If you regularly code queries and have never been
introduced to the *windowing functions*, then
you are in for a treat. I've been meaning to write
about these for over a year, and now it's time to get
down to it.

## Support in Major Servers

SQL Server calls these functions Ranking Functions.

PostgreSQL supports a wider range of functions than MS SQL Server, having put them in at 8.4, and PostgreSQL and calls them Window Functions.

Oracle's support is broader (by a reading of the docs) than SQL Server or PostgreSQL, and they call them Analytic Functions.

I try to stay away from MySQL, but I did a quick Google on all three terms and came up with a few forum posts asking when and if they will be supported.

## The NTILE() Function

In this post we are going to look at NTILE, a cool function
that allows you to segment query results into groups and
put numbers onto them. The name is easy to remember because
it can create any -tile, a percentile, a decile, or anything
else. In short, an * n-*tile. But it is much easier to
understand with an example, so let's go right to it.

## Finding percentiles

Consider a table of completed sales, perhaps on an eCommerce site. The Sales Manager would like them divided up into quartiles, four equally divided groups, and she wants the average and maximum sale in each quartile. Let's say the company is not exactly hopping, and there are only twelve sales, which is good because we can list them all for the example. If we already had the quartiles provided then the query would be easy, so if we were lucky enough to be starting with this:

CUSTTYPE | AMOUNT | QUARTILE ----------+---------+---------- RETAIL | 78.00 | 1 RETAIL | 234.00 | 1 DEALER | 249.00 | 1 DEALER | 278.00 | 2 RETAIL | 392.00 | 2 RETAIL | 498.00 | 2 DEALER | 500.00 | 3 RETAIL | 738.00 | 3 DEALER | 1250.00 | 3 RETAIL | 2029.00 | 4 RETAIL | 2393.00 | 4 RETAIL | 3933.00 | 4

The query would be child's play *if we already
had the quartile*:

Select quartile , avg(amount) as avgAmount , max(amount) as maxAmount FROM ORDERS GROUP BY quartile ORDER BY quartile

## The Problem is We Do Not Have Quartile

The problem of course is that we do not usually have handy columns like QUARTILE provided, but we can generate the QUARTILE column during the query by using NTILE.

Select quartile , avg(amount) as avgAmount , max(amount) as maxAmount FROM ( -- The subquery is necessary -- to process all rows and add the quartile column SELECT amount , ntile(4) over (order by amount) as quartile FROM ORDERS ) x GROUP BY quartile ORDER BY quartile

This query will give us what the Sales Manager wants.

## Dissecting the Function and The OVER Clause

The NTILE() function takes a single argument, which tells the server how many groups to divide the data into. If there are not an exact number of rows in each group, the server decides which groups will be missing one row. So in an exact case all of your groups have the same count of rows, but when it does not divide evenly, one or more of them will be one row short.

If you pass 100 to NTILE(), you get a percentile. If you pass 10, you get a decile, and so forth.

The magic is in the OVER() function. This supports two clauses, and the example shows one, the ORDER BY. Quite simply, the ORDER BY clause tells the server how to line up the rows when adding the NTILE values. The clause is very flexible, and has nothing to do with your query's overall ORDER BY clause.

## The Second Clause: PARTITION

Now we will pretend the Sales Manager is not satisfied, and wants separate numbers for the two Customer Types. We could do this if the NTILE() function would create two sets of quartiles, one for each Customer Type, like so:

CUSTTYPE | AMOUNT | QUARTILE ----------+---------+---------- DEALER | 249.00 | 1 DEALER | 278.00 | 2 DEALER | 500.00 | 3 DEALER | 1250.00 | 4 RETAIL | 78.00 | 1 RETAIL | 234.00 | 1 RETAIL | 392.00 | 2 RETAIL | 498.00 | 2 RETAIL | 738.00 | 3 RETAIL | 2029.00 | 3 RETAIL | 2393.00 | 4 RETAIL | 3933.00 | 4

We can do this by using the PARTITION BY clause, which tells the server to break the rows into groups and apply the NTILE() numbering separately within each group. The new query would be this:

Select custtype , quartile , avg(amount) as avgAmount , max(amount) as maxAmount FROM ( -- The subquery is necessary -- to process all rows and add the quartile column SELECT amount , ntile(4) over (partition by custtype order by amount) as quartile FROM ORDERS ) x GROUP BY custtype,quartile ORDER BY custtype,quartile

## Bonus Points: The Median

Now once again the Sales Manager, who is never satisified,
comes down and says that the average is no good, she
needs the max and the *median* sale value within each quartile.
To keep it simple, she does not need this broken out
by customer type, it can be applied to the entire set.

This is a case where we can use NTILE() twice. The first time we will break all sales up into four groups, to get the quartiles, and then we will break up each quartile into two groups to get the median. The code looks like this:

Select quartile , max(case when bitile=1 then amount else 0 end) as medAmount , max(amount) as maxAmount FROM ( -- The second pass adds the -- 2-tile value we will use to find medians SELECT quartile , amount , ntile(2) over (partition by quartile order by amount) as bitile FROM ( -- The subquery is necessary -- to process all rows and add the quartile column SELECT amount , ntile(4) over (order by amount) as quartile FROM ORDERS ) x1 ) x2 GROUP BY quartile ORDER BY quartile

The magic here is that we know we've divided the data evenly into four sets, so the median will be the maximum value half way through each set. In other words, it will be the maximum value when the value of bitile=1 for each quartile.

## One More Note About Oracle

Once you get down the basics of the OVER clause, Oracle looks really good, because they support the clause over the largest range of functions, at least going by the respective doc pages for each platform.

## 12 comments:

Ken,

Nice post. I am an Oracle developer and frequently make use of analytic functions. They reduce a great deal of work and make writing complex queries easy.

One minor correction : I think you need to add the " as quartile " alias to all the subqueries after the "ntile(4) over " without which it would raise an error (at least in oracle).

Thanks!

Rajesh

www.etl-developer.com

Rajesh, thanks, I've corrected it. I've also realized a mistake in my median query, but that will have to wait until the evening to correct.

I found this blog doing a search for NTILE() function. It's a very interesting blog, but I think the NTILE() can not completely simulate PERCENTILE as TOP N PERCENT.

In case the number of records is less than number in the NTILE function, we will not create 100 groups.

Do you know about this limitation?

Naomi: You are correct, if the count of rows in a partition is less than 100, the highest value of NTILE() will be the row count in that partition.

This is similar to the standard deviation, which returns null on only one row. The limitation is defined by the function itself.

There is also a MEDIAN function, which makes the last query something like :

select quartile

, median (amount)

, max (amount)

from (

select amount

, ntile (4) over (order by amount) quartile

from orders)

group by quartile

I just tried this out and found that ntile(100) does not, in fact, give you a percentile if you have fewer than 100 samples. It just ranks however many samples you have. In my case, I have twenty samples and expected the top ranked out of 20 to be the 95th percentile. Instead it was 20th, exactly the same answer as if I used ntile(20).

After a bit of fumbling I arrived at the following:

100*cast(ntile(20) over(order by score) as numeric)/20 as percentile

The only trouble is that it doesn't look like you can substitute select count(distinct ...) for a hard coded number. That's a problem since the code may not work right after an update to the data.

Hi Ken,

Nice post, well explained. I really started loving those window functions, also for calculating running totals in an accounting/banking application, where the totals have to be calculated on the fly over a set of known transactions. I have posted an article about that on dzone:

http://java.dzone.com/articles/sql2003-window-functions-jooq

But I wasn't aware of the power of the NTILE() function. I'm certainly going to use that more often!

Cheers

Lukas

I soooo struggled with this and your post saved me.... thanks

This is exactly the format I was looking for in order to understand all this. Thanks!

This is a good post, but it should be called out that NTILE groups are *not* percentiles in the true sense for how most think of it. What you should really consider is the PERCENT_RANK() window function.

This article does a good job explaining this.

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