In this project, we analyze differences in performance metrics for collegiate basketball teams that have qualified for March Madness versus those that have not using a variety of Monte Carlo Simulation methods in R.
The aim of this analyis is to identify if the distributions of collegiate basketball metrics differ in teams that qualify for March Madness versus those that do not.
This is done by employing a 2-sample permuational t-test with a difference of means test statistic ().
We justify it's use in Simulations and apply the test in Analysis.
Data used here comes from over the 2010-2019 seasons. The features are a collection of effeciency and miscellaneous stats over those
seasons. Because these files were downloaded only as a result of a paid subscription, I don't find it appropriate to make them publicly available. Feel free to
contact me regarding any questions about data or reproducibility. The feature of focus in the article is 3 point field goal percentage and
is distributed like so:
In this section, we find that our test has at least 95% power with an observed mean difference of +/- 0.5 or greater. In other words, if the observed mean difference is
at least 0.5 in magnitude, the probability of rejecting our null hypothesis when it is not true is approximately 95% or greater. Permutation tests, by design, also
have size no greater than a given alpha level (in this case, 5%), meaning the probability of rejecting our null hypothesis when it is true is no higher than 5%.
This tells us that we can be confident in our results.
Performing our 2-sample permutational t-test shows us that our observed mean difference is approximately -2.9 and is significantly distant from our null distribution.
In other words, the labels of "seeded" and "non-seeded" do make a difference in our observed data than compared to if the labels were randomly assigned. We then
conclude that the distribution of 3 point field goal percentage for seeded versus non-seeded teams do in fact differ.
Since we've identified that the distributions are different we can move to approximate these distributions with .
We could also build and compare a variety of classification models (SVM, Logistic Regression, Random Forest, KNN, etc) to predict if a team will receive a seed for
March Madness given performance metrics in the regular season.
This was my individual final project for Computational Methods in Statistics and Data Science at the University of Michigan.