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Are Initial Seedings Good Predictors of Final Results in Cadet Men’s Epee, Foil and Saber Events at North American Cups (NACs)?

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Initial Seedings and Final Results

The relationship between initial seedings and the final place has been explored by a number of recent studies in a wide range of sports including basketball and tennis. However, there has been very little published research on fencing. In this post, we evaluate the strength of the relationship between initial seedings and final results for cadet men’s foil, epee and saber events at NACs in 2016-2017. We also determine if epee is less predictable than either foil or saber from a statistical perspective.

For the statisticians, Spearman’s rho is used to quantify the strength of the association between the two ranked variables, initial seedings and final results. Given the reasonably high correlation coefficients for the three weapons, we conclude that the initial seedings are a good predictor of the final results. Furthermore, we, find that the correlation coefficients for the weapon pairs of foil – epee and saber – epee are significantly different from each other. We can, therefore, conclude that the final results in epee were less dependent on initial seedings compared to either foil or saber. Epee is, therefore, less predictable than foil or saber, confirming statistically, what many readers already believe!

The seeding adopted by the USFA for national tournaments encompasses the concepts of delayed confrontation and rewarded sincerity. Delayed confrontation is the idea that the two strongest fencers in the direct elimination part of the tournament should not face each other until there are only two fencers remaining, or that the four strongest fencers should not face each other until there are only four fencers remaining, and so on.

Rewarded sincerity is the notion that the highest seeded fencer should have the least arduous path to the finals of the tournament, and that the weakest fencer should face the most difficult path to the finals. For an excellent expose of how the format of national tournaments work, read Will Spear’s article, “How to Follow Fencing (Part 1): National Tournament Structure” at Better Fencer.

The Analysis

For the purposes of our analysis, we used the data from four cadet NAC events between July 2016 and February 2017, beginning with the cadet events at the Summer Nationals in 2016 and ending with the cadet events at the Junior Olympics in 2017. The data can be found on the USA Fencing website. Results for 12 cadet men’s events (4 epee, 4 foil, and 4 saber) were tabulated in order to test the predictability of the three weapons. The events provided 893 foil results, 791 epee results, and 729 saber results.

The initial seedings were determined by National Cadet Rolling Point Standings, followed by classification (A, B, C, D, E, U) and within each classification by year in which the classification was last earned. Same class and year were randomized. In the case of tied results, we provided a rank equal to the average rank of all fencers with the same rank.

The relationship between the initial seedings and the final results for 893 entries in four Cadet Men’s Foil events is illustrated in the accompanying scatterplot. In this example, each dot shows one fencer’s initial seeding (x or horizontal axis) versus their final result (y or vertical axis). The two variables have a moderately positive linear association as the higher seeded fencers typically had a higher finish, whereas lower seeded fencers had a lower finish. While the overall tendency of the data is positive, it is not an absolute relationship. For example, even though fencers who were highly seeded typically had a higher finish, this was not always the case. For example, a number of fencers who were seeded in the top 50 and finished in the top 100 are observed in the scatter-plot.

The relationship between the initial seedings and the final results for 791 entries in four Cadet Men’s Epee events is illustrated in the accompanying scatterplot. Again, the two variables have a moderately positive linear association as the higher seeded fencers typically have a higher finish, whereas lower seeded fencers have a lower finish. While there appears to be a moderately positive linear association, it does not appear to be as strong as foil.

The relationship between the initial seedings and the final results for 729 entries in four Cadet Men’s Saber events is illustrated in the accompanying scatterplot. Again, the two variables have a moderately positive linear association as the higher seeded fencers typically have a higher finish, whereas lower seeded fencers have a lower finish.

Conclusions

Judging the strength of the relationships is difficult to do by simply looking at the scatter plots above. We, therefore, use Spearman’s rho to quantify the strength of the linear association between the two ranked variables, initial seeding and final results. The value of rho always falls between -1 and 1. The resulting rho values were foil: 0.805, saber: 0.799 and epee: 0.739. Foil and saber were almost identical. All three are different from zero at very high standards of statistical significance. (P=<.001)

We now determine whether the correlation coefficients are significantly different from each other by using the correlation coefficients and their associated sample sizes, foil 893, epee 791 and saber 738. Using the Fisher r-to-z transformations we found the probability value and the z-score for the significance test. A probability value of less than 0.05 indicates that two correlation coefficients are significantly different from each other.

Weapon Groups Z-score Probability
Foil & Saber

0.364

0.716

Foil & Epee

3.366

0.001

Saber & Epee

2.857

0.004

Source: National Fencing Club Rankings

We find that the correlation coefficients for the weapon pairs of foil – epee as well as saber – epee are significantly different from each other. We can, therefore, conclude that the final results in epee were less dependent on initial seedings compared to either foil or saber. Epee is, therefore, less predictable than either foil or saber. So, given the reasonably high correlation coefficients for the three weapons, we conclude that the initial seedings are a good predictor of the final results.

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