Why is the effective branching factor used for measuring performance of a heuristic function? For search algorithms with heuristic functions, performance of heuristic functions are measured by effective branching factor ${b^*}$ which involves total nodes expanded ${N}$ and depth of the solution ${d}$. I'm not able to find out how different values of ${d}$ affect the performance keeping same ${N}$. Put another way, why not use just the ${N}$ as the performance measure instead of ${b^*}$?
As you found $N$ is the number of nodes that are expanded. The cost of expansion of each node is equal to the number of children of that node. Hence, we use $b^*$ for each node. In other words, the total number of nodes that are involved in the expansion process is $N \times b^*$.