In a previous post, I wrote: **I have come up with another competition format that passes all criteria relating to fairness, weaker fencer experience, prior ranking information, and most of the resource utilization. It achieves all this by completely disregarding the second BC workload criteria, and using quite complicated mathematics (matrix operations) to sort the fencers based on their match results. That, however, is something to be covered in another blog post.**

Upon reconsideration, I have come to the conclusion that this competition format should be presented in several blog posts, rather than in one overwhelmingly long post. So, this is the start of a series of blog posts in which I lay out my proposed competition format. In this first installment, I limit myself to the specification of the proposed competition format.

Many readers will internally protest along these lines:* “What for? We already have a poule->DE competition format. What is wrong with that?”* To the last question, my answer is: several issues. Allow me to explore that in detail.

First, let us get the positives of the current system acknowledged. There are, for the purposes of this discussion, two important such positives:

**Fairness.**No fencer should have a path to the final in which he repeatedly gets paired up with easily beaten opponents, unless he has earned that privilege by fencing well previously in the competition.**Easy calculations for the competition leadership.**In the present system, all operations needed to perform the seeding, allocation of fencers into poules, ranking of fencers after poules, and ranking of fencers after DE are sorting, addition, subtraction, and division. If you do not worry about lub conflicts in the poules, there is no stage whatsoever in which a straightforward algorithm does not suffice. Should the computer fail, all calculations and steps can be done by hand, albeit significantly slower.

Those are two good things to have, which probably is why the current competition format was adopted. However, the demands of both those criteria in combination led to something that is not so good: lots of lopsided matches, both in the poule and DE stages. If fencers are to be ranked on their **raw** win/match quota and score index, the only way to make the competition fair is to make the poules as equally strong as possible, so that no fencer can coast along to a undeservedly high ranking going into the DE just by having the luck of getting into a poule filled with weak fencers, giving him many easy wins. This was prevented by using the Brazilian system of seeding fencers into poules, a system which ensures that the strongest poule in a competition is not significantly stronger than the weakest poule. So, the Brazilian system accomplishes what it is designed to do, but at a cost. In making the poules approximately equal in strength, it creates poules with lots of fencers of grossly disparate abilities in the same poule. Let us look at this by looking at what the Brazilian system does in a competition in which there are 36 entrants, which are put into 6 poules of 6 fencers each:

Poule 1 Poule 2 Poule 3 Poule 4 Poule 5 Poule 6

1 2 3 4 5 6

12 11 10 9 8 7

13 14 15 16 17 18

24 23 22 21 20 19

25 26 27 28 29 30

36 35 34 33 32 31

Look at poule 1. In a poule of six fencers, there will be 15 matches. How many of those can be expected to be hard-fought? In the case of poule 1, only two of them look promising in that regard – the matchups 12-13 and 24-25. The other matchups are between fencers who are separated by at least 11 steps on the initial ranking. Poules 3 and 4 are better in that regard, but not by much.

The lopsidedness does not stop there. If we for the moment assume that this competition has one round of poules and 100% promotion to DE, and that all matches in the poules went as predicted by the initial rankings, then we will start the DE rounds with an incomplete round of 64 featuring the matchups of 36-29, 35-30, 34-31, and 33-32. Those 4 DE matches will result in 4 losers, who are out of the competition and the competitive field is thus culled from 36 to 32, at which stage full DE rounds follow, each DE round culling the field by half.

Of those 4 DE matches, 3 will be reasonably competitive, but fencer ranked #36 in the initial ranking will end last without ever in the competition having faced an opponent whom he had any significant chance of winning against. Meanwhile, the fencer ranked #32 will have fought a DE match that probably pushed him to his outmost, only to face fencer ranked #1, whom has had the chance to rest during the first round of DE matches. It is not hard to guess how that match will go.

It can actually be proven that the current way of putting fencers into the DE tree is guaranteed to give as large amount of match lopsidedness as is possible. We see this in many competitions – the medal contenders wade through several DE matches in which they are not tested, their opponents are overwhelmed, and the referees are made to work in a blowout that anybody could have seen coming.

All this leads us to a third positive that a good competition format should have:

3. **High proportion of hard-fought matches.** The competition format should ensure that as many matches between fencers who are roughly equally matches as is possible.

The reader will now obviously think along the lines of: **“But why not simply combine all three positives in one competition format, and be done with it then?”**

This can be done. If all fencers fence in a giant poule without a subsequent DE tree, then we have maximum fairness, minimal DT calculation difficulty, and all matches between roughly equal fencers being fought. However, this competition format has one major drawback that makes it unfeasible for the great majority of competitions: The giant poule format is very resource-consuming, both for pistes, referees, and total time needed. It ensures that all hard-fought matches will be fought by seeing to it that all matchups will be fought, which leads to a whole lot of blowouts being fenced also. In addition, the giant poule format is not well suited to the viewers, since a winner can be theoretically sure of his win well in advance of the end of the competition, and it is difficult to keep track of all the interesting bouts since people are always moving around to their new piste.

The obvious fix to that is to avoid as much as possible fencing the bouts that can be predicted to become blowouts, but fence the rest. The simplest way of ensuring that is to put all the best fencers in one poule, the next best ones in poule #2, and so on until the weakest fencers get their own poule – and then rank all fencers in the first poule as #1-6, those in the 2nd poule as #7-12, and so on. That competition format gives all three positives, but there are several big drawbacks:

- There might not be a previous ranking upon which to assign fencers into poules.
- Fencers might come from different geographical regions with different ranking systems, making a fair comparison very difficult.
- If a fencer has improved a lot since his last competition affecting the ranking, he will be put into a far too weak a poule. He will coast through that poule, but he will not have any significant boost in the rankings after the poule compared to the poule. He will, at most, rise from the bottom of the poule to the top of it, but there is no even hypothetically possible way for him to rise in the rankings beyond that. That is not fair.
- If this poule assignment system is used in conjunction with the traditional DE placement used in the current competition format and there is a fencer who was grossly underrated coming into the poules, then that fencer will create a lot of lopsidedness in the DE tree. His first bout will feature two fencers whose combined strength is far and above that of the other matchups in that DE round, and the other matchups will be correspondingly weaker.

Those drawbacks are enough to consign this simple solution to the list of also-ran ideas.

So, we want to limit resource consumption to manageable levels, while at the same time having both fairness, low calculation workload for the DT, and a high proportion of the presumably hard-fought matches to be fought.

Taking the first as a given, we now find ourselves upon the horns of a trilemma. If we choose fairness and calculation workload, we get the current system. If we choose calculation workload and high proportion of hard-fought matches, we get the simple solution outlined above – but that had unacceptable drawbacks.

Instead, my proposed competitive format chooses to fulfill the limits of reasonable resource consumption, high fairness, and a high proportion of hard-fought matches. It does so by tossing the calculation workload criterion to the wind, and capitalizing upon the fact that computers have become much more capable since the time when the current competition format was decided upon.

The inner mathematical workings of that will be presented in the next blog post, in a condensed form.

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