Diversity is Key: Fantasy football dream teams under budget constraints

Given a fixed budget for player salaries, what is the distribution of salaries of the top scoring teams? We investigated this question using the wealth of data available from fantasy premier league football (soccer). Using the players' data from past seasons, for several seasons and several different budget constraints, we identified the highest scoring fantasy team for each season subject to each budget constraint. We then investigated quantifiable characteristics of these teams. Interestingly, across nearly every variable that is significant to the game of football and the budget, these top teams display diversity across these variables. Furthermore, randomly assembled teams would statistically \em not \em display such diversity across these variables. Our results indicate that diversity across these variables, including salaries, is a general feature of top performing teams. Moreover, in the process of obtaining these results we developed a data cleaning (or data reduction) algorithm that drastically reduced the amount of data to be analyzed.