Statistics objects are important to us for allowing SQL to make good estimates of the row-counts involved in different parts of a given query and to allow the SQL Optimiser to form efficient execution plans to delivery those query results.

Statistics get updated automatically when you rebuild (or re-organise) an index they are based on – but we only tend to rebuild indexes that are fragmented, and we don’t need fragmentation for statistics to be stale. We also may have many auto-created statistics objects that are not related to an index at all.

It’s generally recommended to have the database level setting AUTO_UPDATE_STATISTICS turned on, so that SQL can manage the process of keeping statistics up to date for us. The only excuse to turn it off is that you are managing the updates to stats yourself in a different manner. And you can always turn the auto update off at an individual table or statistics level if you need to, rather than for the whole database.

SQL Server has had the ability to automatically update statistics since version 7.0. Nonetheless for a long part of my career working with SQL Server, whenever a performance issue raised its head everyone’s knee-jerk response would be “Update Statistics!” In most cases though the people shouting that didn’t really understand what the “Statistics” were, or what mechanisms might already be in place for keeping them up to date.

Of course SQL Server isn’t perfect and sometimes it is helpful for human intelligence to intervene. But to provide intelligent intervention one has to understand how things work.

So how does the automatic updating of statistics work?

In the background SQL maintains a count of changes to tables that might affect statistics. This can be updates, inserts or deletes. So if I inserted 100 records, updated 100 records and then deleted 100 records, I would have made 300 changes.

When SQL forms an execution plan for a query it references various distribution statistics objects to estimate row-counts and to use that to try find the best plan. The statistics objects it looks at are referred to as being “interesting” in the context of the query.

Before using values from the statistics, the Optimizer will check to see if the statistics are “stale”, i.e. the modification counter exceeds a given threshold. If it does, SQL will trigger a resampling of the statistics before going on to form an execution plan. This means that the plan will be formed against up to date statistics for the table.

For subsequent executions of the query, the existing plan will be loaded from the plan cache. Within the plan, the Optimiser can see a list of the statistics objects that were deemed “interesting” in the first place. Once again it will check each of them to see if they are “stale”. If they are, an auto-update of the statistics object(s) will be triggered and once that is complete the plan will be recompiled, in case the updated statistics might suggest a better way of executing the query. Equally, if any of the statistics objects have been updated since the last execution then the plan will also be recompiled.

One important caveat to this is the database level setting AUTO_UPDATE_STATS_ASYNC (Asynchronously). Generally it is best to have this turned off, in which case the above behaviour is observed. If you turn it on however, in the case of stale stats the query execution will not wait for the stats to be updated, but will start them updating in the background while the query executes. The plan will only recompile to be based on the new stats at the next execution.

From SQL Server2008 R2 SP2 and SQL Server 2012 SP1 we had a new DMF (Dynamic Management Function) sys.dm_db_stats_properties that allows us to see how many row modifications have been captured against a given statistics object as well as when it was last refreshed, how many rows were sampled etc. Modifications are captured on a per column basis (though when statistics were originally introduced in SQL Server it was per table) so the counter will only be affected if the leading column for the statistics object has been affected by a given operation.

SELECT
s.name AS StatsName, sp.*
FROM sys.stats s
CROSS apply sys.dm_db_stats_properties(s.OBJECT_ID, s.stats_id) sp
WHERE s.name = 'IX_Test_TextValue'


Results:

So what are the thresholds?

For a long time the thresholds were as follows. Statistics were considered stale if one of the following was true:

• The table size has gone from 0 rows to more than 0 rows
• The table had 500 rows or less when the statistics were last sampled and has since had more than 500 modifications
• The table had more than 500 rows when the statistics were last sampled and the number of modifications is more than 500 + 20% of the row-count when the statistics were last sampled (when talking about tables with larger row-counts a lot of the documentation just describes this as 20% as the additional 500 becomes less and less relevant the larger the number you are dealing with).

Those thresholds did mean that when a table had a large number of rows, Statistics might not get updated that often. A table with a million rows would only have stats updated if about 200,000 rows changed. Depending on the distribution of the data and how it is being queried this could be a problem.

So, in SQL 2008 R2 SP2 Microsoft introduced Traceflag 2371 which when set would reduce the stale statistics threshold for larger tables. From SQL 2016 this is the default functionality.

That adds the following test for statistics being stale:

• If the number of rows (R) when the statistics were last sampled is 25,000 or more and the number of modifications is more than the square root of R x 1000:

Now, I’m just going to correct myself here, the documentation I’ve found SAYS the threshold is 25,000 but when I started to have a play that didn’t seem to be the case at all.

What actually seems to happen is that whichever of the two estimates is smaller gets used i.e

Either:

Or:

Whichever is smaller.

I don’t know if this means that both get evaluated and the smaller is used, or if the threshold between the two rules is simply defined at the point where the second formula gives the smaller result – which is after 19,682 rows. I discovered that threshold by solving where the two equations above would give the same result – then by experimenting to prove it in practice.

I think this incorrect stating of 25,000 as the threshold probably comes from confusion, taking an approximation (20%) as the actual figure. Remember I mentioned that people often generalise to say that statistics are stale after 20% of the rows change, and forget about the extra 500 rows. If that was true and it was exactly 20%, then the threshold would be 25,000 as that would be the point that both equations are equal.

Anyway it’s not even vaguely important to know that. I just found it interesting! Note that the tests above were carried out on SQL Server 2012 SP3 so could well be different on later versions.

To more visually understand the above rules, here’s a table showing the thresholds for some example table sizes under both the Old algorithm (without the traceflag) and the New algorithm (with the traceflag or on SQL 2016 or later).

R is the number of rows when the statistics were last sampled and T is the number of modifications for statistics to be considered stale:

You can see for the larger table sizes there is a massive difference. If you’ve got large tables you’re querying against and are having to update the statistics manually to keep them fresh then you may find implementing the traceflag is a help.

For large tables statistics are sampled when being updated rather than the whole table being necessarily being read. I have details on that in this post:

Automatic Sample Sizes for Statistics Updates

Got a problem or embarking on a SQL Server project and want some help and advice? I’m available for consulting – please get in touch or check out my services page to find out what I can do for you.

Statistics are vitally important in allowing SQL Server to find the most efficient way to execute your queries. In this post we learn more about them, what they are and how they are used.

Cardinality Estimation

Cardinality is a term originally from Mathematics, generally defined as “The number of objects in a given set or grouping”. In SQL we’re continually dealing with sets so this becomes a very relevant topic, which in our context is just the “number of rows”.

When you have a query across multiple tables there any many ways in which SQL Server could decide to physically go about getting you the results you want. It could query and join the tables in any order and it could use different methods for matching records from the various tables you have joined together. It also needs to know how much memory to allocate for the operation – and to do that it needs to have an idea of the amount of data generated at each stage of processing.

A lot of this requires cardinality estimation, and SQL Server uses something called Statistics objects to perform that calculation.

Let’s look at a simple example:
SELECT *
FROM Person.Person p
INNER JOIN Person.[Address] a
ON p.AddressId = a.AddressId
WHERE p.LastName = 'Smith'
AND a.City = 'Bristol'

When it comes to gathering the results for this query there are a number of ways the database engine could go about it. For instance:

a) It could find all the records in the Person table with a LastName of Smith, look each of their addresses up and return only the ones who live in Bristol.
b) It could find all the Addresses in Bristol, look up the people associated with each address and return only the ones called Smith.
c) It could grab the set of people called Smith from the People table, grab all the addresses in Bristol, and only finally match up the records between those two sets.

Which of those operations is going to be most efficient depends very much on the number of records returned from each table. Let’s say that we have a million people called Smith, but there’s only one address in our whole database that is in Bristol (and let’s say that address does actually belong to someone called Smith).

In the first method above I would grab the million Smiths and then look their address up one by one in the address table until I found the one that lived in Bristol.

If I used method b) though, I would find the one matching address first, and then I would simply look up the owner of that address. Clearly in this rather contrived example, that’s going to be a lot quicker. So if SQL knows ahead of time roughly how many records to expect from each part of the query, hopefully it can make a good decision about how to get the data.

But how can it work out how many rows will be returned without actually running the query?

Statistics

That’s where statistics objects come in. SQL Server maintains in the background data that equates to a histogram showing the distribution of the data in certain columns within a table. It does this any time you create an index – statistics will be generated on the columns the index is defined against, but it also does it any time it determines that it would be useful. So if SQL encounters a Where clause on Person.LastName – and that column isn’t involved in a useful index, SQL is likely to generate a statistics object to tell it about the distribution of data in that column.

I say “likely to” because it actually depends on the settings of your SQL instance. Server configuration is beyond the scope of this post but suffice to say you can let SQL automatically create Statistics objects – or not. You can let it automatically update them when the data has changed by more than a given threshold – or not. And you can specify whether updates to statistics should happen asynchronously or synchronously – i.e. in the latter case if your query determines that statistics needs updating then it will kick that off and wait until the update is complete before processing the query.

It’s generally recommended that auto creation and updating is on, and async updating is off.

Viewing Statistics Objects
Let’s have a look at some actual statistics and see what they hold. There are a couple of ways of doing this, the first is through SSMS. If you look under a table in the object browser you will see a Statistics folder which holds any statistics objects relating to that table:

In the above example you can see some that have friendly names, these are Statistics that  are related to an actual index that has been defined on the table and they have the same name as the Index – e.g. IX_Address_StateProvinceId.

You’ll also see we have some prefixed _WA_Sys and then with some random numbers following. These are statistics objects that SQL has created automatically on columns that aren’t indexed – or at least they weren’t indexed at the time the Statistics objects were created.

You can open these up with a double-click and see what’s inside:

This is the General tab you open up to. You’ll see it tells you what table the Statistics are for and what column(s). There are options for adding columns and changing the order – but you never really need to do this – as well as information to tell you when the statistics were last updated, and a check box if you want to update them now.

In the details tab there’s a lot more info:

I don’t find this the easiest display format to work with though, so rather than delving into what everything means here let’s look at the other way you can view statistics, which is by running the following command:

DBCC SHOW_STATISTICS('Person.Address', '_WA_Sys_00000004_164452B1')

The format is straightforward, you just specify the table you are interested in the Statistics for, and the actual name of the Statistics object you want. You can see the same information as if you double-clicked on it, but the results are output in the results pane like any other query and are (I think) a lot easier to read. Allegedly there will soon be a third way in SQL Server to view Statistics as DBCC commands are considered a bit “clunky” – but we don’t know what that will look like yet.

The command outputs three resultsets:

This post is just an introduction to statistics – and generally you don’t need to know that much, it’s just handy to understand the basics. So let’s just run over the key bits of information you can see above:

First of all in the first recordset – otherwise know as the…

Stats Header

Rows – is the number of rows in your table

Rows Sampled – this is how many rows were sampled to generate the statistics. SQL can generate or update statsitics using sampling rather than reading all the rows. In this case you’ll see it did actually read the whole table.

Steps – If you imagine the statistics as a bar chart – this is the number of bars on the chart. Statistics objects have a maximum of 200 steps so if you have more distinct values in your column than that they will be grouped into steps.

Density – This is supposed to be the probability of a row having a particular value (calculated as 1 / Number of Distinct values in column). According to books online “This Density value is not used by the query optimizer and is displayed for backward compatibility with versions before SQL Server 2008.”  I am using SQL 2012, and this number is just plain incorrect so don’t use it…

Recordset Number 2: The Density Vector

All Density – this is the accurate version of the Density statistic described above. So your probability of a given row having a specific value is about 0.0017. That’s a little less than one in 500. I happen to know there are 575 different Cities in the table so that makes sense. Sometimes SQL will use this value to form a plan – if it knows you’re going to search this table for a specific City and it doesn’t know that City when it makes the plan, then it could guess that about 1/500th of the rows will match your criteria.

Average Length – Is what it says on the can. The average length of data in this column.

Columns – The names of any column measured in this statistics objects. You can have statistics across multiple columns but I’m not going to cover that in this post. In this case it tells us these statistics are based on the “City” column.

Recordset Number 3: The Histogram

This last recordset shows the distribution of the data, and is what you could effectively use to to draw a graph of the relative frequencies of different groups of values. Each row represents a step – or bar on the bar chart – and as mentioned above there can be a maximum of 200 steps. So you can see, a statistics object is quite lightweight, even for a massive table.

RANGE_HI_KEY – This upper limit of each step, so each step contains all the values bigger than the RANGE_HI_KEY of the last step, right up to and including this value.

RANGE_ROWS – This is how many rows in the table fall in this range – not including the number that match the RANGE_HI_KEY itself.

EQ_ROWS – The number of rows equal to the HI_KEY

DISTINCT_RANGE_ROWS – The number of different values in the range that there is data for (excluding the HI_KEY).

AVERAGE_RANGE_ROWS – The average number of rows for a given value within the range.

That’s a whistle-stop tour of the Statistics SQL Server holds on your data.

The algorithms that SQL then uses to calculate the number of rows for a given part of your query are pretty transparent when there’s just one column involved. If we look at the above example and let’s say you wanted to look up the rows where the City is “Abingdon” – the statistics tell us there is 1 matching row and that’s the figure SQL will use for cardinality estimation. Where a value is within a range then it will use a calculation based on the AVERAGE_RANGE_ROWS.

When there’s multiple columns involved it’s more complicated there are various algorithms and assumptions that come into play. If you’re interested in digging deeper, one very good resource is the Whitepaper on the 2014 Cardinality Estimator written by Joe Sack: https://www.sqlskills.com/blogs/joe/optimizing-your-query-plans-with-the-sql-server-2014-cardinality-estimator/

Conclusions

The main takeaway from this should just be the understand the extent – and limitations – of the information about the distribution of your data that SQL holds in the background.

If, when you’re tuning queries, you notice that the estimated row counts don’t match the actual, then this could be encouraging SQL to form a bad plan for the query. In these cases you might want to investigate what’s going on with the statistics.

Maybe your query is written in a way that it can’t use statistics effectively, one example of this can be where you store constant values in variables, then query using that variable in a WHERE clause. SQL will then optimise based on the average, rather than on your actual value.

Maybe the plan is based on one data value that has a very different cardinality to the one currently being queried. For instance when you first run a stored procedure, the plan is formed based on the parameters passed. Those parameters could have a cardinality that is quite different to those used in later executions.

Maybe the statistics are out of date and need refreshing. Stats get updated when approximately 20% of the data in the table changes, for a large table this can be a big threshold, so current statistics may not always hold good information about the data you are querying for.

Or maybe SQL is doing as good a job as it can with the information it has at its disposal. You might need to work out how you can give it a little extra help.

Here are some other recent posts about Statistics you may find useful:

When do Statistics get updated?

Rowcount estimates when there are no Statistics

Got a problem or embarking on a SQL Server project and want some help and advice? I’m available for consulting – please get in touch or check out my services page to find out what I can do for you.

Unlike some other languages, T-SQL doesn’t have the concept of a constant.

As good coders, we’ve all at some point tried to use a SQL variable to hold a constant value within a stored procedure, in order to make our code both more readable and maintainable.

I’ll give you an example. Here I’m querying a Task table, and I want all the rows where the TaskStatus is 0 (zero) which means the Task is Open:

SELECT *
FROM dbo.Task 
WHERE TaskStatus = 0;

If someone else comes along to look at this code they don’t know what the value of zero means. My code’s not clear. Worse I might refer to the same value multiple times in my procedure, so if I need to change it later I have to change it in multiple places.

Good practice from other coding languages would say that I replace it with a meaningfully named constant. As mentioned, in T-SQL we don’t have constants so I’ll compromise and use a variable:

DECLARE @OpenTask tinyint = 0;

SELECT *
FROM dbo.Task 
WHERE  TaskStatus = @OpenTask;

Now that’s much more readable – right?

Unfortunately it’s also a bad idea in SQL . Let’s see why.

I’ll create the aforementioned Task table, add an index on TaskStatus. Then I’ll add million rows with status 1 (which we’ll call closed) and 1 row with the value 0 (zero) which is open:

CREATE TABLE dbo.Task
(
    Id INT IDENTITY(1,1) CONSTRAINT PK_Task PRIMARY KEY CLUSTERED,
    UserId INT,
    TaskType INT,
    Payload VARCHAR(255) NOT NULL,
    TaskStatus tinyint NOT NULL
);
GO

CREATE INDEX IX_Task_TaskStatus ON dbo.Task(TaskStatus);

INSERT INTO dbo.Task (UserId,TaskType,Payload,TaskStatus)
SELECT TOP 1000000 1,1,'This Shizzle Is Done',1
FROM sys.objects a, sys.objects b, sys.objects c;

INSERT INTO dbo.Task (UserId,TaskType,Payload,TaskStatus)
SELECT 1,1,'Do This Shizzle',0;

Once that’s completed I’m going to update the statistics just so we know SQL has the most up to date information to produce an optimal execution plan for our queries:

UPDATE STATISTICS dbo.Task WITH fullscan;

Now let’s go back to our original queries. Before I run them let’s think what we want them to do. We have an index on TaskStatus and we only have one row we are looking for, so we’d hope the query will use the index and go straight to the record. The index doesn’t contain all the columns, but that’s okay. We’re only going to have to output one record so if it has to look up the extra columns up in the clustered index that’ll be pretty damn quick.

Let’s run the first query, we’ll capture the execution plan and the STATISTICS output:

SET STATISTICS io ON;
SET STATISTICS time ON;

SELECT *
FROM dbo.Task 
WHERE TaskStatus = 0;

Here’s the execution plan:

That’s doing exactly what we hoped for, it’s looked up the record in our index using a seek. Then it’s grabbed the rest of the columns from the clustered index using a key lookup.

Here’s the statistics output:
Table ‘Task’. Scan count 1, logical reads 7, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.

SQL Server Execution Times:
CPU time = 0 ms, elapsed time = 1 ms.

So that’s a nice small number of reads and less than a millisecond of CPU.

Now let’s run the “improved” version:

SET STATISTICS io ON;
SET STATISTICS time ON;

DECLARE @OpenTask tinyint = 0;

SELECT *
FROM dbo.Task 
WHERE TaskStatus = @OpenTask;

Here’s the execution plan this time:

That doesn’t look so good. Let’s check the statistics:
Table ‘Task’. Scan count 1, logical reads 5341, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.

CPU time = 109 ms, elapsed time = 96 ms.

Those figures tell us the query has got between 100 and 1,000 times worse. So much for the improved version.

So why is this happening?

The answer is simply that the optimizer doesn’t/can’t look at the values inside variables when a piece of SQL is compiled. Therefore it can’t use the statistics against the indexes on the table to get an accurate idea of how many rows to expect back in the results.

We can see that if we compare the properties of the Index Seek Operator from the first query:

Against the properties for the Index Scan Operator from the second query:

In the first one we can see that the Actual Number of Rows (at the top) exactly matches the Estimated Number of rows (at the bottom). SQL has been able to use the statistics on the index to get an accurate estimate.

In the second this is not the case. We have 500,000 rows estimate, but only 1 actual. This has led SQL down the route of choosing a plan that would have been more effective for 500,000 rows – but is much less effective for 1. In this case it didn’t know what value to optimize for. Lacking that information it used the density value in the statistics and multiplied that by the total number of rows to get the estimate. Or in other words, the statistics tell it that there are two distinct values (0 and 1) in the table. Not knowing which one has been supplied the optimizer figures than on average half the rows will be returned.

So what should do you to make your code clearer?

The simple answer is to use comments, the following is totally clear to its meaning, and will perform optimally:

SELECT *
FROM dbo.Task 
WHERE TaskStatus = 0 -- Open Task;

But what about the maintainability issue, where you may have to refer to the same value multiple times in a given procedure?

Unfortunately you’re just going to have to put up with maintaining the value in multiple places, but in general within a well designed application these should be static values (and hopefully integers) so it shouldn’t be too big a deal.

Note this is not the same for parameters passed to a stored procedure. In that case the queries inside the stored procedure will compile using the values passed the first time the procedure was executed – that can be really useful, but it can also cause its own set of issues to be aware of! Just remember parameters and variables – similar but not the same!

Need Help?

Got a problem and could do with some assistance? Get in touch today to see how I can help.