Optimizing for memory consumption during query processing can be facilitated by enumerating pipeline execution orders to minimize the lifetime of intermediates. The number of possible enumerations is potentially factorial. Recent literature has explored algorithms to enumerate pipeline execution orders for any given query execution plan. However, no methods of calculating the number of pipeline execution orders have been yet provided. Due to the factorial complexity a pre-calculation of the expected enumeration count is necessary. This work will provide the combinatorial framework to calculate the structural complexity, i.e. the expected enumeration count, of any given query execution plan without traversing. Through this, we provide the means to identify expensive query execution plans. The precise calculation then enables optimizers to employ heuristics for memory optimization if the given query execution plan exhibits too many possible pipeline execution orders.