Hey everyone, IOI2026 is over! Congratulations to everyone who participated for their hard efforts. While all the contestants were struggling to solve the problems, I had some free time so I looked into some stats.

Some notes before we get into things:

• It is entirely possible that some of these are wrong/incomplete/misleading. I only made these to satisfy my own curiosity, and they are not an authoritative source
• I expect this to be particularly true for medal cutoffs, where I have not accounted for unofficial contestants Thanks to all the organizers for making IOI2026 a great event! I try to break them down by category so that this blog doesn’t get too long:

IOI vs Codeforces

This has been well researched before, (here, here, here, here, and here and possibly in other blogs as well). Therefore it is no surprise that even if CF and IOI have different formats, performance is to a large extent correlated:

(unfortunately I couldn’t find the CF handles of all IOI participants, which might also be skewing the results. I’ve mostly used the IOI 2026 teams blog and IOI Statistics, and it’s also possible that I’ve made some misclassifications, since I mostly used AI to match names in the blog post to IOI contestant IDs)

But there’s some more interesting questions we can ask:

Are some problems more CF-like than others?

Of course, not all problems are created equal. Particularly, IOI 2026 had a few “communication” tasks, which are not common in codeforces. In those tasks, the contestant needs to implement two separate programs which can’t communicate with each other, to implement e.g. some game strategy with limited information.

So here’s the per-task score

The communication tasks were classroom and partition. ballmachine was also interactive, but much closer to CF-style interactive problems where you make some queries, and land on a solution based on the answers to your queries.

Some comments:

• It is quite interesting to see that the total score is more correlated to CF rating than any individual task, since the increased number of tasks (and possible total scores) takes some of the luck aspects out of the equation.
• Tiling was a slight exception in that it was significantly easier to solve for 100pts than the other problems, so ~⅔ of the people solved it for 100pts, so the correlation was brought down by relatively strong contestants who didn’t solve it fully (e.g. because they were stressed and overcomplicating it, or because they didn’t spend enough time on it, or they just got unlucky, etc, not necessarily because they coudln’t).
• Particularly for tiling, I expect the lack of CF usernames on the lower-end of the scoreboard to have skewed the results

Score distribution

Another interesting aspect is how the score is distributed. When I am part of scientific committees for different competitions, my target is to have scores be close to uniform. Ideally, we don’t want many people getting 0 or the max score, and we want to maximise the distance between people as much as possible.

While not uniform across the 0-600 scores, it looks relatively uniform between 10-350 points, which I think is a great feat of the scientific committee. Thanks for all the hard work!

However, the individual days on their own were not as balanced:

Day 1 had a very large proportion of scores between 100-200pts, and on day 2 most people had 0-150pts, but when combined together that kind of balances out!

A common oddity in olympiads is that competitions usually have 2 contest days. Why do we need 2 days? Wouldn’t people who are good already do well on both days, and people who are weaker do worse on both days? While this is mostly true, there’s still a lot of luck-based elements in a contestant’s score. These can include:

• How well a problem aligns with the contestant’s knowledge/experience
• Outside factors (e.g. didn’t sleep well the night before, or feeling sick)
• Motivation

Because of these, the day 1 and day 2 rankings are not perfectly correlated. There were both people who did better on day 1 and people who did better on day 2:

This has been quite similar for the past few years (perhaps this is even more true for 2021, where we can see a very large number of outliers between day 1 and day 2 ranks):

Problems

Individual problem score distribution

Obviously we can’t expect the distribution of problems to be uniform, since problems have different difficulties, and hence the distribution will be less uniform:

Nevertheless, I am surprised at how uniform the scores in classroom and magiccity were (you might expect that this is easy to achieve for problems with partial scoring, but there’s usually a relatively small number of solutions/strategies you can reasonably come up with, and implementation details usually don't influence the score that much).

On a similar vein, one can ask: are the problems that different? To what extent will contestants who do well on one task also do well in another?

You can see the actual plots instead of just the correlation here. I claim that this is slightly misleading (at least for pairings of problems on the same contest day). The above graphs conflate these two things: - A strong contestant gets lots of points of problem X quickly, so will move on to problem Y quickly and get more points on problem Y as well (suggesting some positive correlation between the problem scores) - However, the story might be different for a weaker contestant. Contestants have a limited amount of time which needs to be distributed between problems. Therefore, it’s probably reasonable to not just spend 5hours/3=100minutes per task, and instead spend some more time on the task where you feel like you’re more likely to get more points. Therefore, this contestant might have spent more time on problem X, which means they have less time to spend on problem Y, and therefore get less points on problem Y, which would suggest some negative correlation between the problem scores.

Therefore, perhaps it doesn’t make too much sense to compare problems directly, and instead calculate some sort of partial correlation, by controlling for a common “skill” factor. Depending on the skill factor chosen, we see a statistically significant decrease in per-problem correlation, meaning that at least to some extent we do see the “time-tradeoff effect” explained.

This supports my hypothesis to some extent, but I’m not sure how sound it is. If you have any ideas for a better way to model this, please let me know in the comments!

Progression on the contest days

Do people gain points at the same rate at the beginning of the contest vs the end of the contest? I think in a perfectly balanced contest, you’d want this to be approximately true, where stronger contestants make progress (i.e. get points) faster, but don’t run out of things to do, so their “rate of gaining points” is roughly constant, and similarly for weaker contestants.

As we can see, on day 1, contestants get a lot of points quickly, but their score plateaus towards the end of the contest, whereas for day 2 this appears to be a lot closer to linear, without much plateauing, except for the very strong contestants getting gold medals.

Preferences in problem difficulty

Some contestants claim things like “I’m generally doing better at harder tasks”. Is this actually true? The problem with being good at harder tasks, is that the “ceiling” for the number of points you can get is lower (assuming that you can get 70pts on the easier task, being in the 30th percentile when everyone else gets 100pts, while also getting 50pts on a harder task, being in the top percentile for that problem).

What would the look like if people who solved the harder tasks were awarded more for it compared to solving easier subtasks? I try to model this in two separate ways:

• Instead of adding up the score of each problem to get a total score, instead convert scores to percentiles for each task, and use those as the scores for the task:

There is a lot of correlation here, but the points furthest from the line are in the opposite direction, i.e. using the percentile-based ranking causes them to drop a lot of places in the rankings. My interpretation of this is as follows: Consider a problem where 95% of contestants scored <40% on. Someone in the top 5% for that problem could’ve scored 100pts, getting 2.5x the score of the majority of the participants. However, with the percentile-based scoring they would only get ~5% more (i.e. close to 100pts instead of close to 95pts). - To account for the above, we can use a slightly different model instead, by using z-scores (i.e. how many standard deviations above the mean each score is)

Here, we don’t see such big swings, and there are quite a few people who do better with this normalized score (but of course some people do worse). Looking at specific examples, this is e.g. because they didn’t get 100pts on tiling, but did very well on the harder tasks.

There’s a lot of data to be looked at from the IOI, and this is just scratching the surface! If you have any ideas on what would be interesting to look into next I’m all ears (particularly connecting multiple data sources together) let me know!