Thursday, November 22, 2007

Prolegomena: The Disposition of True Ratings Progress, Wildcard, Essay Twelve

Colorodo, Land of Mountains, Snow, and Skies

You have all heard me rave about things like 29% or 34% or even 39.9% win ratios, and here is the article—to my way of thinking—which validates the significance of a steady diet of beating opponents higher up+ to us in elo. I found this a year or two ago, and took it to heart, nearly salivated over its every line.

My argument in brief is that there is a significant difference between the chess player, for example, who has 72% wins:

350w/ 140L/ 10d= 500 total games @ 350/500= 70.0%

and the player who has 31% wins--even if they have the same rating:

154w/ 308L/ 38d= 500 total games @ 154/500= 30.8% [1].

In so doing, the prior--to put it in different language--lost 140 of his games or only 28%. By definition this means that such a player did not beat many opponents with an elo much in excess of his own elo, since a 100 point disadvantage in elo should result in 66% loses and a 200 point handicap results in 90% of loses. As is well known, if we are underrated, our rating will ‘self correct' or raise upward until such time as this becomes true, and if we are overrated, it will fall downward until the elo performance curve becomes true. And as regards our assumption here--which is more than valid--is that our illustrative player with excess wins has almost always NOT faced some real numbers of players slightly above his rating and lost all of those games, but RATHER has won most of his games against those rated below him.

Mesa Verda, a Place of Ancient and Mystical Depth

That we loose more often than not to those rated above us and frequently beat those below us cannot be in doubt; the only issue is one of degree, and what it says of our progress in chess improvement. And with that, comes the classic notion that in playing a preponderance of players rated above us we will have our sins punished more rapidly, more frequently, and more reliably we will see more improvement, which also makes us a lot more competitive [2].

Without further ado [3], here is the article in full [4. note on permissions] by Colorodo National Master and chess teacher Todd Bardwick, NM:

Observations about Chess Rating Distribution and Progression
(Colorado Chess Informant - April 2003)

By NM Todd Bardwick

I will attempt to lay out the USCF over-the-board rating system and set out realistic expectations as a player (hopefully!) moves up the rating scale. (Of course, this is based on my subjective opinion as a player and teacher and the players that I polled from various rating levels.)

A rating is a numerical representation of a player’s approximate playing strength…mathematically based on the last twenty or so rated games played, weighted more heavily toward the most recent results. [For adult players with established ratings, an average rating over a reasonable period of time (or years) can be a quite accurate measure of true playing strength.]

The titles associated with USCF ratings, ranging from low to high are: Class E (under 1200), Class D (1200-1399), Class C (1400-1599), Class B (1600-1799), Class A (1800-1999), Expert (2000-2199), and Master (over 2200). There are higher levels of Master (SM, IM, and GM), but since less than 1% of all tournament players fall into this range, I will not focus on them here.

The tournament player’s USCF Quick Chess rating (G/29 or faster) will usually fall in the same range as his standard over-the-board rating. A good speed chess player will typically have a higher quick rating than his standard rating, and visa-versa for slower players.

USCF Standard over-the-board rating scale
The mean rating for adults is somewhere in the 1500’s. For discussion purposes, let’s say it is 1550. The rating distribution of tournament players tends to fall into a normal bell curve distribution about the 1550 mean. Approximately 70% of rated tournament adult players fall between 1200-1900. Statistically, 5% of rated players reach the Expert (2000) level, and 1% achieve the Master (2200) level. The rating scale is linear in nature.

Theoretically and mathematically, a player 200 points higher rated than his opponent is expected to win 3 out of 4 games. In other words, a 1200 rated player has the same odds of beating a 1400 as a 1800 rated player has beating a 2000. Overlaying the linear rating scale with the bell curve distribution of players, it is easy to see that the lower rated player has a much easier time improving his rating than a higher rated player. (This should be obvious since it is much easier for a 1000 rated player to reach 1700 than a 2100 to improve to 2800 …a world champion contender!!?). To understand how a player progresses through the ranks and develop realistic expectations, the linear rating scale must be overlapped over the normal rating distribution bell curve.

Adult rating increases are a separate topic than a child’s (discussed later). Every adult who has been playing chess for years will eventually reach his average rating plateau strength. This could be 1200, 1600, 2000, or anywhere else, depending on many factors (brain speed, calculating ability, study time and efficiency, ability to solve mathematical and logical problems, board game sense, concentration, competitiveness, intelligence, etc.) There are very high rated players who have spent many hundreds of less hours of study time than their much lower rated counterparts. I have met many low rated players who have read tons of books and can seemingly recite every game ever played, but somehow have trouble applying chess concepts to their own game. In this case there are normally several commonalities – too much opening study (sometimes spending time learning traps and garbage openings, which is mainly memorization… chess is not a finite problem that can be memorized), study of game collections of famous player where the concepts are too complex, or too stubborn/unteachable/unreceptive to new ideas or constructive criticism. As with any subject, the more you know about chess, the more you will realize you don’t know. With proper study, anyone can improve their chess game.

Many players falsely expect a linear move up the rating scale through the alphabet levels to expert, master, and beyond. This rarely happens. Normally players move up the rating scale in a stair step fashion. A plateau (small or large), then a vertical jump to the next plateau.
Most adults quickly reach the 1000 level. This is the first main plateau level that a player achieves where he generally sees very basic threats and doesn’t blunder away pieces on a frequent basis.

The next major plateau where many players stop at is the Class B range (1600-1799). The numerical rating jump here is quite large and perhaps intimidating, but the increase in chess knowledge is relatively small. The Class B player just has a better understanding (and more experience) and puts the basic concepts of the game together in a more efficient manner than the 1000 rated player. Remember with this rating jump, we are progressing through the meaty range of bell curve rating distribution. With proper coaching and/or a little natural talent, this rating jump from 1000 to Class B is easily attainable in 1-2 years.

Class B becomes a major sticking point for many players. In Class B, the player has a basic knowledge of all aspects of the game, has for the most part eliminated gross, random blunders, and has an understanding of the concepts of tactical and positional chess. Natural talent can take most players to Class B, but not much further.

After reaching Class B, the rating points get much tougher. As a player reaches 1800, he is statistically better than 80% or so of all rated adult chess players. In order to hold a Class A rating, now the player is expected to score 25% vs. Experts (95th percentile)...and Experts make very few mistakes compared to Class B and C players.

Reaching the 2000 level of Expert is a huge accomplishment (finally a rating that starts with a 2 instead of a 1!). Talent and study are generally required to reach and keep a 2000 rating. The Expert level is the third major rating plateau…and very few climb past it. Most players have several master skins by the time they reach 2000, but in order to hold an expert rating, the player must now score 1 out of 4 against masters…no easy task! The rating points are tough here because we are approaching the very narrow part of the rating bell curve. To move from the 95th percentile of Expert to the 99th percentile of master is a huge step. To hold a master rating, the player must score at least 75% against experts and break even with masters. It is well documented that the toughest 100 rating points to attain are between 2100 and 2200.

Children progress through the rating ranges in a similar fashion to adults (after all it is the same scale), except for a couple differences. For younger children (up to third grade), the first plateau of 1000 is quite pronounced and can take a while to reach. This is because young children are in the process of learning the concept of patience and tend to get excited easily, move too fast, and blunder frequently.

Assuming that a child is above average in ability and talent and has achieved the 1000 plateau, he will almost automatically gain 100 rating points/year do to maturity and increased mental discipline, even if he doesn’t study at all and only plays an occasional game, up to the Class B plateau. Talented children who are coached properly for just an hour a week (or study correctly on there own) and play in one tournament every month or two will jump on average 200-300 rating points/year from 1000 to Class B (1600-1800). This is why today there are half a dozen or so pre-teen children in Colorado who seem to have come from nowhere to Class B.

Realistic Expectations and consistency
It is important to temper your expectations, especially as you reach the main plateau levels of 1000, Class B, and Expert.

Take the case of the adult player who has reached a plateau and has been in the same rating range for years. The rating will tend to fluctuate +/- 100 points depending on whether the player is on a hot or a cold streak (for players rated below 1400, the fluctuation range will be greater). The player’s rating always tends to gravitate back to the mean. In any given game, a player with a stable rating tends to play +/- 200 rating points of his true strength depending on many intangibles: mental sharpness on the day in question, life situations, health, high or low tide, full or half moon, etc. This is why most Class A players have a Master skin to hang on the wall: 1900 + 200 = 2100, and 2300 – 200 = 2100.

Many players do not know that stability is built into the rating scale at the higher levels. For example, once a player goes over 2100, the total number of rating points gained (or lost) in a given game are multiplied by 75%. For players rated over 2300 the multiplier is 0.5. During the 1998 US Championships I asked GM Joel Benjamin (2662) a theoretical question…Did he think that his winning percentage against me (2230) would be higher than my winning percentage against an 1800 (assuming same rating differential)? Joel started to say it would probably be the same, but then thought a little longer and said that he liked his chances against me better because the higher rated player’s rating tends to be more stable.

How close are you to Master?
I will pose an interesting, non-scientific, question. To get a feel for this question, I polled half a dozen masters and a couple experts who have spent significant time over 2200. Their answers were amazingly consistent.

Question 1: “What average rating level would a player have to be at from a knowledge and skill level (ability to link chess concepts together) to reach the halfway point to 2200?”

Before answering this, several masters pointed out that at the higher levels raw talent and a high ability to link complex concepts together is an absolute must (or the player won’t ever make master) and it is assumed that the player in question possesses this ability, for their answer to apply.

Given this, the answers ranged consistently from 1800 – 1850.

Question 2: “Assuming that 1800 is the halfway point to master, what rating would be 75% of the way to 2200?

Again, the answers were quite consistent…2050-2100, with a slight bias toward the upper end of 2100.

This makes sense statistically. The mid-point between 1800 and 2200 is 2000. But remember we are overlaying this linear scale over the normal distribution. This finding may shock many high 2000 experts who think they are really close to 2200 (which they are by adding 100 points to their strength for good days…but the bad days also have to be averaged in!). But to hold a 2200 rating you must beat masters 50% of the time for the math to work out! Based on this poll, a 2075 rated player is, on average, three-fourths of the way to master. Remember, anyone who achieves an average rating of 2100 has a chance to surpass 2200 and get a master certificate from USCF…IF they put together a string of 3-4 good tournaments in a row .

Colorado ratings vs. the rest of the country
An interesting that you will hear from time to time is…”Are Colorado players better players for their ratings than players in other parts of the country?” I cannot answer this one for sure, but guess is probably not. We are kind of on an island in the middle of the country and one theory is that we beat ourselves up…keeping the overall rating pool lower. I played actively in San Diego for a year after college and honestly couldn’t tell any playing strength difference between masters and experts here and there. On the other side of the coin, many players who have moved here from Los Angeles claim that LA ratings are clearly inflated. I found that the overall consensus of players who have played in both Colorado and elsewhere seems to be that ratings are consistent between Colorado and the rest of the nation.

Today vs. 30 years ago
Another interesting question that pops up is…”Were masters of 30 years ago stronger than their counterparts today?” Pre-1960, before the Elo rating system was implemented, this may have been true. USCF has changed the rating formula several times over the years, usually after a significant portion of the membership bands together and starts whining about how their ratings are so low. When the USCF feels ratings have deflated, they add in a bonus point system to inflate them (the last time that happened was about 2 years ago). USCF has also created rating floors in recent years to prop up ratings. Today’s players would no doubt be stronger than their older counterpart in opening theory as a function of computers and our natural advantage in history. More old timers that not that I polled, feel there has been a general inflation in ratings over the years. I don’t have a solid opinion on this – both sides have compelling arguments. If there has been some inflation, it probably isn’t statistically significant.

Taking time off…how much would playing strength drop?
How much does a player’s strength drop after a few years sabbatical from the game? I would guess no more than 100 points for players over 1600, and those 100 points aren’t gone for long, but it may take a few tournaments to get the rust out. Opening book knowledge and accuracy in tactical calculating are probably most affected by taking time off.

Natural aging process
Unfortunately, aging is an unavoidable situation that also contributes to lower ratings. This would vary greatly from player to player and may start to take effect as a player reaches his 40’s (Remember two years ago during the Kasparov-Kramnik match where speculators where commenting on how Kasparov was over-the-hill, at the ripe old age of 37?) Positional judgment and calculation ability may start tapering off in the 40’s as a player loses stamina (many GM’s start declining in their 40’s). The age rating decline usually drops off even faster after 60. The good news here is that chess is a great mind stimulant for older people.

Losing one’s competitive spirit (a personality trait) as one ages, may also contribute to lower ratings. Older players may tend to be mellower, laid back, and more accepting in the ways of the world than younger players.

Positional vs. Tactical styles of play
Positional and tactical chess styles are sometimes viewed as opposites and good chess requires competence in both areas. (If you think of chess as a war, positional chess is the overall war plan and tactical chess would be the individual battles.)

Typically, tactical players are stronger speed chess players and also tend to do better in time pressure because with little time remaining, you must first look for tactics. Tactical players tend to be quicker and more accurate at calculating variations, whereas positional players tend to have a better understanding of the game in general. (Note: a type of hybrid-tactical player is the tricky player who looks for tricks and traps first. The tricky player is very dangerous in quick time controls, but much weaker in slower time controls where his opponent has time to figure things out.)

The tactical player’s rating range tends to be greater than the positional player because, by his nature, the tactical player is looking for the pretty win, not the sure win. (Comparing playing styles of players with the same relative rating strength, tactical players tend to have more wins and losses, while positional players have more draws.)

Personalities tend to have a strong correlation to chess style. The strong tactical player tends to be the eccentric genius type of person. This type of genius is tough to teach or emulate. The positional player tends to be more conservative in life and tends to be more practical and stable. In the few experiences that I have had giving simuls in prisons, I observed that prisoner’s styles tend to be overly aggressive and tactical in nature, an extreme personality trait that may have contributed to this person’s landing in prison in the first place!

Psyching yourself out over ratings
One quick tip on tournament play, I notice that many players refuse to look at their opponent’s ratings because they don’t want to psyche themselves out. I have never understood this reasoning. I would want to know my opponents rating, because it helps me to estimate probabilities of various outcomes and who is playing for what and for whom is a draw acceptable. I would accept a draw from Kasparov (if I was ever lucky enough to get one!) in positions that I would fight on against an Expert. Wouldn’t you want to know? If you tend to psyche yourself out over ratings, my only advice is, “Don’t do it!”

Mental toughness and attitude is probably a player’s greatest strength or weakness. When playing a player several hundred points lower rated, my opponent usually takes one of two attitudes…either “I’m in big trouble and will lose because I am playing a master (gulp?),” or “I have nothing to lose and this my chance to be a hero!!”. The player looking to be the hero has a chance; the intimidated player is usually lost before he pushes his first pawn!"

Video from the final round of the World Blitz Championship today, down to the final penultimate game between WCC Anand and world elo number two, Ivanchuk!

[1] These figures are the pro-rata portion of my recent ICC games versus wimpB, written of in my last post. The prior figures put Goodking in the extreme, at 69% wins, as shown at the table linked next at 2. immediately below:

[2] This same table attempts to concretely define competitiveness by quantifying this, in comparing a broad range of players faced in 50% of my games among only 14% of my opponents.

[3] One of the knights did link to this article in the last six months. I linked to it twice, a year ago. So I am not suggesting that this is completely unknown. And most important of all, my sincere thanks to my very good 'cyberfriend' Robert Pearson who among a series of emails between us somehow knew to tell me that he intended to publish or reproduce it, mid course in my Prolegomena series, when I had already mapped this out as one of my top Wild Card posts [5], and he was kind enough to forgo publishing it, knowing I intended to do so. Thank you Robert.

[4] I tried to contact Mr. Bardwick twice across several days after most assiduous web search for alternate email addresses among otherwise well hidden email, but never heard back from attempts to different sources, more than civil in the cyber world. We thought of calling him since he only lists a telephone, but this seemed way over the top. Hopefully he won't mind more free promotion. We indicate ALL his html links from his homepage. Thank you Todd, and thank you for a great article:

"INSTRUCTION CHESS ACADEMY of DENVER 13th Annual ROCKY MOUNTAIN CHESS CAMPS CHESS LESSONS ARTICLES Rocky Mountain News Chess Column Chess Life & School Mates CSCA Informant EVENTS Tournaments for Kids Simultaneous Chess Exhibitions BOOKS Teaching Chess in the 21st Century BIO National Master TODD BARDWICK Testimonials GENERAL INFO Chess Quotes Chess Sketches"

[5] Reassembler aught to be the next essay, but is not topical here, and will be: "Prolegomena To any Future Blogger Community, or ReAssembler, The Nimble Epicure: Essay Eleven". After I write that essay, I will reorder these posts to preserve the correct sequence.


Blogger likesforests said...

The paradox is that playing weaker opponents makes our statistics and rating appear higher. Currently my win% is 50% but you are right and I will try to lower it somewhat.

I checked out WimpC and WimpB and they seem like good tools. I am currently using Chessmaster XI for similar purposes. One advantage of CMXI is I can tell it to focus on a single opening like the QID. Then I can get lots of practice with the resulting middlegame positions and see how I handle different lines.

Thu Nov 22, 07:46:00 PM PST  
Blogger happyhippo said...

Thanks for sharing the article, dk.

It was a very good read.

One section caught my eye: "Positional vs. Tactical styles of play"

I find my playing style more to be a first positional-then-tactical style. By putting pieces into what looked like "natural-looking" positions and only then do I start looking at tactical possibilities. I am a firm believer of the "tactics only flow out of good positions" school. I think that while training tactics is very important, what is just as important is knowing how to get to the positions you want in order for tactics to work.

I don't see the position vs tactics style as a East v West scenario. I tend to equate one field flows out of the other and they complement each other rather than against each other.

And yes I am absolutely horrible at bullet chess.

Sun Nov 25, 10:49:00 AM PST  
Blogger BlunderProne said...


A very well thought out essay. On a prior occasion when I was on a "chess vission" quest, i ran into the Todd's article on ratings and improvement. It motivated me even more to continue to play stronger players.

I used to stick with the pack, and as a result had a rating associated with that comfort zone. It wasn't until I pushed myself did i see a spike in 300 points ( that and the completion of the circles). But I did find that i played MUCH better agaisnt a stronger opponent depsite winning fewer games.

The gmaes did manage to win gained me more points which compensated nicely the few points i would drop when I lost.

At local tournaments, i tend to play in sections where i am in the bottom 1/3rd of the "pack" else I jump to the next level and enjoy hte "lessons". At big tournaments, i made the mistake a couple times of playing " in my pack" at the top 1/3 and lost more rating points. It's hard because one likes to think with all the training you could get compensation ($$) but 9/10 of the time... I just lose.

Today I am on a mission. I've had my vision quest, I know the path, I must not veer from this.

Mon Nov 26, 10:30:00 AM PST  
Blogger Wahrheit said...

Excellent, I am glad that you have published this now, and indeed it's so much more colorful than what I would have put up that I will just direct readers over here to absorb your wonderful presentation.

Blunderprone on a vision quest is something that will be of World-Historical importance! I will be delighted to hear more!

Mon Nov 26, 04:00:00 PM PST  
Anonymous ChessTyro said...

Great article, haven't absorbed it fully yet, but found the positional vs tactical section most interesting.

I'm sort of from the same school as happyhippo, and I'm also quite pathetic at bullet and have long ago decided to not be involved in such "rubbish". :)

Tue Nov 27, 07:42:00 PM PST  
Anonymous Liquid Egg Product said...

I'm still working on getting back to class B, so calculating what percentage of the way that is to master can only serve to depress. (20%?)

Thu Nov 29, 06:55:00 AM PST  
Anonymous Anonymous said...

I was thinking of Maintaining a page with Chess Blogger information, that way if we play on FICS etc. or visit a Blogger's city we can meet up
[if we want to :) ]

The first step is to decide what to include:

Blog Name:
Real name: (optional)
Blogger Country:
Blogger City:

Handles :

what else?

Rating : (optional)


Please email response to : iwijetunge[at]yahoo[dot]com

Getting to 2000

Thu Nov 29, 09:21:00 AM PST  
Anonymous Anonymous said...

Comment by Dran Race
Over the past 5 years I have gone from 1600 to 2000. Most of the improvement is due to experiance. Over the past 5 years I have played thousands of turn based (postal chess via internet) games. I think it is possible to lay postal chess on ICC. I have also analysed many games using chess base and fritz. Only recently have I started reading books. However before I started my 5 years of "postal" chess I read several books. A few on my narrow selection of openings and combination challange were very helpful.

There was also a medical aspect to my improvement. I suffer from ADD and provigial helps. I also suffer from sleep apnea and a cpap machine helps. I used to be very inconsistent, and I knew at the start of the day weather I was going to play well. ADD and possibly sleep apnea can have a different impact from day to day. With these issues somewhat under control my play is more consistent. However How I feel is no longer a reliable indicator of how I play. I have also learned that 40 moves in 2hr is a better time control for me than game 30.

To become maaster I need to:
Further my study of tactics
master endgames
revamp my openings
improve my physical fitness.

poor endgame play is common amongst experts. While my endgame skill is not a weakness compared to weak experts 200-2100 it is weak compared to masters. I have a lot to learn here. Also I am far more likely to end up in an endgame that you would find in a book. Nearly all games between players below 2000 include one or more serious mistakes that preclude close endgame.

My openings are solid. However it is easy for black to equalize. When I was 1600 it was reasonable for me to say I am going to play this opening every game as white. I will learn to play it like a master. And eventually I shall do very well with it against players below 2000. Now that I want to become master I will have to play my slightly inferior opening like a senior master. That seems unlikely. I am too old and cant spend 60 hours a week on chess. therefore I will have to play openings that yield white a greater chance of retaining his intial edge.

It takes stamina to play a 6 hour game of chess. My favorite tournamnets require 2 six hour games per day. Actually 6 games in 2.75 days. Round 1 starts at 1pm and round six starts at 9am. And it is 4 hours out of 16 ince I sleep for 8. My mental endurance will increase with physical fitness. I will also be more comfortable with better muscle tone.

I hope my personal experiance might be helpful to others who hope to improve. You might find some of I say useful.

I forgot to mention that lessons with NM Nick Conticello during the 1990's had a huge impact. Recently I have been getting lessons from Yudasin. I have a far better chance of reaching 2200 if I continue my lesson with L.Y.

Tue Jan 17, 08:46:00 AM PST  

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