Introduction

ratingslib is a library in Python that implements a plethora of rating methods with several applications and examples. The most of the implemented rating systems are based on pairwise comparisons (or paired comparison) method. Usually, ratings are generated by using linear algebra and computational methods. The most important features of the library are shown below. More details on the functionalities can be found in the API documentation. Also, examples and small tutorials are available as Jupyter notebooks.

Rating/Ranking systems:

  • WinLoss

  • Colley 1

  • Massey 2

  • Keener 3

  • Elo 4

  • Offense - Defense 5 6

  • GeM 6 7 8

  • AccuRATE 9

Ranking Aggregation methods:

  • Borda Count 10

  • Average Rank 11

Rating Aggregation methods:
Comparison metrics:

  • Kendall’s Tau 12

Applications & Examples:
  • Sports (the main application of the library):

    1. Soccer Teams rating

    2. Soccer Teams ranking lists comparison

    3. Hindsight and foresight prediction 11 13 of the final outcome of soccer matches

    4. Combining rating systems and machine learning methods to predict soccer matches outcome

    5. Ranking NFL teams

  • Other Applications & Examples:
    Finance:

    • Examples from investment selection and portfolios rating and ranking.

    Domain Market:

    • An illustrative example which is included in the paper 14 shows the ranking of domain names.

    Movies:

    • Application on a real-world dataset from MovieLens 15.

References

1

Colley, W. (2002). Colley’s bias free college football ranking method: The Colley Matrix Explained.

2

Massey, K. (1997). Statistical models applied to the rating of sports teams. Statistical models applied to the rating of sports teams.

3(1,2)

Keener, J. P. (1993). The Perron-Frobenius theorem and the ranking of football teams. SIAM Review, 35(1), 80–93.

4

Elo, A. E. (1978). The rating of chessplayers, past and present. Arco Pub.

5(1,2)

Govan, A. Y., Langville, A. N., & Meyer, C. D. (2009). Offense-defense approach to ranking team sports. Journal of Quantitative Analysis in Sports, 5(1).

6(1,2,3)

Govan, A. Y. (2008). Ranking Theory with Application to Popular Sports. Ph.D. dissertation, North Carolina State University.

7(1,2)

Brin, S., & Page, L. (2012). Reprint of: The anatomy of a large-scale hypertextual web search engine. Computer networks, 56(18), 3825–3833.

8

Ingram, L. C. (2007). Ranking NCAA sports teams with Linear algebra. Ranking NCAA sports teams with Linear algebra. Charleston.

9

Kyriakides, G., Talattinis, K., & Stephanides, G. (2017). A Hybrid Approach to Predicting Sports Results and an AccuRATE Rating System. International Journal of Applied and Computational Mathematics, 3(1), 239–254.

10

Borda, J. d. (1784). Mémoire sur les élections au scrutin. Histoire de l’Academie Royale des Sciences pour 1781 (Paris, 1784).

11(1,2,3,4,5)

Langville, A. N., & Meyer, C. D. (2012). Who’s# 1?: the science of rating and ranking. Princeton University Press.

12

Kendall, M. G. (1938). A New Measure Of Rank Correlation. Biometrika, 30(1/2).

13

Lasek, J., Szlávik, Z., & Bhulai, S. (2013). The predictive power of ranking systems in association football. International Journal of Applied Pattern Recognition, 1, 27–46.

14

Talattinis, K., Zervopoulou, C., & Stephanides, G. (2014, June). Ranking Domain Names Using Various Rating Methods. Proceedings of the Ninth International Multi-Conference on Computing in the Global Information Technology (pp. 107-114). Seville: IARIA.

15

Harper, F. M., & Konstan, J. A. (2015, December). The MovieLens Datasets: History and Context. ACM Trans. Interact. Intell. Syst., 5. doi:10.1145/2827872