Index Seek Operator Cost

Question

For the AdventureWorks sample database query below:

SELECT 
    P.ProductID, 
    CA.TransactionID
FROM Production.Product AS P
CROSS APPLY
(
    SELECT TOP (1)
        TH.TransactionID
    FROM Production.TransactionHistory AS TH
    WHERE
        TH.ProductID = P.ProductID
    ORDER BY 
        TH.TransactionID DESC
) AS CA;

The execution plan shows an Estimated Operator Cost of 0.0850383 (93%) for the Index Seek:

The cost is independent of the cardinality estimation model in use.

It is not a simple addition of the Estimated CPU Cost and Estimated I/O Cost. Neither is it the cost for one execution of the Index Seek multiplied by the Estimated Number of Executions.

How is this cost number arrived at?

Answer 1

The full cost derivation logic is complex, but for the relatively simple case in the question:

Inputs

1. The number of times the operator is executed
   This is the Estimated Number of Executions: 504

2. The cardinality (total number of rows) in the index
   The TableCardinality property of the Index Seek operator gives this: 113,443

3. The number of data pages in the index: 201
   This number can be obtained multiple ways, for example from sys.allocation_units:

   SELECT 
       AU.data_pages
   FROM sys.allocation_units AS AU
   JOIN sys.partitions AS P
       ON P.hobt_id = AU.container_id
   WHERE
       AU.[type_desc] = N'IN_ROW_DATA'
       AND P.[object_id] = OBJECT_ID(N'Production.TransactionHistory', N'U')
       AND P.index_id = 
           INDEXPROPERTY(P.[object_id], N'IX_TransactionHistory_ProductID', 'IndexID');
   

4. The density (1 / distinct values) of the index: 0.002267574
   This is available in the density vector of the index statistics:

   DBCC SHOW_STATISTICS 
   (
       N'Production.TransactionHistory', 
       N'IX_TransactionHistory_ProductID'
   ) 
   WITH DENSITY_VECTOR;
   

   

Computation

-- Input numbers
DECLARE
    @Executions float = 504,
    @Density float = 0.002267574,
    @IndexDataPages float = 201,
    @Cardinality float = 113443;

-- SQL Server cost model constants
DECLARE
    @SeqIO float = 0.000740740740741,
    @RandomIO float = 0.003125,
    @CPUbase float = 0.000157,
    @CPUrow float = 0.0000011;

-- Computation
DECLARE
    @IndexPages float = CEILING(@IndexDataPages * @Density),
    @Rows float = @Cardinality * @Density,
    @Rebinds float = @Executions - 1e0;

DECLARE
    @CPU float = @CPUbase + (@Rows * @CPUrow),
    @IO float = @RandomIO + (@SeqIO * (@IndexPages - 1e0)),
    -- sample with replacement
    @PSWR float = @IndexDataPages * (1e0 - POWER(1e0 - (1e0 / @IndexDataPages), @Rebinds));

-- Cost components (no rewinds)
DECLARE
    @InitialCost float = @RandomIO + @CPUbase + @CPUrow,
    @RebindCPU float = @Rebinds * (1e0 * @CPUbase + @CPUrow),
    @RebindIO float = (1e0 / @Rows) * ((@PSWR - 1e0) * @IO);

-- Result
SELECT 
    OpCost = @InitialCost + @RebindCPU + @RebindIO;

db<>fiddle