Weighted dyadicity for major league baseball player transaction networks

In this paper, we analyze seasonal transactions between Major League Baseball teams over the years 1922–2021. Our approach is to create a weighted network for each season: each team is a node and the link weight between two teams corresponds to their seasonal transaction frequency. Furthermore, we classify teams (nodes) into three different binary groupings to study the amount of inter- and intra-group transactions. We first group teams according to National or American League membership to consider the historical changes in inter-league transactions. Second, we group teams according to winning record and observe a consistent aversion to transactions between winning teams. Finally, we group teams according to payroll size and observe that transactions between/among higher and lower payroll teams all occur close to expected levels. This network theory approach of measuring inter- and intra-group links relative to expected levels is broadly known as dyadicity . Dyadicity has been well studied for unweighted networks, however, our analysis requires a weighted analogue which we develop and apply. To our knowledge, this is the first definition and use of weighted dyadicity .