Betweenness centrality measures how often a node lies on the shortest path between a pair of nodes. So a node — which, in this situation, is a hockey player — will have a high betweenness centrality score if it acts as a “bridge” in a network between two other nodes, such that information must flow through it so the other two nodes can pass information to each other. Betweenness centrality is often used to measure the “influence” of a node, such that, if a node with a relatively high betweenness score is removed, it will have the greatest relative impact on its respective network’s information flow.
So, that’s a bit confusing. What does this mean for hockey? Well, let’s first try to visualize hockey scoring as a network, such that each player is a node, and the connections — or “edges” — represent primary assists to and from each players’ goals. The above visualization may help.
In terms of hockey, a player will have a high betweenness centrality score if:
- The player scores and assists on a lot of goals
- The player scores and assists on many distinct players’ goals
- A player’s teammates rely on the player for their scoring, such that the teammates’ goals and assists tend to only occur with that player directly involved
- The player fulfills some combination of the above requirements more than that player’s teammates do
Here’s an example — Joe Thornton in 2006 tended to assist on many players’ goals and score from many players’ assists, whereas Jonathan Cheechoo — while scoring 56 goals that season — tended to score from Thornton’s assists. In a way, Cheechoo relied upon Thornton for his scoring, but Thornton did not rely on Cheechoo. While I haven’t tested this hypothesis, Thornton would likely have the higher betweenness centrality score, and, from that, we could assume that Thornton was more influential to his team’s scoring than Cheechoo was.