# The origins of the idea↵
So, I participated in [contest:2210] recently and solved ABC1, and when I moved on to C2 I thought to myself "wow, that's a big difficulty jump!"↵
# The process↵
After the contest was over, I also thought about whether there is a way to put a number to this, and after a bit of thinking, I came up with the following process:↵
↵
- Take the solve counts of each problem (the green numbers at the bottom of the Standings page). Call it $\mathrm{solves}$. This is used as an estimation for how easy the question was.↵
- Say that there are $n$ problems. Define the array $\mathrm{ratios}\left[i\right] = \frac{1+\mathrm{solves}\left[i\right]}{1+\mathrm{solves}\left[i+1\right]}$. (The $1+$ part is to prevent division by zero.)↵
- The imbalance is calculated as $\mathrm{stdev}\left(\mathrm{ln}\left(\mathrm{ratios}\right)\right)$.↵
↵
So I decided to test this method on some recent contests. After playing around, I decided that this function was good to use and then I wanted to make a CSV containing theinformation of contest ID, contest starting time in UTC timezone, contest title, and measured contest imbalance.↵
↵
The way I did this was to first check an already existing CSV file for any data already computed, then for each contest not recorded in the CSV file:↵
↵
- Query the Codeforces API for standings information.↵
- For each participant, if their score is greater than zero for problem $i$, count that as an accepted solution to compute the $\mathrm{solved}$ array.↵
- Use the contest information returned by Codeforces API `contest.standings` to get the contest start time as a Unix timestamp in UTC, and the contest title.↵
- Use the $\mathrm{solved}$ array we computed to calculate imbalance as given above.↵
- For any contest, if the API gives status code 400 (e.g. contest 1597) or returns empty standings (e.g. contest 399), write that to a file named `status400.txt` so that these contests can be skipped on the next run.↵
↵
You can find the source code, computed CSV, and `status400.txt` in [this GitHub repo](https://github.com/onepersonintheuniverse/imbalanced).↵
# The meaning of the measure itself↵
Now, what is imbalance actually measuring? I like to think of it as an estimate of how rough the difficulty jumps between problems are. For example, if until some problem each problem is slightly harder than the last but the next problem is much harder, this makes the imbalance high. On the other hand, if the difficulties progress smoothly the imbalance will be low. The difficulties of the problems are estimated by accepted counts.↵
↵
It's time for some statistics. mbalance is technically a logarithmic scale since the standard deviation computation computes $\ln\left(\mathrm{geometric standard deviation}\right)$.↵
# Some statistics↵
The mean contest imbalance is ~1.1489, with a standard deviation of ~0.5816 (sample) or ~0.5814 (population). The median is ~1.0451, belonging to [contest:1161] and [contest:1610].↵
↵
Out of the last 10 rated contests, the highest imbalance belongs to [contest:221032] at around 1.341. The 676, while the lowest imbalance belongs to [contest:2229] with around 0.538.↵
↵
The planned-rated contest with the highest imbalance that is also"supposed tıo be ordered" by difficulty is [contest:820] due to the fact that the author solution failed on a hack, and most of the accepted solutions for C FSTe'd. The rated contest with the lowest imbalance is [contest:1].↵
↵
Goodbye, that's it for now, also here's a reminder to not go harassing the contests with the high imbalance. at around 0.078.↵
↵
Here's a histogram showing the distribution:↵
↵
↵
Goodbye, that's it for now :3↵
↵
PS: I got IP banned multiple times trying to adjust the interval between each request &x1f940;
So, I participated in [contest:2210] recently and solved ABC1, and when I moved on to C2 I thought to myself "wow, that's a big difficulty jump!"↵
# The process↵
After the contest was over, I also thought about whether there is a way to put a number to this, and after a bit of thinking, I came up with the following process:↵
↵
- Take the solve counts of each problem (the green numbers at the bottom of the Standings page). Call it $\mathrm{solves}$. This is used as an estimation for how easy the question was.↵
- Say that there are $n$ problems. Define the array $\mathrm{ratios}\left[i\right] = \frac{1+\mathrm{solves}\left[i\right]}{1+\mathrm{solves}\left[i+1\right]}$. (The $1+$ part is to prevent division by zero.)↵
- The imbalance is calculated as $\mathrm{stdev}\left(\
↵
So I decided to test this method on some recent contests. After playing around, I decided that this function was good to use and then I wanted to make a CSV containing the
↵
The way I did this was to first check an already existing CSV file for any data already computed, then for each contest not recorded in the CSV file:↵
↵
- Query the Codeforces API for standings information.↵
- For each participant, if their score is greater than zero for problem $i$, count that as an accepted solution to compute the $\mathrm{solved}$ array.↵
- Use the contest information returned by Codeforces API `contest.standings` to get the contest start time as a Unix timestamp in UTC, and the contest title.↵
- Use the $\mathrm{solved}$ array we computed to calculate imbalance as given above.↵
- For any contest, if the API gives status code 400 (e.g. contest 1597) or returns empty standings (e.g. contest 399), write that to a file named `status400.txt` so that these contests can be skipped on the next run.↵
↵
You can find the source code, computed CSV, and `status400.txt` in [this GitHub repo](https://github.com/onepersonintheuniverse/imbalanced).↵
# The meaning of the measure itself↵
Now, what is imbalance actually measuring? I like to think of it as an estimate of how rough the difficulty jumps between problems are. For example, if until some problem each problem is slightly harder than the last but the next problem is much harder, this makes the imbalance high. On the other hand, if the difficulties progress smoothly the imbalance will be low. The difficulties of the problems are estimated by accepted counts.↵
↵
I
# Some statistics↵
The mean contest imbalance is ~1.1489, with a standard deviation of ~0.5816 (sample) or ~0.5814 (population). The median is ~1.0451, belonging to [contest:1161] and [contest:1610].↵
↵
Out of the last 10 rated contests, the highest imbalance belongs to [contest:22
↵
The planned-rated contest with the highest imbalance that is also
↵
Goodbye, that's it for now, also here's a reminder to not go harassing the contests with the high imbalance.
↵
Here's a histogram showing the distribution:↵
↵
↵
Goodbye, that's it for now :3↵
↵
PS: I got IP banned multiple times trying to adjust the interval between each request &x1f940;
