Subject: Now, Sharon... I meant no offence
Of course you fared better than a 0.3% win ratio against your opponents. My crazy friend would have against me, too, if only he had bothered to read even one chess book! Compared to the 20,000 chess masters on the planet, the rest of us are all poor players. Every 200 points on the ELO scale is a norm representing 3 times as much chess skill as the norm below! Consider that there are 15 such norms! If I can only beat someone 1 game out of 20, then I'm a poor player by comparison!
Regarding your suggestion that I "...may find it difficult to consider that there are many people that play chess as well as you", that too is relative. Among rated US players there are about 20,000 who play better and 60,000 who do not. If 1 in 5 people play chess, most at amateur level, then of the 1.25 billion players in the world, it is reasonable to portray my playing strength as sufficient to prevail over 1.15 billion of them! It's the remaining 100 million that *@#* me off. No, I am not a pushover by a long shot. When you propose that I "...overestimate your successes and underestimate the capabilities of others (compared to your skills)..." I can only say that you are exactly wrong, because the assessment of my playing strength is not my own. It is a coldly analytical appraisal predicated on the ELO system of measuring atheletic performance and it is furnished to me (and to every rated player) by the US Chess Federation.
Invented by Dr. Arpad Elo, the "father" of both Statistical Theory and Probability Theory, the ELO system incorporates both of those theories. As a chess historian and instructor, it's my duty to be able to explain it authoritatively. With only slight variance it is used by the US Chess Federation and FIDE (Fédération Internationale des Échecs - the World Chess Federation), and most of its 161 member nations.
I have never overestimated my skill. The ELO scale is a 3,000-point bell curve with a ±56-point standard deviation, tested in practice on chessplayers in millions of games. Its accuracy is proven with less than 2% margin of error. The deviation reflects real-world skill changes due to external factors. Most commonly, players' ratings strengthen with study and deteriorate with advanced age. A bad breakfast or spousal argument can lower a rating during the course of any given tournament game. Hence, the ±56-point standard deviation.
Ratings are acquired under fire. Unrateds acquire a Provisional Rating by playing 25 games against known rateds. This provides sufficient time to become accustomed to playing in strange venues against strange opponents, using the clock, and notating every move by both players - all requirements of rated play. A special formula is used during the first 8 games, after which the "standard" formula applies. After 25 rated games a player is deemed to have an Established Rating. Thereafter ratings fluctuate much less dramatically and are more predictable.
From the difference in ratings between any two opponents, a Win Expectancy Ratio is calculable, providing an indicator for predicting performance, which usually (but not always) conforms to expectation. Higher rated winners will win fewer points from beating lower rated players. Lower rated winners will conversely win significantly more points from upsetting higher-rate opponents. It's a handicap system. The ELO system is also used to evaluate athletes in a wide variety of sports pursuits.
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I never suggested that you had a 0.3% success rate but that is exactly what my crazy friend has against me! He only won one game out of 300!
Against an unrated, my playing strength is necessarily a projection. Everyone has a chess rating but most people have never bothered to establish it. Therefore, only rated players have known ratings. The rest of you are guessing. If it takes some sting out of my remarks, know that there are 10-year-old boys and 13-year-old girls who have ratings that insure victory against me in 99 out of 100 games. They are ultra-special, considering that adults with master ratings comprise an extremely rare elite echelon of fewer than 2% of all rated players! There are strong unrated players and the advent of chess computers and software provokes speculation about "closet masters". But when you speak of defeating other players in 3 or 4 moves, you are speaking about some very specific and well-known mating patterns. Since the Arabs began recording games in the 9th Century, all such patterns are well-known to seasoned club players who will never fall prey to any such easily-parried attempts.
When I stated that my exactly-in-the-middle (1516) rating places me in the 76th performance percentile of rated players, I qualified my remark by pointing out that this was due to a constant influx of children joining the US Chess Federation. If children stopped joining, my percentile status would plumment to about the 51st percentile to match my rating.
I have played only 63 rated games. But I have played hundreds of rated players in thousands of non-rated games, and I have played hundreds of non-rated players also in thousands of games. I started playing at age 16 and was active during 24 of my 57 years. Between 1983 and 1987 I played over 3,000 games per year! I would assert that any chess player who has invested 100 hours of book study will prevail 95 games out of 100 against anyone who has never studied. It is one thing to play 100 games against a friend and to win 95 of them. To take 95 of 100 games from me, one would have to have the equivalent of an Established Rating of at least 2030 and still wouldn't be a Master! To give you some idea of where I am in relation to all rated players:
2400-2999 = Senior Master (Highest rated player in world - Garry Kasparov at 2831)
2200-2399 = Master
2000-2199 = Candidate Master ("Expert" in USA)
1800-1999 = Class A
1600-1799 = Class B
1400-1599 = Class C (here's me, right in the middle)
1200-1399 = Class D
600-1199 = Class E
If you've never read through a chess book and if all your skill was acquired playiing friends who are similarly versed, then your rating would probably be about 1000. The Win Expectancy Ratio between a 1000 and my rating of 1512 - is 0.951:0.049. Essentially, the higher rating is predicted to win 95 of 100 games. To put it another way, the higher rated player enjoys a 95% chance of winning any one game against a player 500 rating points below. To my crazy friend who was sure that statistics would guarantee him a win sooner or later, I can only say, "Of course they do, but let us hope that it is still while we are young."
To appraise the US Chess Federation ELO formulas, click on this link:
http://math.bu.edu/people/mg/ratings/approx/approx.html
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