Could someone please explain to me or describe the graph of Elo ratings across all known players in the world today. I suggested to a friend that everytime you increase your Elo rating by 100 points you halve the number of players who are better than you. Is my statement roughly true, vaguely true or entirely erroneous? (Obviously I realize that there must be a top end where a 100 point increment would be impossible, but I am more talking about in the range from 1200-2000).
Originally posted by Anthony Patonusually, someone rated 200 pts higher than someone else, wins roughly 75% of the games against the lower rated guy. that's what professor elo suggested anyway.
Could someone please explain to me or describe the graph of Elo ratings across all known players in the world today. I suggested to a friend that everytime you increase your Elo rating by 100 points you halve the number of players who are better than you. Is my statement roughly true, vaguely true or entirely erroneous? (Obviously I realize that the ...[text shortened]... 0 point increment would be impossible, but I am more talking about in the range from 1200-2000).
Originally posted by Anthony PatonI don't have data for the entire world, but I do have USCF data. Assuming that the USCF data are fairly representative of the world data, your statement is entirely erroneous. Take a look at Figure 8 near the end of Mark Glickman's paper at this link - http://math.bu.edu/people/mg/papers/acjpaper.pdf
Is my statement roughly true, vaguely true or entirely erroneous?
In general, the number of better players reduced for every 100 rating points is much less than half.
For example, by just eyeballing Glickman's distribution chart, a rating increase from 1500 to 1600 would only reduce the players better than yourself by about 15 percent. Of course, the number will be a little different as you go to other parts of the distribution curve.
the amount of people you beat after every 100 pt increment is not linear (and has no pragmatic use here), as the elo system assumes a gaussian distribution. the cumulative distribution function is known, as is the rating function, so it is possible to calculate the increase of 'beatable players' after every 100 pt increment. not practical, though. it will vary very very much depending on what point of the curve you are. - 75% for every 200 pts difference is far more practical way to look at it.
Originally posted by wormwoodWormwood, while everything you said is completely correct, you seem to be trying to answer a question different from the one that Anthony asked. You seem to be saying that the answer to his question has no pragmatic use, so you decided to give him information unrelated to his question. It seems to me it would be simpler to just answer his question.
the amount of people you beat after every 100 pt increment is not linear (and has no pragmatic use here), as the elo system assumes a gaussian distribution. the cumulative distribution function is known, as is the rating function, so it is possible to calculate the increase of 'beatable players' after every 100 pt increment. not practical, though. it will v ...[text shortened]... the curve you are. - 75% for every 200 pts difference is far more practical way to look at it.
Originally posted by Mad RookIndeed.
Wormwood, while everything you said is completely correct, you seem to be trying to answer a question different from the one that Anthony asked. You seem to be saying that the answer to his question has no pragmatic use, so you decided to give him information unrelated to his question. It seems to me it would be simpler to just answer his question.
I started at my own rating (currently I am the 585th in the player tables). I checked various points and found the following (tables
were constructed Jan 15 2007):
Position Ranking
==============
1170 1634
585 1743
292 1846
146 1951
73 2057
37 2136
18 2218
9 2315
Actually not far from each 100 points halving the number of better players. Whether this is of practical value or not, I can't say, but it is at least interesting.
Techsouth, your RHP ranking numbers are intriguing. The RHP distribution curve seems to be much narrower than the USCF distribution curve (assuming I haven't misinterpreted the USCF curve). Using the RHP data, it seems Anthony is about correct in his statement, but using the USCF data, he seems to be way off the mark. Is it possible that correspondence chess has a much more compressed distribution curve than OTB? No answers from me, but just wondering.
Originally posted by techsouththat's because you're looking only at the highest 1170/16067 = 7.28%. the tail of the gaussian is almost linear on that area.
Actually not far from each 100 points halving the number of better players. Whether this is of practical value or not, I can't say, but it is at least interesting.
Originally posted by Mad RookI am not sure how to access the USCF data in a useful form. Of course I can look up anyone's rating.
Techsouth, your RHP ranking numbers are intriguing. The RHP distribution curve seems to be much narrower than the USCF distribution curve (assuming I haven't misinterpreted the USCF curve). Using the RHP data, it seems Anthony is about correct in his statement, but using the USCF data, he seems to be way off the mark. Is it possible that correspondence ches ...[text shortened]... has a much more compressed distribution curve than OTB? No answers from me, but just wondering.
One thing that may cause a difference is that RHP constucts a table consisting only of those who have moved in the last 100 days (i.e. active players). I am not sure how the USCF would construct their tables, but there are numerous kids who get involved for a short while and drop out quickly. This type of thing can create a serious unbalance in distribution, although I don't guess even that would make a difference if you only look at the upper half of the distribution.
Originally posted by wormwoodRHP Player Table Data
that's because you're looking only at the highest 1170/16067 = 7.28%. the tail of the gaussian is almost linear on that area.
Rank Rating
=============
7436 1300
4650 1400
2702 1500
1464 1600
Going back to almost the center of the RHP distribution curve (there are a little more than 16, 000 players in the list), the number of better players are not quite halved (about 63 percent), but the RHP data is still much more compressed than the USCF data (the comparable USCF number is around 80 to 90 percent, depending on whether you look at the 2002 USCF "Non-Scholastic Members" or the "All Members" distribution chart on the link that Wulebgr gave).
Originally posted by Mad RookIndeed, it does not seem to hold on USCF data. Although at the very highest range it does seem to be close. I wonder if they removed all players who have not played in the last 6 months where this distribution would be.
RHP Player Table Data
Rank Rating
=============
7436 1300
4650 1400
2702 1500
1464 1600
Going back to almost the center of the RHP distribution curve (there are a little more than 16, 000 players in the list), the number of better players are not quite halved (about 63 percent), but the RHP data is still much more compressed than the US ...[text shortened]... -Scholastic Members" or the "All Members" distribution chart on the link that Wulebgr gave).
Ranking PlayersAbove
=================
2500 160
2400 293
2300 540
2200 1241
2100 2073
2000 3533
1900 5502
1800 8187
1700 11286
1600 14783
(I didn't pull out scholastic players, but there numbers are insignificant at these levels).