The first thing I needed to do was to figure out which starting positions were weak and which were strong. To do this, I programmed a Monte Carlo simulation of Catan, which has AIs play about 30 games of Catan every second and outputs statistics from each game to an Excel spreadsheet, which I can then analyze. In particular, it keeps track of which resources each player chooses to start with  this can be used to see what resources winners tend to start with and what resources losers tend to start with, which can in turn indicate which resources are stronger to start on. If all starting positions were completely fair, the results of that graph would look like this:
