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The New Rules Book - Sidelights and Comments : V. Resolving Ties in Round-Robin
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October 1941
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The New Rules Book - Sidelights and Comments
V. RESOLVING TIES IN ROUND-ROBIN EVENTS
By MIGUEL A. DE - CAPRILES
Chairman of A. F. L. A. and I. C. F. A. Rules Committees
I had planned in this article to explain at length the general theory of round-robin competition, including the "pool" system which is followed in most of our individual contests and in some team events. However, this is the first issue of The Riposte since the untimely death of Dr. Scott D. Breckinridge, of Lexington, Kentucky, whose contributions to our sport are only inadequately acknowledged in the Preface of the Rules Book and elsewhere in this magazine. Consequently, it seemed a fitting, though small tribute, to devote part of this article to one of the many subjects in the Rules which interested Dr. Breckinridge, and to present only a brief survey of the theory of round-robin competition as background for that subject.
A. ROUND-ROBIN THEORY
In my experience, the round-robin and "pool" methods of conducting competitions have puzzled spectators who witness our championships for the first time. They think of fencing as a "match" sport, similar to tennis, squash, and boxing, in which one man pits his skill against his opponent’s in personal combat. Therefore, their natural reaction is that the loser of a fencing bout should be eliminated from the competition.
If you have had a similar experience, I suggest that you point out to your friends that the round-robin method is far from unusual. On the contrary, it is widely used in sports. Take, for instance, two of the most popular spectator-sports in this country; track and golf. It is true that occasionally we have foot races in which two contestants are matched; and "match play" golf tournaments are very common. But there are a great number of events in which each man competes, not against a single opponent, but against the whole field. "Medal play" in golf is similar in theory to a huge round-robin. Each starter in a final race is contesting against every other starter—again the round-robin idea.
From the complete round-robin to the "pool" method is but a short step. When the field is too large to permit a single round-robin, it becomes necessary to split the contestants into preliminary qualifying round-robins or "pools." Thus, we have qualifying events, conducted on the basis of "medal play," for the major golf tournaments. And the analogy to important foot-races is perfect: The contestants are first required to run in one or more "qualifying heats," often including preliminary, quarter-final and semi-final heats, before the final race. In each new "heat" or "pool," the qualified competitors start all even, regardless of their relative placing in the prior qualifying heat. This is exactly the theory of round-robin and "pool" competition in fencing.
I hope that this analysis will solve one of the questions most frequently raised. If Fencer A beats Fencer B in a preliminary pool, and both are drawn in a subsequent pool, Fencer A often feels that he should not be required to meet Fencer B again. From time to time we have suggestions that the victory in the early round should be carried forward to subsequent rounds. The adoption of such suggestions would destroy the fundamental concepts of round-robin competition—that a contestant in the round-robin is competing against all his rivals in the round-robin, and that all start the round-robin on an even basis. Victories in individual bouts count only for the purpose of determining the relative standing of the competitors in that round-robin, and for this purpose all such victories are of equal value, regardless of the identity of the defeated contestant. If a carryover were permitted to a subsequent round, the value of a bout won in a preliminary round-robin would be great or small depending upon whether the loser qualified or not; and also upon whether, if the loser qualified, he happened to be placed in the same subsequent "pool" as his conqueror. Obviously, such a situation would greatly complicate the problem of conducting competitions fairly and squarely.
B. RESOLVING TIES UNDER THE RULES
Let us remember, then, that bout victories in a round-robin are used only to calculate the relative "order of finish" in the round-robin. In fact, the original rules of the F.I.E., which are the foundation of our own, used to read as follows (when tied bouts were possible in epee): "Each victory shall count 2 points, a tie shall count 1 point, and a defeat 0 points." We have simplified the count, scoring 1 point for a victory, and in college matches, ½ for a tie. But the idea is the same: Bout victories simply give a fencer a number of points, toward his relative standing in the round-robin.
Now, the next problem, is that of resolving ties, when the number of bout victories or "points" in the round-robin are equal. One method of resolving the tie is to hold a fence-off; another is to refer to the touch-scores in the bouts of the round-robin and to determine the relative standing of the fencers on a count of touches received and scored. The present rules make use of both methods of "breaking" ties. (See, for example, Rule 46, page 42.) Historically speaking, there has been a good deal of change in the relative use of each method, according to the various situations which may arise.
Theoretically, the fence-off of all ties, regardless of the touch score in the bouts of the round-robin, is probably the soundest procedure. The trend is definitely in that direction. Thus, prior to 1932, all ties for qualifying places in preliminary "pools" in the Olympic Games were decided by counting touches. The same rule was followed in cases of ties for second and third places in the final round (although the fence-off for first place was even then an old custom). Then, in 1932, the Rules were amended to provide that, in case of ties in the semi-final, touches would not be counted but a fence-off would be ordered. Finally, in 1936, the fence-off rule was extended to all ties for qualification in any preliminary pool. Thus, the system of counting touches in the Olympic individual championships was used only to resolve ties for second and third places. We have followed suit to some extent: The rule of a fence-off for first place has been extended to all official competitions. (At one time, we used the rule only in championships; in other competitions, touches could be counted for first place.) Likewise, we have provided fence-offs for qualification for the final in the National Championships if the final pool consists of less than six fencers (Rule 87-d, page 60). The Intercollegiate Fencing Association during the last two years has gone even further than the 1936 Olympic Rules: All ties (for qualification or for final places) must be fenced off. But there are some practical difficulties in extending the rule in the A.F.L.A.
The most obvious difficulty—one which is often controlling—is the time element involved in a fence-off. The length of a competition may be increased beyond possible pre-calculation, and the majority of our competitions must of necessity be held within reasonable time limits. Another difficulty is that fencers involved in ties may be asked to compete in a substantially greater number of bouts than their other rivals, thus increasing their burden in a long competition. Therefore the continued use of the count of touches for settling ties.
C. COUNTING TOUCHES
It is in connection with the system of counting touches to "break" ties that I wish to tell you about Dr. Breckinridge's ideas. As you know, our rules provide that, in case of a tie in bout victories, the fencer who receives the least number of touches is the winner; touches scored by the fencers are counted only if there is an equality in bout victories and in touches received. Dr. Breckinridge was the originator of the "percentage" system of counting touches, designed to give simultaneous weight both to touches received and to touches scored. I quote his letter dated November 19, 1940, and an accompanying article:
"Dear Mr. de Capriles:
"A number of weeks ago, in a letter to me, you suggested that I make some form of presentation of the 'percentage system' of breaking ties, as you might wish to make use of it in discussions of the new Rule Book during the coming winter.
"I am enclosing such a discussion and thought that a prestatement as to the origin of the idea might interest you. I do not recall the exact date, but it was in 1914, '15, or '16. There was a triple tie for first place in the Jusserand Trophy Competition which was a regular annual event in Washington at that time. When the tie had been broken by the 'touches against' method, I was impressed by the fact that the score of the individual who won by this system was appreciably inferior to that of the individual who placed second. In seeking a cause, I was impressed by the fact that the 'touches against' system was based entirely upon a fencer's defensive efficiency, completely ignoring the touches made by him. Of course, in the final analysis, it is obvious that it is the touches made that decide victories. In the particular instance mentioned, I tried such an analysis and found that my impression was correct—that the No. 2 man had really been more efficient than the one who was declared winner by the 'touches against' system.
"If my accompanying discussion fails in clarity, or if there is any additional information that I can give, I hope that you will not hesitate to call upon me.
"Very sincerely yours,
(Signed) Scott D. Breckinridge.
D. PERCENTAGE SYSTEM OF BREAKING TIES
By Scott D. Breckinridge
"In the Rule Book we find the following statement: 'in the case of a tie in the number of bouts won ... the contestant receiving the lowest total of touches in all bouts ... shall be declared the winner.'
"It is obvious that this method of scoring absolutely ignores the offensive strength of both contestants, placing the decision upon defensive efficiency alone. It would seem equally obvious that in breaking a tie in number of bouts won, it is desirable to give equal weight to the offensive as to the defensive efficiency of each fencer. Such weight can be given in either of two ways, in the first by forming a fraction in which the number of touches made is the numerator and the number of touches received is the denominator; or, second, forming a fraction of which the number of touches made is the numerator and the sum of the touches made and received the denominator. Either of these fractions, when reduced to decimals, will show the efficiency of the fencer's offense, either as compared to his defense or as compared to his combined offense and defense.
"An example of superior fairness of this method of breaking a tie may be found in the following instance. Let us assume a seven-man round-robin in which two men tie for first place with five wins and two losses. Let us assume that one of these fencers, designated A, wins his five bouts by the score of 5 to 3 each and that the other fencer, designated B, wins four of his by the score of 5 to 3 and the fifth by the score of 5 to 4. Under the 'touches against' system fencer A is declared the winner without considering the two bouts lost, 'the touches against' in these bouts being equal. Let us assume that fencer A is defeated in both of these bouts by the decisive score of 5 to 2 and that fencer B loses both of his bouts by the close margin of 5 to 4. Upon close examination it is immediately evident that fencer B has given a stronger exhibition. Although he has won one of his bouts by a narrow margin, he has lost both of the lost bouts by an equally narrow margin. By the first method of the 'percentage system' fencer A has a common fraction of 29/25 or a decimal of 1.16. By the same system fencer B has a common fraction of 33/26 or a decimal of 1.269. This constitutes the 'unit of efficiency'. If the second method is employed we obtain the fraction by taking A's 'touches made' (29) as the numerator and the sum of his 'touches made' and 'touches against' (54) as the denominator, obtaining the fraction 29/54. By a similar process we obtain B's fraction 33/59. Reducing to decimals, we have A .537 plus and B .559 plus. This is the 'percentage of efficiency'. The giving of equal consideration to the offensive shows the definite general superiority of B, although the 'touches against' system has awarded the victory to A."
E. COMMENTS
Space does not permit a critical comparison of our system of counting touches and the "percentage" method invented by Dr. Breckinridge. Perhaps the opportunity will soon arise to present the argument for our present rules, and, I may say now, it is not a bad argument.
At any rate, after World War I, our Foreign Secretary, Mr. George H. Breed, recommended the percentage system for adoption by the F.I.E. in international competitions. The A.F.L.A. was asked to experiment with it, and from 1924 to 1928, we used the system officially. After this experience, the percentage method was dropped. The F.I.E. never adopted it, and it never was used in the Olympic Games.
It is interesting, nevertheless, to find that at least one division (Northern California) follows the percentage system (variation #2) in local competitions, and, for some esoteric reason, calls it the "Olympic Score."
The New Rules Book - Sidelights and Comments
The New Rules Book - Sidelights and Comments : II. Those Pesky Classifications
The New Rules Book - Sidelights and Comments : III. More About Classification
The New Rules Book - Sidelights and Comments : IV. The National Championship Tournament
The New Rules Book - Sidelights and Comments : V. Resolving Ties in Round-Robin
Sidelights on the New Rules Book : The Scoring System
Sidelights on the New Rules Book : A New Competitive Plan for the I.C.F.A.
