【文章內(nèi)容簡介】 performance of the players per game played The results presented in Figure 1 do not disclose the information about players who had significant performances during a few years and then retired Figure 2 shows the distribution of efficiency among players during their careers in the NBA In this work we define the efficiency of a player as the sum of his points assists and rebounds achieved in a period divided by the total number of games he played in this period The vertical lines in Figure 2 show the midrange and the 90 percentile of the distribution We see again that more than 90 of the players have career efficiencies below the midrange efficiency value Figure 1 Distribution of points assists and rebounds of NBA players Figure 2 Distribution of the efficiency among playersin the NBA Figures 1 and 2 lead us to think that only a few players have significantly contributed to a team in terms of the box score statistics analyzed Moreover if we consider that the only way to predict a team success is to analyze box score statistics then we are restricted to the analysis of a small fraction of players Figure 3 illustrates this point It shows the average rank gain with its standard deviation a player produces when he is transfered from a team to another one The rank rty is a percentage that indicates the amount of teams that had a worse performance than team t in year y The rank gain gm indicates how much the team the player left tout lost and how much the team the player joined tin won with the transaction1 m The rank gain gm for a transaction m is defined as rtin y rtin y1 rtout y1rtout y The term rtin y rtin y1 indicates how much tin won with the transaction and the term rtouty1 rtouty shows how much tout lost High values of the rank gain indicate that the team the player left decay its performance with his departure and the team he joined improves its performance If the rank gain is zero no significant change occurred We observe in Figure 3 that there is no rule for the rank gain based on the player efficiency that is the average rank gain is zero for all efficiency values below 40 For the efficiency values greater than 40 we can not state anything The number of transactions involving players that have efficiency values higher than 40 is not significant only 20 in the history of the NBA Figure 3 The average rank gain of a transaction In summary we have seen that most of the players do not significantly contribute to box score statistics they exhibit values that do not differ from the averages We have also seen that the impact of a transaction on the behavior of the involved teams does not follow any rule when we consider only the efficiency of the involved player This suggests that a team success does not depend directly and solely on the efficiency of the players it is signing in Therefore in the next section we explore the plex work formed by the teams and the players of the NBA This plex work allows us to formulate new models to predict team success 4 THE NBA COMPLEX NETWORK In order to clarify the understanding of the analysis developed here we need to briefly explain the history of the NBA The NBA was founded in 1946 with the name of Basketball Association of America BAA and had 11 teams Prior to that the American Basketball League and the National Basketball League NBL had been earlier attempts to establish professional basketball leagues The BAA was the first league to attempt to play primarily in large arenas in major cities The BAA became the National Basketball Association in 1949 when the BAA merged with the NBL expanding to 17 franchises From 1950 to 1966 the NBA initiated a process of reducing its teams and in 1954 it reached its smallest size with 8 franchises We will call this time period PINI from now on From 1966 to 1975 the opposite process was initiated and the NBA grew from 10 franchises in 1966 to 18 in 1975 During this period the NBA faced the threat of the formation of the American Basketball Association ABA which was founded in 1967 with 11 franchises and succeeded in signing major stars such as Julius Erving The ABA did not last for too long and in 1976 both leagues reached a settlement that provided the addition of 4 ABA franchises to the NBA raising the number of franchises in the NBA to 22 The period the ABA existed from 1967 to 1975 we will call PABA From 1976 to 2021 the number of teams in the NBA kept growing and in 2021 the NBA reached 30 franchises We call this period PNBA from now on Table 1 summarizes the time periods of the NBA The time evolution graphics present two vertical lines marking the three periods of time Table 1 Historical periods of the NBA In order to confirm the relevance of the periods listed in Table 1 and help us to understand the evolution of the NBA over time we plotted in Figure 4 the number of active players and transactions per year We first observe a high correlation ie the correlation coefficient is 0908 between these factors in a way that the number of transactions grows with the number of active players in the league We also notice the sharp existence of three different behaviors representing the peculiar characteristics of three periods described in Table 1 Figure 4 Active players and transactions per year The remainder of this work is aimed at studying the NBA as a plex work in evolution as did in [6] We construct two works the Yearly NBA Network and the Historical NBA Network built in a way that the set of players P and the set of teams T are united to form the set of vertices V Thus there are two types of vertices the player vertex and the team vertex Each work has a different configuration in each year y of the analysis The vertices of the Yearly NBA Network in the year y are only the players and teams that are active in the league in year y