Migrate rating system from Topcoder to Elo-MMR

[int-y1]

Elo-MMR is a rating system that has more desirable properties than Topcoder's rating system. For example, Elo-MMR converges faster, prevents users from farming volatility, and has a more reasonable performance calculation.

Change in the rating curve (ratings rounded to the nearest 100x+50):

Change in each user's rating (i.e. users can expect their rating to increase by +100):

Due to the expected +100 rating increase, I modified the rating cutoffs:

• Old: RATING_VALUES = [1000, 1200, 1500, 1800, 2200, 3000]
• New: RATING_VALUES = [1000, 1300, 1600, 1900, 2400, 3000]

Change in performance (on my virtual machine):

• It takes 8 seconds to rate all 111 contests using Topcoder.
• It takes 12 seconds to rate all 111 contests using Elo-MMR. The biggest bottlenecks are recalculate_ratings() (4.5 seconds), and the query for historical_p (1.5 seconds).

[codecov-commenter]

Codecov Report

Merging #1751 (0517a63) into master (64da46b) will decrease coverage by 0.29%.
The diff coverage is 18.51%.

@@            Coverage Diff             @@
##           master    #1751      +/-   ##
==========================================
- Coverage   46.52%   46.22%   -0.30%     
==========================================
  Files         221      222       +1     
  Lines       12461    12612     +151     
==========================================
+ Hits         5797     5830      +33     
- Misses       6664     6782     +118     

Impacted Files	Coverage Δ
judge/models/tests/test_profile.py	100.00% <ø> (ø)
judge/views/api/api_v1.py	23.52% <0.00%> (ø)
judge/views/api/api_v2.py	47.79% <0.00%> (ø)
judge/ratings.py	21.19% <17.39%> (+3.01%)	⬆️
judge/migrations/0123_contest_rating_elo_mmr.py	18.33% <18.33%> (ø)
judge/models/contest.py	95.48% <100.00%> (+0.01%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 64da46b...0517a63. Read the comment docs.

[quantum5]

Otherwise looks pretty good.

[Ninjaclasher]

Please also create a PR to https://github.com/DMOJ/docs/blob/master/docs/site/api.md with any API changes.

[quantum5]

Code looks fine to me. Has anyone tested the migration? If it works I am going to approve.

[Xyene]

LGTM and applied to prod.

Thanks everyone who worked on this!