Recently, I put out a poll in the unofficial USACO server to collect data about which USACO divisions correspond to each Codeforces rating (and vice versa). This blog contains the results of that study.

## General Thoughts

In total, I collected data from 116 survey participants across all 4 divisions. The data was collected after the February USACO contest, so it may not be fully up to date; I had planned to release the results earlier, but it took about a month total to get the results ~~(and then I didn't really have time to compile the results for a few weeks)~~. I only got about 5 responses from the Bronze division, so I chose not to make any estimates from those responses. Since Bronze is the lowest division, it is possible that many Bronze competitors don't even have Codeforces accounts (or do not compete regularly in contests).

Some bias in the survey could come from ratings that had not converged yet or the method of sampling (I wasn't able to contact the entire USACO competitor population). I asked competitors whose rating hadn't converged to fill out the survey anyway, in order to avoid selection bias. Overall, these responses made up a small enough proportion of the samples that they likely did not affect the results very much. I did also get a few troll responses (ex: USACO camp + 4500 Codeforces rating), but these were easy to remove from the final results.

## Collection Process

In the survey, participants were asked to provide their USACO division, current Codeforces rating, and max Codeforces rating. The poll also asked participants whether they felt like they were in the lower, middle, or upper third of their division. However, I didn't get enough responses to this question to provide accurate analysis of these results. I also realized that most people probably don't know how they stand relative to other participants, so incorporating this data could have skewed the results.

## Final Results

I compiled a few relevant sample statistics (mean, std. dev, etc.), as well as 95% confidence intervals for the mean of the data. If you aren't familiar with a confidence interval, it essentially states that given the sample data is obtained without huge bias, the mean should be within the interval about 95% of the time.

### Bronze

As stated above, I did not get many responses from competitors of the Bronze division. Using the statistics from the Silver division, however, we can estimate that competitors from the Bronze division generally fall between $$$0$$$ and $$$1200$$$ rating.

### Silver

I got a total of 35 responses from the silver division. There was one outlier at $$$2250$$$ rating, but it didnt seem to affect the data too much.

#### Current Rating

Mean: $$$1272.46$$$

Standard Deviation: $$$342.27$$$

Max: $$$2250$$$

Min: $$$694$$$

Confidence Interval: $$$[1154.89,1390.03]$$$

#### Max Rating

Mean: $$$1306.91$$$

Standard Deviation: $$$359.09$$$

Max: $$$2286$$$

Min: $$$694$$$

Confidence Interval: $$$[1183.56,1430.27]$$$

#### Conclusion

It's probably safe to conclude that most Silver competitors are between $$$1000$$$ and $$$1500$$$ Codeforces rating.

### Gold

There were a total of 26 responses from the Gold division.

#### Current Rating

Mean: $$$1534.62$$$

Standard Deviation: $$$432.86$$$

Max: $$$2140$$$

Min: $$$400$$$

Confidence Interval: $$$[1318.40,1689.84]$$$

#### Max Rating

Mean: $$$1554.23$$$

Standard Deviation: $$$449.16$$$

Max: $$$2288$$$

Min: $$$400$$$

Confidence Interval: $$$[1352.62,1735.65]$$$

#### Conclusion

Based off of these estimates, we can conclude that most Gold competitors are between $$$1300$$$ and $$$1800$$$ Codeforces rating.

### Platinum

A total of 42 Platinum competitors responded to the survey (the largest out of any group). Note that the Platinum division includes previous USACO camp attendees.

#### Current Rating

Mean: $$$2045.45$$$

Standard Deviation: $$$334.47$$$

Max: $$$2776$$$

Min: $$$873$$$

Confidence Interval: $$$[1898.24,2111.94]$$$

#### Max Rating

Mean: $$$2083.19$$$

Standard Deviation: $$$347.51$$$

Max: $$$2844$$$

Min: $$$873$$$

Confidence Interval: $$$[1971.49,2191.48]$$$

#### Conclusion

Based off of these estimates, we can conclude that most Platinum competitors are between $$$1800$$$ and $$$2300$$$ Codeforces rating.

### USACO Camp

Only 7 USACO campers responded to the poll, so the conclusion may not be very accurate, but most campers appear to be between $$$2100$$$ and $$$2600$$$ Codeforces rating.

## Conclusion

As USACO contests get more difficult, these estimates will likely not be as accurate, but hopefully they can serve as a decent estimate for now. I'm not very skilled with data analysis, so if others would like to try to interpret the data more accurately, it is available here. As always, please provide any feedback that you have, and don't be afraid to point out any errors or inconsistencies that you find.