oscar-anderson/Boules-resampling

An implementation that simulates games of Boules between two players, then uses resampling to test whether the difference between the performance of the two players is statistically significant.

Boules games simulation and resampling test

This series of functions simulates a number of games of Boules between two players of different skill levels, then applies a resampling test to examine the statistical significance of the observed difference between the players' final scores.

Requirements

• MATLAB 2019a or later.
• TruncatedGaussian() function by Bruno Luong (2023). Truncated Gaussian (https://www.mathworks.com/matlabcentral/fileexchange/23832-truncated-gaussian), MATLAB Central File Exchange. Retrieved June 13, 2023.

Usage

This code consists of 11 functions:

• throwJack() simulates the throw of a jack, aiming for the centre of the lawn (as in a real game of Boules), by randomly generating x and y coordinate values from a truncated Gaussian distribution. The TruncatedGaussian() function centres the distribution around zero, so the midpoint of the lawn is adjusted before and after the function call.
• throwBall() simulates the throw of a player's ball, aiming for the centre of the lawn (where the jack is aimed to land), by randomly generating x and y coordinate values from a truncated Gaussian distribution. The TruncatedGaussian() function centres the distribution around zero, so the midpoint of the lawn is adjusted before and after function call.
• calcDistance() calculates the distance between the simulated player's thrown ball and the virtually-thrown jack, using the Euclidean distance formula.
• calcMatLabScore() calculates the final score from one game of Boules by first calculating the distances between the jack and each player's ball using the calcDistance function. Points awarded to the winning player are calculated as the difference between the worst and best player's scores, and stored in the score array.
• throwStandardPlayer() utilises the previously-defined throwBall() function to simulate the throw of a moderately-skilled (standard) Boules player. The player's skill level is operationalised by the sigma input to the truncated Gaussian, used by throwBall() to simulate the aim of the throw. In this case, the sigma/standard aim is defined as a standard deviation of 1.
• throwBadPlayer() utilises the previously-defined throwBall() function to simulate the throw of a poorly-skilled (bad) Boules player. The player's skill level is operationalised by the sigma input to the truncated Gaussian, used by throwBall() to simulate the aim of the throw. In this case, the sigma/standard aim is defined as a standard deviation of 1.5.
• standardVsStandardScore() uses the previously defined throwStandardPlayer() function to simulate an input number of Boules games between two moderately-skilled (standard) players, outputting the final scores of all games in an array.
• badVsStandardScore() uses the previously defined throwStandardPlayer() and throwBadPlayer() functions to simulate an input number of Boules games between one poorly-skilled (bad) and one moderately-skilled (standard) player, outputting the final scores of all games in an array.
• genSamplingDist() simulates 1000 sessions of Boules games between two standard players to generate a sampling distribution of the final scores from each session.
• testBadPlayer() runs a game of Boules between a bad and a standard player, generates a sampling distribution of score differences from 1000 sessions of games between two standard players, then determines whether the observed score difference is significantly different to those established from standard vs. standard games, to establish whether the bad player's ability is indeed significantly worse than a standard player's.
• boulesResampling() uses the functions defined above to simulate five games of Boules between the two players, throwing 10 balls per game, then run the resampling test to examine whether the bad player indeed performs significantly worse than the standard player. The sampling distribution is visualised as a histogram and is output alongside the test statistic and significance of the observed bad vs. standard player score difference.

To run the simulation of games and resampling test, simply download boulesResampling_full.m and run the command:

[pValue, testStats, dist] = boulesResampling()

This will output the significance of the observed score difference, the observed bad vs. standard score difference, and a histogram depicting the sampling distribution of score differences between standard vs. standard player games.