Itzik Ben-Gan has started a series of articles on optimizing queries which use grouping and aggregating with a reverse-engineering of the stream aggregate algorithm:
As you may already know, when SQL Server optimizes a query, it evaluates multiple candidate plans, and eventually picks the one with the lowest estimated cost. The estimated plan cost is the sum of all the operators’ estimated costs. In turn, each operator’s estimated cost is the sum of the estimated I/O cost and estimated CPU cost. The cost unit is meaningless in its own right. Its relevance is in the comparison that the optimizer makes between candidate plans. That is, the costing formulas were designed with the goal that, between candidate plans, the one with the lowest cost will (hopefully) represent the one that will finish more quickly. A terribly complex task to do accurately!
The more the costing formulas adequately take into account the factors that truly affect the algorithm’s performance and scaling, the more accurate they are, and the more likely that given accurate cardinality estimates, the optimizer will choose the optimal plan. At any rate, if you want to understand why the optimizer chooses one algorithm versus another you need to understand two main things: one is how the algorithms work and scale, and another is SQL Server’s costing model.
So back to the plan in Figure 1; let’s try and understand how the costs are computed. As a policy, Microsoft will not reveal the internal costing formulas that they use. When I was a kid I was fascinated with taking things apart. Watches, radios, cassette tapes (yes, I’m that old), you name it. I wanted to know how things were made. Similarly, I see value in reverse engineering the formulas since if I manage to predict the cost reasonably accurately, it probably means that I understand the algorithm well. During the process you get to learn a lot.
Our query ingests 1,000,000 rows. Even with this number of rows, the I/O cost seems to be negligible compared to the CPU cost, so it is probably safe to ignore it.
As for the CPU cost, you want to try and figure out which factors affect it and in what way.
I give this my highest recommendation.