Fix PlackettLuce ties.

[xelandernt]

Description of Changes

In #174 that was supposed to resolve #173 I only fixed part of the problem. Plackettluce, model still produces the following results on the main branch:

from openskill.models import PlackettLuce

model = PlackettLuce()

player_1 = model.rating()
player_2 = model.rating()

print(player_1)
print(player_2)


ranks = [1, 1]

new_ratings = model.rate([[player_1], [player_2]], ranks=ranks)

print(new_ratings) 
# [[PlackettLuceRating(mu=27.635389493140497, sigma=8.06590141354368)], [PlackettLuceRating(mu=27.635389493140497, sigma=8.06590141354368)]]

--> Both players gain rating even in a tie.

So I read through the paper and verified with the code and I believe there was a small mistake made here:

I fixed this and this has resolved the issue.

How has this affected benchmarks?

Please Double Check!!

• no changes in draw.ipynb
• no changes in rank.ipynb
• no changes in win.ipynb
• changes in benchmark.py only for the PlacketLuce Model

So now the benchmark is slightly worse, but is consistent with the change of performance of all the other models in #174

Benchmark Results:
               Rating System Benchmark Results - Margin Comparison               
┏━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┓
┃ Model                  ┃ Margin ┃ Accuracy       ┃ Predictions ┃ Avg Time (s) ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━━━┩
│ PlackettLuce           │ 0.0    │ 62.30% ± 1.58% │ 1342/2154   │ 1.76         │
│ PlackettLuce           │ 1.0    │ 64.53% ± 1.32% │ 1390/2154   │ 1.66         │
│ ThurstoneMostellerPart │ 0.0    │ 59.89% ± 0.88% │ 1290/2154   │ 1.69         │
│ ThurstoneMostellerPart │ 1.0    │ 61.00% ± 0.48% │ 1314/2154   │ 1.66         │
│ ThurstoneMostellerFull │ 0.0    │ 65.32% ± 1.47% │ 1407/2154   │ 1.71         │
│ ThurstoneMostellerFull │ 1.0    │ 65.18% ± 1.24% │ 1404/2154   │ 1.69         │
│ BradleyTerryFull       │ 0.0    │ 62.30% ± 1.58% │ 1342/2154   │ 1.77         │
│ BradleyTerryFull       │ 1.0    │ 63.97% ± 0.97% │ 1378/2154   │ 1.66         │
│ BradleyTerryPart       │ 0.0    │ 62.30% ± 1.58% │ 1342/2154   │ 1.57         │
│ BradleyTerryPart       │ 1.0    │ 63.97% ± 0.97% │ 1378/2154   │ 1.58         │
└────────────────────────┴────────┴────────────────┴─────────────┴──────────────┘

Issue(s) Resolved

Fully fixes

#173

Affirmation

By submitting this Pull Request or typing my (user)name below,
I affirm the Developer Certificate of Origin
with respect to all commits and content included in this PR,
and understand I am releasing the same under openskill.py's MIT license.

I certify the above statement is true and correct: xelandernt

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (d5226bc) to head (c5db88a).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #176   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           10        10           
  Lines         2047      2047           
  Branches       513       513           
=========================================
  Hits          2047      2047           

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[xelandernt]

@vivekjoshy I have double-checked all the benchmarks and everything is as described in the PR.

If you have time, could you please have a look at this PR?

[vivekjoshy]

Thanks! I kinda forgot about this PR, I'll go over it soon!

[vivekjoshy]

I have reviewed this. I'll merge this for now and push a fix that improves accuracy in a few days.

[vivekjoshy]

Thank you btw for the fixes you put in :)