Two Master's Degree Project Presentations in Mathematics: Gustaf Holmqvist and Jonathan Falk

10:15 Gustaf Holmqvist

Title: A comparison of longitudinal prostate specific antigen modeling

Abstract: The thesis compares five different models for modelling Prostate Specific Antigen (PSA), a biomarker for prostate cancer, trajectories for undiagnosed men 45-80 years old in Sweden. The models tested are one independent Linear Regression model for each individual in the data base, two Linear Mixed Models and two hidden autoregressive models of order one. The models are viewed from a Hidden Markov Model point of view and compared. The data was split into a training and testing subset and the models were evaluated using mean Continuous Ranked Probability Score on the training data and
mean Continuous Ranked Probability Score with Expanding Window Cross-Validation on the testing data. There was a substation computational cost for the parameter fitting of the most complicated hidden autoregressive model. This lead to the parameter fitting
being done on both a 1000 individual subset of the training data with more iterations and on the whole data set with fewer iterations. The resulting parameters did not differ that much. The Linear Regression model performed best on the training data but on the testing data a hidden autoregressive model performed best. The most complex model
which utilized Sequential Monte Carlo for estimating posterior distributions performed the worst. This might be due to the relatively few particles used or that the parameter optimization step did not converge.

Opponent: Jonathan Falk

11:05 Jonathan Falk

Title: Predicting Post-Transfer Player Development Using Player–Team Fit

Abstract: Predicting player performance after a transfer is one of the most difficult problems in professional football recruitment. While traditional evaluation often focuses on player quality alone,
successful transfers may also depend on how well a player’s profile fits the tactical environment of the destination team. This thesis investigates whether player–team fit can improve the prediction of post-transfer player development.

Player performance is measured using Twenty player quality metrics developed by Twelve, while destination team context is represented through seven team style metrics. A baseline model is constructed using pre-transfer player qualities together with team style variables. An
interaction model is then introduced by adding interaction terms between player qualities and destination team styles. Interaction terms are selected using AIC-based forward selection and OLS significance testing, while model estimation is performed using ridge regression.

The results show that pre-transfer player quality and destination team context provide meaningful predictive power. Including team style variables improves performance compared to using player quality alone, indicating that the destination club environment is important for player development. However, explicit interaction terms provide only limited additional improvement. Only a small number of interactions are retained, and for most target qualities the interaction model performs nearly identically to the baseline model. The largest observed improvement was for Box Threat for midfielders, where test-set R2 increased by approximately 2 percentage points, although this improvement may partly reflect sampling variation.

The conclusion is that player quality and general team environment explain most predictable post-transfer development, while explicit player–team fit interactions contribute only marginal additional explanatory power.

Opponent: Gustaf Holmqvist