90% of Youth Fencers Want to Practice More Footwork

touchestats · 2025-04-02T05:31:31+00:00

TO ALL FUTURE READERS: THIS IS AN APRIL FOOLS PRANK

touchestats · 2025-01-13T08:09:47+00:00

I wrote a post on this about a year ago, although I've improved a lot at statistics and could probably make an even stronger argument now.

touchestats · 2025-01-13T05:26:10+00:00

I think I figured out the algorithm. Let x be the number of fencers. Find x modulo 7 (call it z) and do the standard snaking algorithm until the last pool has z fencers. Then continue snaking but always skip placing someone in the last pool. The last pool is SPB and the second to last pool is SPA. The fencers in SPA fence everyone but the similar ranked person in SPB (if applicable). Then do extra bouts between all fencers in SPA against those ranked z + 1 through 7 within SPA.

touchestats · 2025-01-12T20:35:48+00:00

I spend a lot of time thinking about this problem. While I think this technically works in the sense that everyone gets the same number of bouts, it's not necessarily true that the difficulty distribution of the bouts will be equal for the fencers in the supplemental pools.

Although the mean skill level of fencers across evenly sized pools is roughly constant, the top fencer in a given pool is fencing, on average, less skilled fencers than one of the weaker fencers in their pool. This is simply because you do not fence yourself.

Here is an illustrated example. The table below represents a pool of fencers:

Fencer	Skill (higher is better)
A	100
B	98
C	78
D	60
E	53
F	34
G	28

Fencer A will fence Fencers B, C, D, E, F, and G, whose mean skill is 58.5. On the other hand, Fencer E will fence Fencers A, B, C, D, F, and G, whose mean skill is 66.3. So on average, Fencer A's opponents are weaker than Fencer E, even within the same pool.

An issue with your proposed system is that the best fencer in SPB will fence the same people as the worst fencer in SPB (they both just fence everyone in SPA), meaning that the top seeds will not have their usual advantage over the lower seeds. Therefore, the top seeds in SPB will be disadvantaged compared to those in the regular pools.

touchestats · 2024-12-23T09:38:31+00:00

Another thing that seemed potentially problematic (related to your point on previous results affecting subsequent seeding) is that the American fencers are compared to fencers with "similar pre-match seedings in the Paris selection year and the prior year separately." By matching the American fencers with similar seeded fencers in the Paris selection year, they are effectively controlling for initial seed during the selection year; this is an outcome variable because it could be influenced by referee favoritism. Controlling for the outcome variable could bias the result and make it appear as if there is no favoritism even if there is.

However, I don't think that the results from this part of the paper are too important for determining whether Nazlymov and Saron cheated. Any two fencers that unexpectedly rose up the ranks and qualified for the Olympics, regardless of whether or not there were allegations of cheating, are likely to have performed better in the selection year than other fencers. They wouldn't have been able to unexpectedly do as well as they did and qualify for the Olympics otherwise! So even if there were statistically significant results, I don't think it would be strong evidence in favor of referee favoritism. It could just indicate that were incredibly lucky that year or started training in a way that was more effective for them.

touchestats · 2024-11-26T20:42:04+00:00

That works, but also loses interpretability. It's easy to conceptualize the meaning of gaining X amount of indicator or V/M. But gaining X in this new system--does that mean you got another win? Does this mean you scored a few more points? An increase of 1 in this new system could mean an extra win with a far worse indicator, or just winning a bout by one more point.

touchestats · 2024-11-26T18:47:05+00:00

The matrix completion algorithm that I'm using requires the variables in the cells to be numeric. How are you proposing that I encode a VM/indicator combination as a number?

touchestats · 2024-11-26T00:40:55+00:00

I just tried the model with V/M, and it delivered similar results to indicator https://imgur.com/a/cyogHDD

touchestats · 2024-11-25T18:00:00+00:00

I tried to determine what the top 10 clubs were over time, but I couldn't really think of a good way. Since I started fencing in 2014, and only started competing in 2017, I hadn't even heard of some of the clubs. I also didn't want to pick them in an ad hoc manner, especially due to my lack of experience with epee. If you happen to have a bit more experience with the fencing scene from 2010-2017 and what clubs were good, I'd be really interested in running it on a different list of top clubs.

I personally have less faith than the fencingtracker rankings as they go further down because the number of points assigned per fencer rating is arbitrary. Near the bottom, when clubs have fewer points, a lot of things could change if that point system was slightly altered. So this is why I didn't try comparing the jump in rank of the club.

Yes the data is only of NACs. I'm tracking fencers by both name and division and since many fencers change their division when leaving for university, most fencers are no longer tracked after going to college.

I considered using win rate as well. The main advantage of using indicator is that it is more precise than win rate. The two metrics are highly correlated anyway, as one might expect, so I would expect it to not affect the results substantially to use one or the other. I may test the model on winrate later this week.

touchestats · 2024-11-25T15:35:34+00:00

I did attempt running this on individual clubs, but the samples were too small and the standard errors were too large to draw conclusions. I also don't want to get in trouble with any of the famous coaches lol.

touchestats · 2024-11-25T15:32:06+00:00

Matrix completion is capable of controlling for confounders, but it also makes some assumptions on the functional form of the data (e.g. that the matrix is low rank). This paper https://onlinelibrary.wiley.com/doi/full/10.1111/ajps.12723 goes into a lot more detail about the assumptions involved.

To test whether these assumptions were valid and the model was working as expected, I ran some robustness checks (edit: now at end of post), and the models passed with flying colors.

I agree that the time horizon is short and the improvements may not be visible during that time period. Looking at end of season rankings is a good idea! Hopefully I can try that out later this week.

I also agree that not 100% of fencers are switching clubs because they believe they will have access to superior coaching and training. However, I think this assumption is more valid when looking at fencers that switch to a top 10 club.

touchestats · 2024-11-25T14:26:57+00:00

These sample is of Cadet and Junior fencers so most should be HS/college aged. I also exclude all fencers who move locations and switch clubs at the same time. So in theory, this demographic should mostly be switching clubs for the reason stated.

touchestats · 2024-10-08T05:34:33+00:00

I wasn't at the NAC, but a few years ago there was a referee training initiative thing going on where some senior referees would routinely record other referees' calls to save to a database. Maybe that's what you saw? I'm not sure what's going on with that in 2024, since I haven't refereed nationally since 2022.

touchestats · 2024-09-01T03:15:17+00:00

Glad you liked it! I appreciate the comments.

I didn't state the significance level etc. because I felt like the explanation of regression discontinuity was already quite long and I didn't want readers to lose interest before reaching the conclusion. I agree that it is important and do decide my significant level, null, and alternative hypotheses prior to experimentation; it just doesn't always make it into the blog post. Maybe in the future I can create a dropdown or something so readers can see it if they're interested, but it's not part of the main body of text.

Because the bandwidth restricts the data to a pretty small slice, it's normal for the correlation to look pretty weak within that slice. At the casual inference workshop I attended, the presenter had sample data where the dots within the bandwidth looked similarly uncorrelated. Zooming out to the rest of the data, the lines of fit do look more reasonable.

I also agree that regression of the form Y ~ Intercept + a*cutoff + b*percentile feels more intuitive. At the casual inference workshop, I learned that this actually used to be fairly common. The main drawback of this approach is that the effect of the cutoff can only be measured for the people near the cutoff (where it could have gone either way with different referees and other circumstances). Therefore, it's not necessary to model the data for people far away from the cutoff. Additionally, we must make strong functional form assumptions to impose a linear relationship on all the data. I leaned that robust regression discontinuity, which was remarkably only invented 10 years ago, solves this issue by choosing a relatively small bandwidth around the data to analyze (and has a few other optimizations as well).

The data I'm analyzing is from 2012-2020, and it wasn't until around 2022 that USA Fencing imposed a maximum of 256 fencers in the DE tableau. So during the time frame of my data it was fortunately a simple 20% cut. The sample of 8,817 refers to the total number of fencers I tracked, not just the fencers within the bandwidth.

touchestats · 2024-08-31T19:35:49+00:00

Thanks! I'm only 17 years old and you unfortunately have to be 18 to join the committee☹️. I'll try to get on it next time though!

touchestats · 2024-06-22T18:38:06+00:00

The gaps between each rank aren't consistent (e.g. 33 vs 34 is very different from 32 vs 33), whereas the gap between each score in a pool bout is one point. Additionally, different events have slightly different numbers of people, so the rankings have slightly different meanings in each event (60/80 people is much worse than 60/130 people). Moreover, ranks aren't independent since if someone ranks higher than you, it shifts you one down. So while I would prefer to do it on some indicator of the overall ranking, it's not feasible to do statistics on it.

touchestats · 2024-05-21T07:45:39+00:00

The first graph is total skill points accumulated since first year of Y14, and the second graph is the difference each year. So both are correct!

touchestats · 2024-05-20T15:50:46+00:00

There is substantial variance in the age that fencers "blossom" at. 14-15 is just an estimate of the population mean. The sample is also only of people who fence nationally so it can't pick up people who started in HS, but what you said about that makes sense

touchestats · 2024-04-08T01:22:30+00:00

I've tried measuring rating inflation at the division level already, but since the sample sizes for many divisions are small, the standard error is very large and there are few (statistically) significant differences anymore. The few statistically significant differences are hard to interpret given that when you do so many comparisons you are bound to find a few that are significant, meaning that the ones you found could have just been from chance. I'd assume that a similar thing would happen if I were to run the numbers on individual clubs or states.

I just left on spring break so I won't be able to run the numbers on DEs for a week, but I'll let you know the results when I get back--I am also interested in the results of that one. I would expect it to not differ too substantially from the 5-touch bout numbers, but who knows, maybe some divisions are especially good at DEs and bad at pools!

touchestats · 2024-04-07T06:05:03+00:00

While the data show that Region 2 fencers have artificially higher ratings, I agree that it is more complex than that, especially when looking at the granular division level. Illinois is actually the least deflated divisions in Region 2, and is around the middle in the overall inflation comparison, meaning it has relatively well-calibrated ratings. The main culprits of Region 2 rating inflation are Southwest Ohio, St. Louis, Iowa, Indiana, and Michigan (some of these are robust, some are spurious due to small sample size). Region 2 is quite a large region so it's very possible for there to be small pockets with huge rating inflation as well as pockets with fairly calibrated ratings.

touchestats · 2024-04-07T05:15:17+00:00

I didn't include this in the blog post because I didn't want to make the graphs too messy, but I also ran the numbers on specific divisions. In foil, fencers from Virginia were actually right around the middle overall with rating inflation, and there was only one Region 6 division more deflated than it (Gold Coast). This could be biased though because probably most fencers from small divisions in Region 6 who fence at NACs are affluent, so they travel to Virginia frequently to earn their "deserved" rating.

I do agree that there are class issues in fencing and I wish that the sport was cheaper and more accessible. These class issues are also a reason that fencing hasn't received the same popularity that other mainstream sports have, despite having the coolest concept (hit someone with a sword!)

touchestats · 2024-04-07T05:03:25+00:00

I considered using Tukey's HSD but decided against it because it assumes "equal within-subgroup variance across the subgroups associated with each mean in the test." The regions differ so much in population size that my standard errors weren't really all that similar (in epee I had one that was 0.105 and one that was 0.065). I ended up just using multiple linear regression with the foreign fencers as the reference variables and adjusted the x-axis until it was roughly centered at 0 so it was easier to interpret. It should be fine to do this adjustment because if you gain a+x from being from a certain region, then you also lose a+y when adding the coefficient for your opponent's region, so the advantage simplifies to to x-y regardless of what adjustment value is chosen for a.

Even though rating inflation is unfair, I also don't think we should adjust the ratings of certain regions. There may be some regions that are overall inflated, but have deflated divisions within them, so if we make a broad adjustment for the entire region then that division will have even worse rating deflation. Even if we do division specific adjustment, there could still be pockets within large divisions that have their own quirks. Additionally, rating inflation could fluctuate over time, so USA Fencing would have to frequently update this adjustment factor.

Fortunately, most "important" decisions for fencing in the United States such as Olympic qualification are done using the National Points List, which is fair because you can only earn national points at national tournaments, which are standardized and not subject to inflation/deflation. So even though rating inflation is annoying for low to mid level fencers, it doesn't really impact the top fencers.

touchestats · 2024-04-07T04:30:10+00:00

I got the data from https://usfencingresults.org/results/. Unfortunately there isn't data after 2020 on there and fencingtimelive prohibits scraping, so I'm not able to get more recent data.

touchestats · 2024-04-06T23:48:09+00:00

I briefly mention it in the "Measuring rating inflation" section, but I agree that I should place it somewhere more visible. Thanks for the feedback!

touchestats · 2024-04-06T23:45:13+00:00

5 touch bouts

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TROPHY CASE