https://github.com/michael-borck/bowling-scoring-mathematics
Formalizes ten-pin bowling scoring as a mathematical object, analyzing its domain, recursive structure, state space, symmetry properties, and score distributions.
https://github.com/michael-borck/bowling-scoring-mathematics
bowling formal-methods mathematical-analysis mathematics probability-distribution research scoring-system teaching
Last synced: 14 days ago
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Formalizes ten-pin bowling scoring as a mathematical object, analyzing its domain, recursive structure, state space, symmetry properties, and score distributions.
- Host: GitHub
- URL: https://github.com/michael-borck/bowling-scoring-mathematics
- Owner: michael-borck
- License: mit
- Created: 2026-03-22T07:32:34.000Z (4 months ago)
- Default Branch: main
- Last Pushed: 2026-06-30T08:56:41.000Z (24 days ago)
- Last Synced: 2026-06-30T10:27:20.578Z (24 days ago)
- Topics: bowling, formal-methods, mathematical-analysis, mathematics, probability-distribution, research, scoring-system, teaching
- Language: Python
- Size: 73.2 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# The Mathematics of Ten-Pin Bowling
**A Formal Analysis of the Traditional Scoring System**
This project develops a rigorous mathematical treatment of the traditional ten-pin bowling scoring function. We characterise the scoring system as a formal object -- defining its domain, range, recursive structure, state space, symmetry properties, dependency graph, and score distribution -- and investigate extremal problems, information content, and natural generalisations.
## Target Venue
Mathematics Magazine, The College Mathematics Journal, or The American Mathematical Monthly
## Project Structure
```
data/ Computed distributions and tables
src/ Core scoring and distribution code
notebooks/ Exploratory analysis notebooks
figures/ Publication-quality figures
paper/ Manuscript drafts and research plan
references/ Key papers and background material
tests/ Unit tests
```
## Related Projects
This is one of three papers in a series on bowling scoring mathematics:
1. **Skill, Sequence, and Scoring** (JQAS) -- scoring system comparison via simulation
2. **Win Probability Analysis** (JQAS) -- in-game win probability model
3. **This paper** (Mathematics Magazine) -- pure mathematical analysis of the scoring function
## Key References
- Cooper & Kennedy (1990). "A Generating Function for the Distribution of the Scores of all Possible Bowling Games." *Mathematics Magazine*, 63(4), 239-243
- Hohn (2009). "Generalized Probabilistic Bowling Distributions." WKU Masters Thesis
- Balmoral Software. "All About Bowling Scores." balmoralsoftware.com
- VanDerwerken & Kenter (2018). "A Generative Markov Model for Bowling Scores." *JQAS*, 14(4), 213-226