02 October 2017

The Harkness System Explained

My previous post on early U.S. chess ratings, The Harkness Rating System, ended with a direction for further investigation.

This was the first in a series of eight articles under the title 'How the Rating System Works'. I'll look at the following articles in the next post.

1952-05-20: That first Harkness article was in the 20 May 1952 edition of Chess Life (CL). Here is its first paragraph repeated:-

Many readers of CHESS LIFE were favorably impressed by our recent forecast of the results of the international tournament at Havana. With one or two exceptions, which we will hasten to explain now that the race is over, the predictions were about as near as you can come without the use of a crystal ball. [...]

1952-06-05: Following are the first paragraphs from subsequent articles in the series. They provide some insight into the technical underpinnings of the rating system.

The National Rating System, now in operation for two years, is like one of those mechanical brains you read about in the papers. Tournament results are fed in at one end and ratings come out at the other. The machine has no feelings or emotions. When presented with the results of a tournament, it pays no attention to fancy titles. The sponsors may call it a Masters' Tournament to Decide the Championship of Fifteen Counties; but the system adds up the ratings of the players, strikes an average, and calls the contest an 1843-point Class B event, if that is how it turns out.

If you win a tournament you get the highest rating. Others may claim that you were just lucky and got all the breaks, but the system looks at your score. It knows nothing about luck. Never heard of it. Sad to relate, though, the eagle eye of the rating system sees your name as clear as can be if it shows up at the bottom of the final standings. The machine measures your failures as well as your successes. This is not a one-way system. Your rating can go up or down. [...]


If your ambition is to become recognized as a chess Master the rating system gives you the opportunity to prove your ability and earn the title. In fact, the system will seek you out and shout Your name from the housetops. You are listed as a Master if you average 2300 points or more in at least two tournaments, not counting preliminaries. Or you are listed as an Expert if you average 2100 to 2299. Other officially rated players below the Expert division are grouped in Classes A, B, C and D, each class covering a range of 200 points.

In the upper echelons, there are grades of Masters, too. The common or garden variety ranges from 2300 to 2499. Above this comes the Senior Master class, between 2500 and 2699. At the top of the pyramid is the Grandmaster Class, from 2700 points up. The air up there is pretty thin.

Unless you live in one of the big chess centers, where strong players congregate, you cannot expect to qualify as a Master by playing only in local events. You can probably reach the rank of Expert, but you will not go beyond this point until you compete in stronger tournaments. [...]


The use of median values to represent the average strength of tournaments is one of the latest refinements of the rating system. As another example, we give below the results of the 1951 Pittsburgh Metropolitan Championship.

[list of 7 players in order of rating]

The sum of the ratings divided by the number of contestants (13,143 divided by 7) gives 1878 the average, but a player who made an even score in this company would not be entitled to such a high rating. The distortion is caused by the presence of one highly-rated expert among two Class A and four Class B players. In such cases, a median value is more accurate.

Since there is an odd number of contestants, one rating is at the middle of the list. Waltz' 1785 is lower than the top three and higher than the bottom three. However, one player's rating in such a small group may be off center, so we find a better medium value by averaging the three middle ratings. Thus, we add the figures 1922, 1785 and 1750 (the ratings of Taylor, Waltz and Leiter) for a total of 5,457, and divide by 3 to get an average of 1818 points for this tournament. [...]

1952-07-20: '5. Round Robin Performance Ratings'

After the average strength of a round-robin tournament has been determined, each player is given a performance rating. When there are ten or more rounds, the ratings are issued as follows:

1. A player who makes a 50% score gets the tournament average as his performance rating

2. A player who makes a score of more than 50% gets the tournament average plus 10 rating points for each percentage point of his score above 50%.

3. A player who makes a score of less than 50% gets the tournament average less 10 rating points for each percentage point of his score below 50%.

Applying these rules to the 1951 Log Cabin Chess Club Championship, performance ratings were issued as shown in the table below and in the chart [below].

1952-08-05: '6. Rating Short Tournaments'

When a tournament has ten or more rounds, the performance ratings are issued in proportion to the percentage scores, but this relationship cannot be maintained successfully when rating shorter tournaments. As the number of rounds decreases, ratings based on percentages become less and less accurate.

The natural inclination of a statistician is to reject competitive events that do not furnish data in sufficient quantities to use percentages. Fortunately, the popularity of short tournaments in the United States has forced us to labor and bring forth a practical method of evaluating performances in thew contests. A new measurement scale makes it possible for us to rate competitions with any number of rounds from one to nine and opens the way to rate team tournaments and matches, hitherto impossible.

The development of this yardstick required several weeks of unpaid labor in tests and experiments, but the result is beguilingly simple. We just substitute game scores for percentage scores. As before, a 50% score earns the tournament average. but for each half-game above or below an even score, a player gets the average plus or minus 50 rating points. This puts a necessary brake on the number of points that can be won or lost in a short tournament or match. [...]

The last two articles in the Harkness explanation of his rating system described rules for rating a Swiss System. I'll cover that in my next post in this series.

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