Why are logical reads for windowed aggregate functions so high?

Question

I've found that in execution plans using common subexpression spools that the reported logical reads get quite high for large tables.

After some trial and error I've found a formula that seems to hold for the test script and execution plan below. Worktable logical reads = 1 + NumberOfRows * 2 + NumberOfGroups * 4

I don't understand the reason why this formula holds though. It is more than I would have thought was necessary looking at the plan. Can anyone give a blow by blow account of what's going on that accounts for this?

Or failing that is there any way of tracing what page was read in each logical read so I can work it out for myself?

SET STATISTICS IO OFF; SET NOCOUNT ON;  IF Object_id('tempdb..#Orders') IS NOT NULL   DROP TABLE #Orders;  CREATE TABLE #Orders   (      OrderID    INT IDENTITY(1, 1) NOT NULL PRIMARY KEY CLUSTERED,      CustomerID NCHAR(5) NULL,      Freight    MONEY NULL,   );  CREATE NONCLUSTERED INDEX ix   ON #Orders (CustomerID)   INCLUDE (Freight);  INSERT INTO #Orders VALUES (N'ALFKI', 29.46),         (N'ALFKI', 61.02),         (N'ALFKI', 23.94),         (N'ANATR', 39.92),         (N'ANTON', 22.00);  SELECT PredictedWorktableLogicalReads =          1 + 2 * Count(*) + 4 * Count(DISTINCT CustomerID) FROM   #Orders;  SET STATISTICS IO ON;  SELECT OrderID,        Freight,        Avg(Freight) OVER (PARTITION BY CustomerID) AS Avg_Freight FROM   #Orders;  

Output

PredictedWorktableLogicalReads ------------------------------ 23 

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Table 'Worktable'. Scan count 3, logical reads 23, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0. Table '#Orders___________000000000002'. Scan count 1, logical reads 2, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0. 

Additional Info:

There is a good explanation of these spools in Chapter 3 of the Query Tuning and Optimization Book and this blog post by Paul White.

In summary the segment iterator at the top of the plan adds a flag to the rows it sends indicating when it is the start of a new partition. The primary segment spool gets a row at a time from the segment iterator and inserts it into a work table in tempdb. Once it gets the flag saying that a new group has started it returns a row to the top input of the nested loops operator. This causes the stream aggregate to be invoked over the rows in the work table, the average is computed then this value is joined back with the rows in the work table before the work table is truncated ready for the new group. The segment spool emits a dummy row in order to get the final group processed.

As far as I understand the worktable is a heap (or it would be denoted in the plan as an index spool). However when I try and replicate the same process it only needs 11 logical reads.

CREATE TABLE #WorkTable   (      OrderID    INT,      CustomerID NCHAR(5) NULL,      Freight    MONEY NULL,   )  DECLARE @Average MONEY  PRINT 'Insert 3 Rows'  INSERT INTO #WorkTable VALUES      (1, N'ALFKI', 29.46) /*Scan count 0, logical reads 1*/  INSERT INTO #WorkTable VALUES      (2, N'ALFKI', 61.02) /*Scan count 0, logical reads 1*/  INSERT INTO #WorkTable VALUES      (3, N'ALFKI', 23.94) /*Scan count 0, logical reads 1*/ PRINT 'Calculate AVG'  SELECT @Average = Avg(Freight) FROM   #WorkTable /*Scan count 1, logical reads 1*/ PRINT 'Return Rows - With the average column included'  /*This convoluted query is just to force a nested loops plan*/ SELECT * FROM   (SELECT @Average AS Avg_Freight) T /*Scan count 1, logical reads 1*/        OUTER APPLY #WorkTable WHERE  COALESCE(Freight, OrderID) IS NOT NULL        AND @Average IS NOT NULL  PRINT 'Clear out work table'  TRUNCATE TABLE #WorkTable  PRINT 'Insert 1 Row'  INSERT INTO #WorkTable VALUES      (4, N'ANATR', 39.92) /*Scan count 0, logical reads 1*/ PRINT 'Calculate AVG'  SELECT @Average = Avg(Freight) FROM   #WorkTable /*Scan count 1, logical reads 1*/ PRINT 'Return Rows - With the average column included'  SELECT * FROM   (SELECT @Average AS Avg_Freight) T /*Scan count 1, logical reads 1*/        OUTER APPLY #WorkTable WHERE  COALESCE(Freight, OrderID) IS NOT NULL        AND @Average IS NOT NULL  PRINT 'Clear out work table'  TRUNCATE TABLE #WorkTable  PRINT 'Insert 1 Row'  INSERT INTO #WorkTable VALUES      (5, N'ANTON', 22.00) /*Scan count 0, logical reads 1*/ PRINT 'Calculate AVG'  SELECT @Average = Avg(Freight) FROM   #WorkTable /*Scan count 1, logical reads 1*/ PRINT 'Return Rows - With the average column included'  SELECT * FROM   (SELECT @Average AS Avg_Freight) T /*Scan count 1, logical reads 1*/        OUTER APPLY #WorkTable WHERE  COALESCE(Freight, OrderID) IS NOT NULL        AND @Average IS NOT NULL  PRINT 'Clear out work table'  TRUNCATE TABLE #WorkTable  PRINT 'Calculate AVG'  SELECT @Average = Avg(Freight) FROM   #WorkTable /*Scan count 1, logical reads 0*/ PRINT 'Return Rows - With the average column included'  SELECT * FROM   (SELECT @Average AS Avg_Freight) T        OUTER APPLY #WorkTable WHERE  COALESCE(Freight, OrderID) IS NOT NULL        AND @Average IS NOT NULL  DROP TABLE #WorkTable