Pools are a critical part of fencing. When you don’t perform well in pools, you often have a hard path in DEs and lose earlier than you would expect. In cases where the total number of competitors is not divisible by 7, it’s common to have uneven pool sizes, resulting in some fencers being assigned to pools of 6 while others are placed in pools of 7. The purpose of pools is to create a level playing field, giving both lower-seeded and higher-seeded fencers an opportunity to excel. This means that even less experienced fencers can potentially perform well by defeating stronger opponents within their respective pools, ultimately influencing their overall standing in the event. Despite the intention to ensure fairness, individuals in smaller pools face a disadvantage.
How are pools created?
Imagine a tournament with 20 fencers. This would normally be divided into two pools of 7 and one pool of 6. Typically, pools are made with a “snaking algorithm.” The first three seeded fencers would be in pools 1-3 respectively, and the rest of the pool would look something like this:
While the algorithm also aims to diversify clubs in a pool, for simplicity, let’s assume each tournament participant is from a different club.
Surprising pool results
Let’s say every one does “as expected” in pools, meaning that the higher seeded fencers always beat the lower seeded fencers. Let’s also assume that higher seeded fencers always have higher indicators than lower seeded fencers. The pool results would end up looking like this:
Fencers who are in the correct positions in the pool results are gray, fencers who are higher are green, and fencers who are lower are red.
Notice that how even though everyone did “as expected,” the pool results do not line up with the initial seeding. This is because the 4th seeded fencer, for example, is getting one less opportunity to win a pool bout than the 6th seeded fencer, since they are in a pool of 6. Therefore they will be lower in the pool results irrespective of indicator.
Since the 4th, 10th, and 16th seeded fencers are all two places lower than they should be in the pool results with an event with only 20 people, the effect is compounded in a larger event. For example, in an event with 139 people, the 20th, 60th, and 100th seeded fencers will be NINETEEN places lower than they should be in the pool results. This is quite significant.
Is this a real problem in tournaments?
You could argue that this is a hypothetical scenario and in tournaments small pools do not cause a disadvantage. However, the numbers prove otherwise. I looked at NAC events with at least 50 people and found that fencers in a pool of 6 do worse in their final result than their initial seed 57% of the time. This implies that being in a small pool is a disadvantage in real life. Specifically, people in pools of 6 tend to place about 4% lower than their initial seeding, meaning for a tournament with N people a fencer will place 0.04N lower than they should have (on average). Here is how many places lower someone would be in a tournament of 200 people.
Looking at rounds also indicates an advantage for pools of 7. Losing in an earlier round means that you lost one DE earlier than you should have to be able to make your initial seeding. People in pools of 7 have a 27% chance of getting eliminated in an earlier round than their initial seeding, as compared to 32% for people in a pool of 6.
What does this mean?
In conclusion, being in a small pool is a slight disadvantage, since the real world data show that people in smaller pools had lower final results on average than they should have. However, I wouldn’t say that it’s such a huge problem that the competition format should be changed. Luck plays a role in fencing, including opponent styles, injuries, and fatigue. Events with a prime number of participants necessitate uneven pool sizes, since those numbers only divide 1 and themselves, so it is impossible to rectify the issue. While it’s disheartening to encounter more unfairness in fencing, it’s an opportunity to practice resilience in the face of such challenges and disparities.
