DOI: 10.5061/dryad.kh18932fc
title: Data from: Luck, skill, and depth of competition in games and social hierarchies

description: Patterns of wins and losses in pairwise contests, such as occur in sports
 and games, consumer research and paired comparison studies, and human and
 animal social hierarchies, are commonly analyzed using probabilistic
 models that allow one to quantify the strength of competitors or predict
 the outcome of future contests. Here we generalize this approach to
 incorporate two additional features: an element of randomness or luck that
 leads to upset wins, and a "depth of competition" variable that
 measures the complexity of a game or hierarchy. Fitting the resulting
 model we estimate depth and luck in a range of games, sports, and social
 situations. In general, we find that social competition tends to be
 "deep," meaning it has a pronounced hierarchy with many distinct
 levels, but also that there is often a nonzero chance of an upset victory.
 Competition in sports and games, by contrast, tends to be shallow and in
 most cases there is little evidence of upset wins.
description: This data set of pairwise comparisons has been aggregated across
 a variety of sources given in our paper. These directed interactions are
 given in adjaency matrix, graph modeling language, and edge list
 formats.
description: # Luck, skill, and depth of competition in games and social hierarchies
 [https://doi.org/10.5061/dryad.kh18932fc](https://doi.org/10.5061/dryad.kh18932fc) ## Description of the data and file structure A collection of data sets from various sports leagues, human and animal hierarchies, compiled for a comparative study of the depth and luck involved in the various competitions. ### Files and variables #### File: data\_CC0.zip **Description:** .zip file containing all files, contains the following when unzipped: #### Folder: adj\_matrices **Description:** Folder containing .txt files with space-separated adjacency matrices representing the data sets. For each file, the entry in row i and column j contains the number of times player i beats player j in the data set. Contains the following data sets with the appropriate citations: * chess.txt: Online chess games on lichess.com in 2016 * soccer.txt: Men’s international association football matches 2010–2019. #### Folder: gml\_files **Description:** Folder containing .gml files, representations of the directed networks in Graph Modeling Language (GML) format.  #### Folder: matches **Description:** Folder containing .txt files with space-separated edgelists representing the data sets. For each file, each row consists of the winner followed by the loser of a given match. #### File: pairwise-ranking.zip (Zenodo) **Description:** .zip file archiving the python package hosted at [https://github.com/maxjerdee/pairwise-ranking](https://github.com/maxjerdee/pairwise-ranking) to fit the model presented in the paper. Contains README.md file explaining usage. Also includes further data sets in the same format under the data/ directory within the CC BY-NC-SA 4.0 license.  ## Code/software No software is required in order to view the data. To perform the analysis described in the paper we have created a python package hosted at: [https://github.com/maxjerdee/pairwise-ranking](https://github.com/maxjerdee/pairwise-ranking) and archived in pairwise-ranking.zip ## Access information Other publicly accessible locations of the data: * [https://github.com/maxjerdee/pairwise-ranking](https://github.com/maxjerdee/pairwise-ranking) Data was derived from the following sources: * baboons.txt: M. Franz, E. McLean, J. Tung, J. Altmann, S. C. Alberts, Proceedings of the Royal Society B 282, 20151512 (2015). * business_depts.txt: A. Clauset, S. Arbesman, D. B. Larremore, Science Advances 1, e1400005 (2015). * chess.txt: [https://www.kaggle.com/datasets/arevel/chess-games](https://www.kaggle.com/datasets/arevel/chess-games). Accessed: 2023-10-07. * cs_depts.txt: A. Clauset, S. Arbesman, D. B. Larremore, Science Advances 1, e1400005 (2015). * dogs.txt: M. J. Silk, M. A. Cant, S. Cafazzo, E. Natoli, R. A. McDonald, Proceedings of the Royal Society B 286, 20190536 (2019). * history_depts.txt: A. Clauset, S. Arbesman, D. B. Larremore, Science Advances 1, e1400005 (2015). * hyenas.txt: E. D. Strauss, K. E. Holekamp, Proceedings of the National Academy of Sciences 116, 8919 (2019). * mice.txt: C. M. Williamson, B. Franks, J. P. Curley, Frontiers in Behavioral Neuroscience 10, 152 (2016). * monkeys.txt: C. Vilette, T. Bonnell, P. Henzi, L. Barrett, Behavioral Ecology 31, 1379 (2020). * soccer.txt: M. J ̈urisoo, International men’s football results from 1872 to 2023, [https://www.kaggle.com/datasets/martj42/international-football-results-from-1872-to-2017](https://www.kaggle.com/datasets/martj42/international-football-results-from-1872-to-2017). Accessed: 2023-10-07. * sparrows.txt: D. J. Watt, Animal Behaviour 34, 16 (1986). * tennis.txt: J. Sackmann, ATP tennis data, [https://github.com/JeffSackmann/tennis_atp](https://github.com/JeffSackmann/tennis_atp). Accessed: 2023-10-07.