Ironically, my 9-5 job served as the foundation for Brunhild. I work in construction and wrote a scraper in Python to pull product specifications from construction front-end documents. Similar to ISU protocols, front-end docs follow predictable formats. Around the same time, I built a project-tracking dashboard with Shiny App.

Neither project was recognized fully (surprise!), and I stewed for a bit. I thought I had been sent on, not one but two, pointless sidequests where I devoted a lot of time and energy to building things that never saw the light of day. In hindsight, both experiences provided me with enough training to build Brunhild from the ground up.

I’ll stop yapping. Let’s take a look at the dashboard.

Head to the main page to filter results by season(s), gender, country, and competition. On any of the element tabs, you can sort by individual competition or season. As an FYI, these take a little longer to load than the main page. (The dashboard is currently hosted on the cheapest Amazon EC2 server tier.)

I’m proud to say there are over 58,000 elements in the database. After digging further into older protocols (shoutout to the Wayback Machine), the dataset now spans from the 2018-19 season to the present day.

Before 2022, protocol formats weren’t standardized. At first glance, they look the same, but they contain minor variations that make it hard to pull the data, so I ended up writing eight different scrapers for each format. I did my best to ensure that everything looks correct on the front end, but if you see anything that looks off, please let me know.

The biggest driver behind all this was fan accessibility to data. Just being able to look at scores is great, but I don’t want anything hidden behind a paywall. I also don’t want to be bombarded with advertisements. ISU protocols are free and publicly available, except that the numbers are buried in PDFs, so you can’t easily copy and paste the information into Excel.

That’s where Brunhild lands. I’m a sucker for a scatter plot, and pulled the data below from the dashboard. You can make your own chart too, using whatever stats you want!

I can’t believe how quickly everything has come together over the past three months. Without your support, I’m just spewing thoughts into the endless void of the internet.

Before I sign off, I have one tiny ask: I’m terrible at self-promotion. I’ve been relying on cold outreach and word-of-mouth for marketing Brunhild Analytics and Fullmetal Analyst. If you have a moment, I ask that you share both with anyone you think would be interested, whether it’s friends, family, or the person behind you in line at the grocery store. Every little bit helps!

I hope everyone has a lovely summer! Talk soon.

— Maddie

Whether it was his new haircut or the turbulent Olympics finally out of his rearview mirror, Malinin seemed looser and more relaxed on the ice. He posted a 111.29 short program score, eclipsing his previous personal best of 110.4. The model placed a 90th percentile short program at 111.48, which was within 0.19 points of his actual score. (See my previous article for a full explanation of the model.)

Earlier in the week, Malinin had practiced his signature quad axel, but left it out of his free program. Entering the free program (SP: 111.29), he held a 9.44 point lead over Adam Siao Him Fa (SP: 101.85), so the jump wasn’t needed. He generated a 218.11 free program score, landing in the 79th percentile of the sans-quad-axel scenario. Afterwards, he remarked, “I decided not to go for the quad Axel because I thought that would be a big risk, but I'm sure that that's not gonna be the last time you'll see it.”

It’s worth flagging the 79th percentile score. Malinin skated a level three step sequence (StSq3, BV: 3.30) in four of six programs over the 2025-26 season. Despite this, the model projected a level four step sequence (StSq4, BV: 3.90) at Worlds with the parameter set to 3.50. This was slightly below the 3.60 midpoint between the StSq3 and StSq4’s base value. Going forward, this is something to double-check to ensure I’m not overinflating any element. The quad lutz in his combination jump (4Lz+1Eu+3S) received a quarter call, but it still netted 17.44 points with the second half jump bonus.

A 79th percentile free program for Malinin was still 5.24 points ahead of Yuma Kagiyama’s 212.87 score. That’s not to discredit Kagiyama, who bounced back with a personal best free skate after a subpar short program. The spread between their final scores was 22.73 points.

Malinin’s free program landed within the predicted distribution, which is a reasonable result for the first version of the model. Overall, it placed a 329.22 total at the combined 90th percentile. His actual score was 329.40 for a difference of 0.18 points.

You might be wondering why the table shows 90th percentile outcomes for both segments when his free program ranked in the 79th percentile.

The combined percentile isn’t an average of the two segments. The model treats the short and free program as correlated events that drive a joint outcome. A skater who posted a strong short program usually carries their momentum into their free program. Malinin broke his short program ceiling and was no exception.

Moreover, percentiles aren’t linear data. They live inside their own distributions and can’t be treated like raw scores that you can sum/average. For example, the sum of the individual 90th percentile markers for the SP and FP is 334.25, but the combined 90th percentile is 329.22. Malinin’s 89th percentile short program paired with a 79th percentile free program produced a combined 90th percentile score.

Receipts

I originally ran the model on March 1st, twenty-three days before I tweeted the terminal screenshots. See below for the timestamp (ignore the random baseball-related spreadsheets and graphs).

Limitations

Admittedly, Malinin skating clean at Worlds was the best-case scenario for the model’s test run. A single competition is a promising start, but it’s not proof of concept… yet. The model had placed his 2026 Olympic score at the 2.5th percentile, so it wasn’t blind to worst-case scenarios.

Next Steps

Over the past month, I created a database for a more sophisticated prediction model by pulling historical protocols. I originally wasn’t going to touch the data until the late summer/early fall, but I realized that I could do something with it in the meantime. While conducting research for these pieces, I found myself aimlessly clicking through multiple websites for data and ran into several dead ends.

Some of the websites looked like they were coded when George W. Bush was still in office. I was unaccustomed to this, as baseball has a literal buffet of statistics websites to choose from. I channeled my frustration into building a figure skating dashboard to showcase historical averages and element-level data. Check it out here.

One thing worth noting: not every protocol is included in the database. It spans from the 2021-22 season to the present day. Some older competition websites looked sketchy, and I didn’t want to infect my computer with a virus, so I prioritized major events. I’m hoping the ISU eventually shifts to a standardized format to make it easier to pull protocols.

With the figure skating season wrapping up, I’d like to add a few features (including filtering by individual competition) to the dashboard before my attention fully shifts to baseball. Stay tuned, and go Red Sox!

Scoring Prediction Model TL;DR

My model is a Monte Carlo simulation that runs 100,000 scenarios based on individual element base values, historical grade of execution (GOE) distributions, and program component score (PCS) trends. It also considers that performance tends to be correlated within a program. If a skater is having a bad day, it affects their entire performance, not just one jump. It doesn’t assume a perfect track record equates to a zero percent chance of failure.

The model builds a margin of uncertainty, especially for elements with small sample sizes, e.g., a quad axel attempted 3 times in a season. Component scores rise and fall with technical performance. As discussed in Part 1, a natural extension would be an expected GOE metric (xGOE) derived from biomechanical data.

For the initial test run, I wanted to keep things simple and predict one skater’s score distribution. Why not Ilia Malinin? Having 6 different quad jumps in his arsenal is a game-changer. To a data nerd, he’s the most interesting skater in the world because of his volatility. Malinin’s scores have a wide distribution, a nearly 70-point spread between his best and worst scores over the 2025-26 season.

To start, I gathered data by pulling scores from ISU protocols. They all follow the same format, which made it fairly straightforward to extract the relevant information. The model factors Malinin’s elements from events across the 2025-26 skating season (the Lombardia Trophy, Grand Prix de France, Skate Canada, Grand Prix Final, U.S. Championships, and the 2026 Winter Olympics).

Limitations

Malinin’s element-level clean rates and scoring ranges reflect the simulation parameters calibrated specifically to his 2025-26 season data (see above) and may differ slightly from raw protocol averages. Moreover, the model only predicts Malinin’s score; it doesn’t simulate the rest of the field or compare him to other skaters. I also chose to exclude the Olympic team event because skaters can be more conservative or aggressive depending on their team’s needs.

This is only version one. Looking ahead, I’d like to incorporate individual judge-level scoring patterns, multiple seasons of data, and projected rankings alongside scores.

With these caveats in mind, let’s explore what the model says.

What’s in a quad?

Yeah, the quad axel is cool and attention-grabbing, but it also happens to be the most difficult jump to execute in the sport. The catch is that it doesn’t help or hurt Malinin’s average score. There’s only a 0.24 point difference between Malinin, including a quad axel, and not including it in his free program. The jump functions as a coin toss, expanding the range of outcomes.

With a quad axel, the range is about 64 points:

• 95th percentile: 336.28 points

• 5th percentile: 272.73 points

Without the quad axel, the range is about 58 points:

• 95th percentile: 333.03 points

• 5th percentile: 275.30 points

This isn’t a huge spread, and the model suggests the 4A is most valuable when trailing after the short program. Practice reports from journalists like Jackie Wong can signal whether Malinin plans to include the 4A, but the model quantifies what that decision means for his score distribution.

Malinin has attempted the jump three times over the 2025-26 season. At the Grand Prix Final, he slotted a quad axel into his solo jump, where it was quarter-called (-5.71 GOE). This contributed to a 94.05 point short program that left him in third. He later landed an elite 4A (+4.46 GOE) in his free program and won the competition. A couple of months later, at the Olympics, he ranked first after the short program and included the quad axel in his free program anyway. It popped to a 1A (-0.06 GOE), and his performance unraveled.

Any projection model has a blind spot for human nature, which factored into Malinin’s decision. In an interview following the Olympics, he said, “I think I would be much better to be known as ‘Quad God,’ as you say, rather than winning gold medal.”

Not All Quads Are Equal

Ball knowers are aware that the quad axel is a high-risk, high-reward jump. Unsurprisingly, it has the highest ceiling (18.4 points) and the lowest clean rate (38%). Meanwhile, the quad flip is Malinin’s safest bet, marking the highest clean rate (86%) and second-highest mean (15.3 points). Though the quad toe loop and quad salchow are generally considered “easier” quads, Malinin’s clean rates (65%, 58%) on them aren’t substantially greater than his quad lutz (64%), indicating they’re not the points insurance you’d expect them to be.

2026 Worlds Predictions

The quad axel is just one of 19 total elements in a skater’s entire program. Zoom out to the full competition, and the picture shifts. The red line is Malinin’s Olympics score, which was an extreme outlier (2.5th percentile event) compared to the rest of his season (the green range).

97.5% of the Worlds simulations fare better than Malinin’s Olympic score. The 309.9 median is lower than four of his six season results. The model factors the downside risk that the Olympics put on full display. His personal best of 333.81 points sits around the 93rd percentile.

The distribution’s left tail stretches further than the right, emphasizing that every elite skater carries more downside risk than upside. A figure skater’s routine needs to align perfectly, and they only have one shot to nail every element. Malinin can lose more than 10 points on a popped jump, but a perfectly executed one only gains a few extra points above base value. There’s almost no floor to how poorly a program can go, but the ceiling has a rough cap.

If anyone can break their ceiling, it’s the Quad God.

Looking forward to seeing how these predictions fare! Czech back here for Part Four.

Figure skating fandom is very cliquey, which I am 100% guilty of. Over the years, I’ve found myself rooting for skaters from various countries rather than defaulting to whatever team U.S. Figure Skating puts forward. (Sorry, Alex and Maia Shibutani. Mitchell and Claire are my favorite sibling ice dance pair.) Yet there’s something inherently likable about the U.S. figure skating team competing in Milan. They’re very memeable. Everyone seems to genuinely enjoy each other’s company. The cliquishness or hyper-competitiveness you normally see among figure skating teammates isn’t present. With Russia out of the picture, I was excited to see Team USA make its presence known on the biggest stage in the sport.

After winning the team figure skating event, Team USA hasn’t fared as well in the individual events. French pair Guillaume Cizeron and Laurence Fournier Beaudry narrowly edged U.S. skaters Madison Chock and Evan Bates by 1.43-points to take home gold in the Ice Dance event. The result sparked outrage online about whether Jézabel Dabouis, the French judge, showed bias towards Cizeron and Fournier Beaudry.

Figure skating is a sport of fractions, determined by subjective judges. To combat bias, figure skating’s rules delineate: “There will be a panel of a maximum of 9 Judges per segment. The scores of these Judges will form the result. Out of these scores, the highest and lowest score of each element or program component are ignored and the average will be taken from the remainder, generating the trimmed mean (average score).”

In the free dance, Cizeron and Fournier Beaudry’s twizzles were visibly out of sync. Dabouis (J1) was among the three judges (J3, J7) who graded the element a +3. One judge (J4) marked a 0, three (J2, J5, J6) gave them a +2, and two (J8 and J9) were generous with a +4. Dabouis wasn’t even off the mark here. The more pressing issue is the five-point spread on a poorly executed element.

Dabouis scored 10.00 for Cizeron and Fournier Beaudry’s composition in the free dance, as did another judge (J6). Only one of their scores was trimmed. She gave Chock and Bates a 9.50 (tied for the lowest). This is a half-point gap, factored by 2.00, on a narrow 1.43-point margin. In a sport of fractions, these small margins compounded into the difference between gold and silver on the sport’s biggest stage.

Just as fans are predisposed towards their favorite skaters, judges are no exception. Studies show nationalist bias is prevalent in the sport. Skatingscores.com (the closest thing to FanGraphs for figure skating) has a nifty National Bias O-Meter tool that indicates virtually every judge was more lenient toward their home country in scoring.

The ISU’s Official Assessment Commission reviews scores flagged as potential outliers. The commission consists of former ISU judges, technical controllers, and referees. The rub is that the baseline for comparison is the other judges on the panel. Financial audits require independent third-party accounting firms. Tennis has the International Tennis Integrity Association. Figure skating’s accountability chain is part of an insular ecosystem. It’s akin to the fox guarding the henhouse. If multiple judges skew in the same direction – whether from bias, political alliances, or plain groupthink – the commission sees consensus. “Safeguards” don’t catch incremental inflation across a full program.

What makes Dabouis’ pattern more troubling is that it wasn’t present from the start of the international competition season. At the 2025 Grand Prix de France, her scores for Cizeron and Fournier Beaudry were actually below the panel average. The bias emerged at the 2025 Grand Prix Final, continued at the 2025-26 European Championships, and culminated at the 2026 Winter Olympics. Moreover, she isn’t just one rogue judge. At the 2025 Finlandia Trophy, Christine Hurth, another French judge, demonstrated a similar bias, scoring her home country’s pair +5.73 points above the deviation in the rhythm dance and +3.84 points in the free dance.

If figure skating’s scoring system doesn’t fully account for human subjectivity, what if we reduced it by quantifying the sport?

Under-rotation occurs when a skater misses more than ¼ rotation (90 degrees) but less than ½ revolution (180 degrees). The base values of under-rotated jumps drop significantly. If a skater lands more than ½ revolution short, the jump is downgraded entirely. Under-rotations are notoriously difficult to call in real time. Motion capture technology could measure the exact degrees completed, negating discrepancies from an eye test.

Rotational velocity (how fast a skater spins in the air) could help predict which skaters are more likely to under-rotate under fatigue. Takeoff angles could explain why some skaters land certain jumps cleanly while others don’t. Jump height and air time could contextualize why some skaters have more margin for error than others.

The most tangible benefit of advanced analytics in figure skating is connecting biomechanical data to scoring outcomes. Historically, scoring has been determined by the eye test alone. Program Component Scores (PCS) and Grades of Execution (GOE), the most subjective parts of the scoring system, have measurable physical inputs, e.g., edge depth, speed, and ice coverage. These could establish quantitative baselines and build models that identify which metrics are the best predictors for PCS and GOE.

Baseball’s analytics revolution has evolved from debates over the significance of on-base percentage to analyzing biomechanical data tracking swing mechanics, pitch movement, and defensive tendencies. Expected statistics take physical outcomes, exit velocity, launch angle, and sprint speed to calculate what a player’s batting average, slugging percentage, or weighted on-base average should have been based on the quality of contact. Hitters directly control the exit velocity and launch angle of a batted ball, along with their sprint speed, but have no influence over what happens when the ball is put in play.

Expected stats remove defense from the equation to isolate what the player actually did. The gap between expected and actual tells you who’s overperforming or underperforming, and whether the results are driven by skill or luck.

Figure skating could implement the same framework for a different purpose. Skaters control their jump height, take-off angle, and rotational velocity, but after their program concludes, the outcome is in the judges’ hands. Expected scores would bridge the gap between what happened on the ice and what the judges graded. You could compare a jump’s measurable characteristics against a database of thousands of previous jumps, each paired with the scores they received. Then, measure the expected score against what the judges actually gave. If the same judge consistently inflates one team/skater’s score above their expected output while deflating their competitors, you have a paper trail of bias.

The discourse around controversial scores revolves around asking, “Did this judge score differently from the other judges?” With biomechanical data, you’re taking the analysis a step further by questioning, “Why did this judge score differently from what the data says happened?” Fans and the media would add a new layer to their analysis, and judges would be held to a new kind of accountability they’ve never faced before.

Advanced figure skating analytics are already underway, opening the floodgates for new information to help optimize performance, modernize the sport, and hold judges accountable. U.S. Figure Skating partnered with 4D Motion Sports, a wearable technology company. Some biomechanical data, like RPM and jump height, occasionally appear on NBC’s Olympic broadcast and NHK’s coverage in Japan.

Figure skating analytics are still in their infancy. There’s far more data to be captured than what’s currently being used, and we’re just scratching the surface.

Part Two will explore markerless motion capture technology’s application in figure skating. Stay tuned!