This is a review of the NBA research using bipartite graph algorithms conducted by Sohum Misra.
Basketball is ever growing in its popularity. Teams look for new techniques to help them gain advantages over their competitors. One technique increasing in its use is advanced statistics. These statistics help teams determine the intangible value of an individual player.
Graph theory is one technique that can be used. A bipartite graph was constructed using data from five NBA seasons – from the 2012-13 season through to the 2016-17 season. It included 812 players and 36045 line-ups. A bipartite graph is one that takes two graphs and combines them into one. They are typically used to determine relationships between two different classes of objects. In this case, the graph looked at players and five-man units that play together. Six components were used to construct the graph including assist to turnover ratio, field-goal percentage, offensive rebound percentage, steals to possessions ratio, opponent field goal miss percentage, and defensive rebound percentage.
It was determined that this model had an inherent flaw. Players who played for the same team over the five years were ranked higher than players who played for multiple teams. Some of the league’s top ranked players were not listed in the top rankings as they had played on more than one team. A player’s importance to one team is not necessarily the same as their importance on another team as their effectiveness is related to the other players on the team.
In order to deal with this a second graph was constructed. In this graph, the average tenure on a team was calculated. All players who played with a team for less than the average had their weightings boosted and all players who played for a team for more than the average had their weightings decreased. The level of the boost or decrease was varied per player depending on how big the difference was between their length of time with the team and the average tenure. This helps put all players on a level playing field when looking at their importance to a team. However, the results were only marginally better than those of the first model.
Consequently, it was decided to model each team on a separate network. This resulted in a more accurate ranking of the players, but the results were still mediocre (57 to 67% accurate). The better defenders and offenders on a team were ranked higher than their teammates. However, comparing players across teams was not effective. Players playing on a balanced team would have a lower ranking overall while players on a less balanced team would have inflated rankings.
These findings outline the idea that analysts and coaches need to be cautious when looking at making trades. They need to understand that a player’s effectiveness on one team will not necessarily correspond to that player’s possible effectiveness on a new team. However, coaches can use this model to look at how their players rank against each other on their team in order to determine which players are being used most effectively.
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