyone's ratings shift simultaneously then there is no difference, because the Elo formula is designed to measure relative performance and nothing more.