thurstone

Convert winning probabilities to relative abilities using the fast ability transform.

What it does

Given market odds or winning probabilities, infer the relative abilities of competitors.

Input: Market odds [3.2, 4.8, 12.0, 7.5, 20.0]
Output: Relative abilities [1.15, 0.73, -0.88, 0.21, -1.21]

The model assumes each competitor's performance = true ability + random noise, and the best performance wins.

Usage

pip install thurstone

from thurstone import UniformLattice, Density, AbilityCalibrator, STD_L, STD_UNIT

# Setup
lattice = UniformLattice(L=STD_L, unit=STD_UNIT)
base = Density.skew_normal(lattice, loc=0.0, scale=1.0, a=0.0)
calibrator = AbilityCalibrator(base)

# Convert odds to abilities
odds = [3.2, 4.8, 12.0, 7.5, 20.0]
abilities = calibrator.solve_from_dividends(odds)
probabilities = calibrator.state_prices_from_ability(abilities)

Applications

• E-commerce product ranking
• Search result relevance scoring
• Financial instrument comparison
• Sports betting analysis
• Any competitive scenario with market-implied rankings

Examples

python examples/global_calibration_demo.py      # 500 competitors
python examples/dynamic_calibration_demo.py     # Time-varying abilities
python examples/diffeomorphism_demo.py          # Advanced mappings

Documentation

📖 Full Documentation & Interactive Demos

Citation

Cotton, Peter. "Inferring Relative Ability from Winning Probability in Multientrant Contests." SIAM Journal on Financial Mathematics 12.1 (2021): 295-317.

Development

pip install -e ".[test,viz]"
python scripts/format-code.py
pytest