DuckDb Performance: min, max, and median vs quantile

I was playing with some classical statistics in DuckDB and I ran into something I'd like to share. It's about the measures minimum, maximum and median, and quantiles in general.

The short of it is:

1. Descriptive statistical measures minimum, maximum, and median occur rarely on their own: they are typically collected together, along with a number of other core descriptive statistics.
2. These measures are all special cases of quantiles: minimum is the 0th-quantile, maximum the 1st-quantile and median the 0.5th-quantile.
3. DuckDB provides aggregate functions for each of these measures. It was found that queries using min( expr ), max( expr ), and median( expr ) together are quicker than when using equivalent separate calls to quantile( expr, 0), quantile( expr, 1), and quantile( expr, 0.5) respectively.
4. Interestingly, quantile()'s second argument also accepts an array of quantile specifications, requesting multiple quantiles at once to be returned; also as an array. Calling quantile( expr, [0, 1, 0.5] ) was found to be considerably faster and less memory-intensive than multiple single quantile( expr, quantile ) calls for the 0th-, 1st- and 0.5th-quantile. This particular array-version call to quantile() was found to be only slightly slower than calling the min(), max(), and median() trio.
5. Some applications require a more extensive set of quantiles besides just the minimum, maximum and median, such as deciles or even percentiles. In those cases, collecting all quantiles of interest in one quantile()-call should be preferred over multiple calls each retrieving a single quantile.

You can skip directly to the benchmarks if you like; or you can read on from the top for some background info, and to learn about the considerations and ideas that went into this benchmark.

min, max, median, and quantiles

Just a bit of background on quantiles, and their relation to the classic measures min, max, and median.

Imagine a list of values, and sorting them in ascending order. (We'll assume it's already clear how the values can be compared to each other to determine their position in the sorted list.) Values may or may not be unique: after sorting, duplicate values simply appear adjacent to each other. Once this is done:

• The minimum is the first value of the sorted list.
• The maximum would be the last value of the sorted list.
• The median is the value found halfway the sorted list.

To get from here to the quantiles: imagine taking all list positions, and dividing each by the length of the list. (Here it's assumed list positions start counting from 1.) This yields the fraction of the number of values up to that position in the list.

Now, in essence, a percentile is one such position in the list, so that one can say:

the <fraction>th-quantile is <value>

Be careful when turning the wording around though:

<value> is the <fraction>th-quantile

Duplicate values span multiple quantiles. If that's the case, you should probably express that fact by specifying the quantile range:

<value> spans the <x>th- to the <y>th-quantiles

Stating some value is the xth-quantile implies there is exactly one quantile for that value, which in turns implies that value is unique. If that's the case, you should probably state that explicitly to remove any doubt.

Note: this is just a practical explanation: a quick refresher of what quantiles are, and how they relate to the classic statistical measures. This is not necessarily how an algorithm might calculate these measures; And, as we are about to see, there are some loose ends too.

Discrete vs Continuous Quantiles, and value-extrapolation

The method illustrated above features quantiles that correspond to concrete positions in the list; each has an actual fractional value. In the jargon, these are known as discrete quantiles.

But in practice, quantiles are often treated as a continuum: one could name any number from 0 to 1, and ask for its quantile value. If the required quantile doesn't match an actual position in the list, then the value corresponding to the smallest actual fraction including the required quantile is selected.

Example:

If there are 3 values with positions 1, 2, 3, and respective fractions 1/3, 2/3, 3/3, then the 0.5thquantile is the value at position 2. Why? No actual quantile corresponds to 0.5: 1/3 is too small and 2/3 is too large. But 2/3 is selected since it's the smallest actual quantile that covers the requested 0.5 proportion of the values.

There are more sophisticated implementations that try to return the "true" quantile value. This requires extrapolation between the value of the actual quantiles that occur in the list (i.e., the discrete quantiles) right before and after the required quantile.

Extrapolation applies in particular to values of numerical types, or of types that can be treated as if they are numerical, such as DATE, TIME, and TIMESTAMP. In these cases, the geometrical mean is used to extrapolate.

While value extrapolation may appear intuitive and harmless, I feel it's actually less so:

• By definition, extrapolation creates values that are not actually observed in the dataset. This in itself does not have to be a problem as long as you're aware of it, but it does add complexity and may lead to paradoxical results.
• Geometrical mean extrapolation may result in values that have a different type than that of the input domain, while the minimum and maximum will always retain the type of the argument. Again, one may work around this but it does introduce some untidiness which may be undesirable.
• Using the geometrical mean to extrapolate between the quantiles right before and after the requested quantile may lead to misleading results. Suppose you have 100 values. Let's say the 50th value is 50, and the 51st value is 51. With a naive geometrical mean the 0.5th quantile would be 50.5. But what if all prior values are all 50 while values 51 through 100 are more evenly distributed? It seems clear to me that if the purpose of extrapolation is to find a more true value, it should take the distribution of values into account, and the 0.5th-percentile should be a lot closer to 50 than 50.5.

However, this need not concern us right now: for several reasons, extrapolation doesn't matter much for how quantiles are used. (Some of the reasons are that for realisticly sized data sets, the difference between the extrapolated value and the discrete value becomes smaller and smaller; another reason is that the descriptive statistics can still provide a good or good-enough description of the dataset as a whole, even if the actual measure values are somewhat incaccurate. There are probably counter-arguments too, but that's not the topic of this article. )

Generalization: min, max, and median as Quantiles

With the rule in place to select the actual quantile value, the definitions of minimum, maximum, and median given earlier can now be generalized to quantiles:

• The 0th-quantile corresponds to the minimum. Of course, there is no actual fraction that corresponds to 0. But the smallest fraction that includes it, corresponds to the first value in the list, i.e. our original definition of the minimum.
• The 1th-quantile corresponds to the maximum, i.e. the last value in the list.
• The median corresponds to the 0.5th-quantile, as 0.5 is halfway between 0 and 1. For median, value extrapolation is often mentioned, probably because the simple definition as "halfway the list" poses an easy-to-spot problem when the list has an even number of values.

Quantiles in DuckDB

All these measures have an implementation in SQL as an aggregate function. And of course, DuckDB provides them too:

• min( expression ) implements minimum.
• max( expression ) implements maximum
• median( expression ) implements median.
• quantile( expression, quantile(s) ) implements quantile.

A few remarks concerning the implementation of these functions in DuckDB:

• While min() and max() are straightforward, median() applies value extrapolation for numeric types and temporal types. This means that the return type of median() may not match the type of its argument.
• The quantile()-function is actually an alias for quantile_disc(): the postfix _disc indicates it implements discrete quantiles. DuckDB also provides quantile_cont(), which implements continuous quantiles.
• While quantile_disc() and quantile_cont() examine the entire set of values, DuckDB also offers a family of approximate aggregate functions, including a few to estimate quantiles. These are approx_quantile() and reservoir_quantile(), which work by examining a sample of the values rather than all values. The idea here is that these functions may be faster to compute, but at the expense of returning an estimate of the quantile, rather than a precisely determined one.

What to use, under what circumstances, and how

Considering there are quite a number of options to potentially achieve the same or similar results, the question naturally arises, which should one use, and under what circumstances?

For now I just want to decide a simple dilemma:

The functions min(), max() and median() are well-known and have intuitive names, which is why I would prefer them. But quantile() is more general, and can achieve similar or even equivalent results, as well as handle other, more fine-grained quantiles. Is there a good reason to prefer one over the other?

So in the remainder of this article, I won't be looking into approximate quantile functions: I won't be measuring whether they are faster, and how much; nor will I be exploring how accurate their estimates are as compared to exact methods.

Also, I'm focusing only on quantile(), that is to say: quantile_disc(). That's because for my particular use case, I'm treating the descriptive statistics as summary of my dataset. For that purpose I prefer the quantile values to be drawn from my dataset rather then extrapolated.

With that said, this article will answer the question: when to use min(), max(), and median() vs quantile().

Calling quantile()

As the function signature suggests, quantile( expression, quantile(s) ) takes two parameters: the expression which provides the values as first argument, and a second argument. The second argument can be a single number between 0 and 1, specifying what quantile to return.

The interesting thing is that the second argument can also accept a list of numbers, each specifying a particular quantile. In this case, all specified quantiles are calculated in one go and the function returns the list of corresponding quantile values.

For statistical applications, this makes a lot of sense! Surely with regard to minimum and maximum: these measures almost always occur as a pair to indicate the entire value range. The median is a natural complement, adding basic but valueable information about the distribution of the data along the range. But many applications (for example in demographics) go even further, and are interested in deciles (quantile increments of 10%) or even percentiles (increments of 1%).

Quantiles must be specified as constants

Regardless of whether you're using quantile() to collect a single quantile, or multiple quantiles at once, the argument that specifies the quantiles must be a constant value. It can not be an expression that depends on a column. This makes sense: considering that quantile() is an aggregate function, the percentile definition should be invariant for the entire statement.

However, the requirement for a constant percentile specification may be inconvenient when its value is also to be used elsewhere. In those cases, one can sometimes store the percentile definition in a DuckDB-variable. As argument, the variable may be referenced using a call to getvariable( 'variablename' ), which is considered a constant value.

Benchmarking quantile()

After all this background, it's time to do some measurements to try and find some answers to my questions. To benchmark the functions, I used one of the NYC taxi trip parquet data files, in this case the "High Volume For-Hire Vehicle Trip Records" for January, 2023. The file is called fhvhv_tripdata_2023-01.parquet and has 24 columns and 18,479,031 (~18 million) rows.

All tests are performed using the DuckDB command line, version 1.5.5 with standard settings, running on my laptop (HP EliteBook 850 G8 with an Intel i7-1185G7 and 32GB RAM, on Windows 11).

There's two different benchmarks:

1. Comparing 'classic' measures min(), max() and median() against quantile() - checking both the single- and multi-quantile mode.
2. Comparing the single quantile vs the multi-quantile version of the quantile() function. This tests the impact of adding more quantiles.

Each query provides real, user and sys timings. For this purpose, the real timings matter most, but the split allows for some interesting observations.

Comparing classic measures against the quantile()

As I explained, my first instinct would be to use min(), max() and median(). Because these are all just specific cases of quantiles, I'm trying to figure out whether there's any reason (not?) to switch to quantile() instead. Because these classical statistics are often collected together, and considering that quantile() can collect multiple quantiles in one go, both single- or multi-quantile versions of quantile() should be compared.

This benchmark tests one column at a time; the idea behind that is that the data type and the number of NULL-values in a column may reveal different aspects of the different aggregation functions.

A graph of the results is shown below:


The column name is on the vertical axis, and the query runtimes are on the horizontal axis. For each column, there are 3 series: green, blue and orange; for each color there are three shades: darkest (user), lighter (real) and lightest (sys).

1. The green groups are the classic aggregates min(), max() and median(). For each column, there is one such group. So in this case the query looks like:

   SELECT min( <column> )
   , max( <column> )
   , median( <column> )
   FROM read_parquet( 'fhvhv_tripdata_2023-01.parquet' );
   

2. The blue groups are the multi-quantile() calls, using [0, 1, 0.5] as quantiles specification, equivalent to the classic aggregates min(), max() and median(). So in this case the query looks like:

   SELECT quantile( <column>, [ 0, 1, 0.50 ] )
   FROM read_parquet( 'fhvhv_tripdata_2023-01.parquet' );
   

3. The orange groups are the single-quantile() calls, using 3 individual quantile() calls passing 0, 1 and 0.5 for the quantile argument. So in this case, the query looks like:

   SELECT quantile( <column>, 0 )
   ,      quantile( <column>, 1 )
   ,      quantile( <column>, 0.5 )
   FROM read_parquet( 'fhvhv_tripdata_2023-01.parquet' );
       

Observation #1

Classic statistics are fastest, but only slighly so as compared to a multi-quantile()

• For each column, the green group, calling the classical statistics min(), max() and median() is the fastest. (Avg: 0.75seconds; Stdev: 0.16)
• The blue group, calling the multi-quantile variant of quantile() is slightly slower than the green group. (Avg: 0.78seconds; Stdev: 0.20) The difference is consistent, but really quite small - on average, about 5% slower compared to the green group.
• The orange group, with multiple calls to the single-quantile variant of quantile(), is substantially slower than the blue and green groups (Avg: 1.52; Stdev: 0.43). On average they last twice as long as the classic statistics (50% slower).

In general we can conclude that if you only need min(), max() and median(), you're probably best off sticking to those functions. However, if you for some reason would want to use quantile(), performance will probably be acceptably close, provided you use the multi-quantile variant. It's also clear that the single-quantile variant of quantile() really incurs significant negative impact on performance, and this should probably be avoided.

Observation #2

The column data type and distinct value-count really appears to have a discernible effect, which is a little different for the classical statistics as compared to quantile():

• For the VARCHAR columns (hvfhs_license_num , originating_base_nu, dispatching_base_num, shared_match_flag, wav_request_flag, shared_request_flag, access_a_ride_flag, and wav_match_flag), the user-timing for the classical statistics appears to be a bit lower or the same as the real-timing. Both types of quantile() calls tend to have a user timing that is often a bit higher than the real-timing.
• For the TIMESTAMP-columns (request_datetime, on_scene_datetime, pickup_datetime and dropoff_datetime), as well as for the BIGINT columns (PULocationID and DOLocationID), the user timing is typically somewhat lower than the real timing. This applies to both the classical statistics as well as the quantile() calls. The BIGINT column trip_time is a bit of a mystery in this regard, as its user-timing is higher than the real timing.
• For the DOUBLE-columns (trip_miles, base_passenger_fare, tolls, bcf, sales_tax, congestion_surcharge, airport_fee, tips, and driver_pay), user time consistently exceeds the real time somewhat.

Even though the column type appears to have some effect on the performance, it is not clear whether and how this could be used to an advantage. Also, the differences are quite slight, and do not appear to affect the main observation. Perhaps more significant difference can be detected with either larger data sets or with other data types or column value distributions.

Observation #3

For the classic statistics and the multi-quantile version of quantile(), sys measurements appear to be inconsequential: they are consistently low compared to the real and user measurments (green: 0.12; blue: 0.11), and their averages are virtually the same. I suspect that for these groups, the sys time measurement mostly has to do with time spent reading the parquet data which needs to happen anyway, regardless of what functions are tested. But for the single quantile calls to quantile() the sys measurements are consistently higher (Avg: 0.26), and not only in absolute sense: the share of the sys measurement in proportion to the real measurements is also noticeably higher: 0.17 (green: 0.16, blue: 0.14). To be sure, this may be a small increase which does not have an immediate practical consequence. But it does show that more quantile calls require more system calls, which I suspect come down to memory allocation.

More info on that in the next benchmark.

Comparing single- vs multi- quantile() variants

The idea behind this benchmark is to compare the single- and multi- variants of the quantile() function to see which one you should prefer. The results are shown in the chart below:


The query runtimes are on the vertical axis, and the number of quantiles on the horizontal axis.

For the quantiles, a set of 11 values 0.00, 0.01, 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95, 0.99 and 1.00 is tested. For convenience these are stored in a DuckDB variable:

SET VARIABLE quantiles = [0.00, 0.01, 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95, 0.99, 1.00];

There are 2 series: blue and orange, again in three shades (user: darkest; real: lighter; sys: lightest).

1. Again, the blue groups are the multi-quantile quantile() calls. The function is applied to all columns using a COLUMNS( * ) expression. So in this case the query looks like:

   SELECT quantile( COLUMNS( * ), getvariable('quantiles')[1:<iteration>] )
   FROM read_parquet( 'fhvhv_tripdata_2023-01.parquet' );
   

   The <iteration> is varied, starting with 1, and incremented to 2, 3, and so on, all the way up to 11, requesting a new additional quantile for each iteration.
2. The orange groups again are the single-quantile quantile() calls. Like for the blue series, the call is applied on all columns using a COLUMNS( * ) expression. The difference is that here, for each iteration, an additional call, including a COLUMNS( * ) expression is required.
   
   So, for the 1st iteration the query looks like:

   SELECT quantile( COLUMNS( * ), getvariable('quantiles')[1] )
   FROM read_parquet( 'fhvhv_tripdata_2023-01.parquet' );
   

   For the 2nd, it becomes

   SELECT quantile( COLUMNS( * ), getvariable('quantiles')[1] )
   ,      quantile( COLUMNS( * ), getvariable('quantiles')[2] )
   FROM read_parquet( 'fhvhv_tripdata_2023-01.parquet' );
   

   ...And so on.
   
   One might guess this should go up all the way up to 11 too, but alas: the series stops at 7. Further iterations resulted in an out of memory error, so the benchmark could not be completed. That said, the iterations that did run already provide ample information!

Observation #1

The blue group - the multi-quantile calls - demonstrate moderate and predictable runtime increases as more quantiles are requested. Each iteration is a few percents slower than the previous one, but considering the fact that each iteration also collects another quantile, that seems perfectly acceptable.

The orange group with the single-quantile calls fares quite differently! Here, each next iteration takes about twice the time of the previous iteration. As a result, it becomes unacceptably slow very quickly, and even then runs into an out of memory error after iteration 7.


Perhaps the slowdown for each iteration is all down to time required for memory allocation, or perhaps there is some other reason - this cannot be concluded from this test. But we can definitely conclude that the multi-quantile call should be preferred whenever collecting more than quantile at once.

In conclusion

I hope you enjoyed this post! I'm happy I could just resolve some questions from my end. I think the takeaways are clear:

• If you only need min(), max() and median(), you're fine! You don't need to switch to quantile() for performance reasons. That said, it also doesn't hurt, provided you use the multi-quantile() version of quantile().
• If you need to collect multiple quantiles beyond min(), max() and median(), you should probably be using quantile( expr, [...quantiles...] ).
• If you're using single quantile quantile() calls, you're either doing something very special, or you're doing something wrong. At any rate, beware of out of memory errors, and investigate whether you can bunch up several single quantile calls into one multi-quantile call - it will save memory and probably increase performance, potentially a lot!

If you found this interesting, you might want to investigate some of the topics that were mentioned but not explored any further, such as:

• Approximate aggregate functions, like approx_quantile() and reservoir_quantile().
• Using quantile_cont() instead of quantile_disc(), especially if you require value extrapolation.
• The quantile_cont() function also supports array syntax for specifying multiple quantiles. It's definiteley worth comparing that to both its single quantile version, as well as to quantile_disc(). They appear to have quite different implementations, going by their type signatures. Therefore, there may be interesting and perhaps unexpected differences in performance.

Feel free to leave some feedback - I read and respond to your comments.

Year-to-Date on Synapse Analytics 5: Using Window Functions

For one of our Just-BI customers we implemented a Year-to-Date calculation in a Azure Synapse Backend. We encountered a couple of approaches and in this series I'd like to share some sample code, and discuss some of the merits and benefits of each approach.

TL;DR: A Year-to-Date solution based on a SUM() window function is simple to code and maintain as well as efficient to execute. This as compared to a number of alternative implementations, namely a self-JOIN (combined with a GROUP BY), a subquery, and a UNION (also combined with a GROUP BY).

Note: this is the 5th post in a series.

• For sample data and setup, please see the 1st post in this series.
• For a solution based on a self-JOIN and GROUP BY, please find the 2nd post in this series.
• For a solution based on a subquery, please find the 3rd post in this series.
• For a solution based on a UNION, please find the 4th post in this series.

(While our use case deals with Azure Synapse, most of the code will be directly compatible with other SQL Engines and RDBMS-es.)

Using window functions

Nowadays, many SQL engines and virtually all major RDBMSes support window functions (sometimes called analytic functions). A window function looks like a classic aggregate function. In some respects it also behaves like one, but at the same time there are essential differences.

Aggregate functions

Consider the following example:

select sum(SalesAmount) as SumOfSalesAmount
,      count(*)         as RowCount
from   SalesYearMonth

The example uses two aggregate functions, SUM() and COUNT(). It returns a result like this:

SumOfSalesAmount	RowCount
109,846,381.43	38

Two things are happening here:

• Even though there are multiple rows in the SalesYearMonth table, the result consists of just one row. In other words, a collection of source rows have been aggregated into fewer (in this case, only one) result row.
• The functions have caclculated a value based on some aspect of the individual rows in the source collection. In the case of SUM(SalesAmount), the value of the SalesAmount column of each individual row was added to obtain a total. In the case of COUNT(*), each row was counted, adding up to the total number of rows.

Because the previous example uses aggregate functions, we cannot also select any non-aggregated columns. For example, while SalesYear and SalesMonth are present in the individual underlying rows, we cannot simpy select them, because they do not exist in the result row, which is an aggregate.

Window functions

Now, SUM() and COUNT() also exist as window functions. Consider the following query:

select SalesYear
,      SalesMonth
,      SalesAmount
,      sum(SalesAmount) over() as TotalOfSalesAmount
,      count(*)         over() as RowCount
from   SalesYearMonth

You might notice the last two expressions in the SELECT-list look almost identical to the aggregate functions in the previous example. The difference is that in this query, the function call is followed by an OVER()-clause. Syntactically, this is what distinguishes ordinary aggregate functions from window functions.

Here is its result:

SalesYear	SalesMonth	SalesAmount	TotalOfSalesAmount	RowCount
2011	5	503,805.92	109,846,381.43	38
2011	6	458,910.82	109,846,381.43	38
...more rows...
2014	6	49,005.84	109,846,381.43	38

Note that we now get all the rows from the underlying SalesYearMonth table: no aggregation has ocurred. But the window functions do return a result that is identical to the one we got when using them as aggregate functions, and that for each row of the SalesYearMonth table.

It's as if for each row of the underlying table, the respective aggregate function was called over all rows in the entire table. Conceptually this is quite like the construct we used in the subquery-solution. The following example illustrates this:

select SalesYear
,      SalesMonth
,      SalesAmount
,      (
           select sum(SalesAmount) 
           from   SalesYearMonth
       ) as TotalOfSalesAmount
,      (
           select count(*)
           from   SalesYearMonth
       ) as RowCount
from   SalesYearMonth

The window and the OVER()-clause

Thinking about window functions as a shorthand for a subquery helps to understand how they work and also explains their name: a window function returns the result of an aggregate function on a particular subset of the rows in the query scope. This subset is called the window and it is defined by the OVER()-clause.

The parenthesis after the OVER-keyword can be used to define which rows will be considered as window. When left empty (like in the example above) all rows are considered.

Controlling the window using the PARTITION BY-clause

If you compare the previous example with our prior subquery-solution, you'll notice that here, we do not have a WHERE-clause to tie the subquery to the current row of the outer query. That's why our result is calculated over the entire table, rather than with respect to the current year and preceding months, as in our prior subquery-solution. This is equivalent to the empty parenthesis following the OVER-keyword in the corresponding window-function example.

In the subquery-solution we wrote a WHERE-clause to specify a condition to tie the rows of the subquery to the current row. For window functions, we can control which rows make up the window window by writing a PARTITION BY-clause inside the parenthesis following the OVER-keyword.

The PARTITION BY-clause does not let you specify an arbitrary condition, like we could in a subquery. Instead, the relationship between the current row and rows in the window must be expressed through one or more attributes for which they share a common value. The following example may illustrate this:

select SalesYear
,      SalesMonth
,      SalesAmount
,      sum(SalesAmount) over(partition by SalesYear) as YearTotalOfSalesAmount
from   SalesYearMonth

In the example above, sum(SalesAmount) over(partition by SalesYear) means: calculate the total of SalesAmount over all rows where the value of SalesYear is equal to the value of the SalesYear in the current row.

The equivalent query using subqueries would be:

select OriginalSales.SalesYear
,      OriginalSales.SalesMonth
,      OriginalSales.SalesAmount
,      (
           select sum(YearSales.SalesAmount) 
           from   SalesYearMonth as YearSales
           where  YearSales.SalesYear = OriginalSales.SalesYear
       ) as YearTotalOfSalesAmount
from   SalesYearMonth as OriginalSales

The result is shown below:

SalesYear	SalesMonth	SalesAmount	YearTotalOfSalesAmount
2011	5	503,805.92	12,641,672.21
2011	6	458,910.82	12,641,672.21
...more rows...
2014	6	49,005.84	20,057,928.81

(Note that 12,641,672.21 is the sum of the SalesAmount for SalesYear 2011; 20,057,928.81 is the total for 2014.)

A partition for the preceding months?

It's great that the PARTITION BY-clause allows us to specify a window for relevant year, but it's still too wide: we want the window to contain only the rows from the current year, but only for this month and its preceding months. In the subquery-solution this was easy, as we could write whatever condition we want in the WHERE-clause. So we wrote:

where  SalesYtd.SalesYear   = SalesOriginal.SalesYear
and    SalesYtd.SalesMonth <= SalesOriginal.SalesMonth

Specifying SalesYear in the window functions' PARTITION BY-clause is equivalent to the first part of the subquery's WHERE-clause condition.

It's less clear what our partition expression should look like to select all months preceding the current month. It's not impossible though. For example, we can write an expression to mark whether the current SalesMonth is equal to or less than a specific month. For example:

-- every month up to and including june is 1, all months beyond june is 0
case
    when SalesMonth <= 6 then 1 
    else 0
end

If we can write such an expression, then of course, we can also use it in a PARTITION BY-clause, like so:

sum(SalesAmount) over (
  partition by 
    SalesYear
  , case
      when SalesMonth <= 6 then 1 
      else 0
    end
) 

Let's try and think what this brings us.

Suppose the value for SalesMonth is 6 (june), or less? The CASE expression would return 1, and the window function would take all rows into account for which this is the case. So january, february, march and so on, up to june would all get the total of those six months - that is, the YTD value for june.

On the other hand, if SalesMonth is larger than 6, the CASE expression evaluates to 0. So all months beyond june (that is: july, august, and so on up to december) form a partition as well, and for those months, whatever is the sum over those months would be returned.

Now, it's not really clear what the outcome means in case the month is beyond june. But it doesn't really matter - what is important, is that we now know how to calculate the correct YTD value for a given month. And, what we did for june, we can do for any other month. So, once we have the YTD expressions for each individual month, we can set up yet another CASE-expression to pick the right one according to the current SalesMonth.

Putting all that together, we get:

select SalesYear
,      SalesMonth
,      SalesAmount
,      case SalesMonth
         -- january
         when 1 then SalesAmount
         -- february
         when 2 then
           sum(SalesAmount) over(
             partition by 
               SalesYear
             , case when SalesMonth <= 2 then 1 else 0 end
           ) 
           
         ...more cases for the other months...
           
         -- december
         when 12 then
           sum(SalesAmount) over(
             partition by 
               SalesYear
             , case when SalesMonth <= 12 then 1 else 0 end
           ) 
       end as YtDOfSalesAmount
from   SalesYearMonth

Like with the UNION-solution, we are taking advantage of our knowledge of the calendar, which allows us to create these static expressions. We would not be able to do this in a general case, or where the number of distinct values is very large. But for 12 months, we can manage.

While it's nice to know that this is possible, there is a much, much nicer way to achieve the same effect - the frame specification.

Frame Specification

The frame specification lets you specify a subset of rows within the partition. The way you can specify the frame feels a bit odd (to me at least), as it is specified in terms of the current row's position in the window. Hopefully the following example will make this more clear:

select SalesYear
,      SalesMonth
,      SalesAmount
,      sum(SalesAmount) over(
         partition by SalesYear
         order by SalesMonth
         rows between unbounded preceding
         and current row
       ) as SalesYtd
from   SalesYearMonth

We already discussed the PARTITION BY-clause, all the clause after that are new.

The ORDER BY-clause sorts the rows within the window, in this case by SalesMonth. We need to rows to be ordered because of how the frame specification works: it lets you pick rows by position, relative to the current row. The position of the rows is undetermined unless we sort them explicitly, so if we want to pick rows reliably we need the ORDER BY-clause to guarantee the order.

The frame specification follows the ORDER BY-clause. There are a number of possible options here, but I will only discuss the one in the example. In this case, it almost explains itself: we want to use the current row, and all rows that precede it. Since we ordered by SalesMonth, this means all the rows that chronologically precede it. As this selection applies to the current partition, we will only encounter months here that are within the current year.

So here we have it: a YTD calculation implemented using a window functions. It's about the same amount of code as compared to the subquery solution, but more delcarative, as we do not need to specify the details of a condition. On the other hand, it is also less flexible than a subquery, but in general one should expect the window functions to perform better than the equivalent subquery.

Generalizing the solutions

So far all our examples were based on the SalesYearMonth table, which provides SalesYear and SalesMonth as separate columns. One might wonder what would it would take to apply these various methods to a realistic use case.

For example, it is likely that in a real dataset, the time would be available as a single column of a DATE or DATETIME data type. A single date column potentially affects the YTD calculation in two ways:

• Year: As the YTD is calculated over a period of a year and almost all solutions we described used the SalesYear column explicitly to implement that logic.
• Preceding rows: To calculate the YTD for a specific row, there has to be a clear definition of what rows are in the same year, but which precede it. In our examples we could use the SalesMonth column for that, but this might be a but different in a realistic case.
• Lowest Granularity: The lowest granularity of the SalesMonthYear table is at the month level, and we collected the YTD values at that level. (If we'd want to be precise we'd have to call that year-to-month).

Apart from the time aspect, the definition of the key affects all solutions that generate "extra" rows and require a GROUP BY to re-aggregate to the original granularity.

The Year

The ON-condition of the JOIN-solution and the WHERE-condition of the subquery-solution both rely on a condition that finds other rows in the same year, and the window function-solution uses the year in its PARTITION BY-clause.

It is usually quite simple to extract the year from a date, date/time or timestamp. In Synapse Analytics or MS SQL one can use the DATEPART or YEAR function to do this.

The UNION-solution has no direct dependency on the year.

The preceding rows

The need to find the preceding rows applies to all solutions that use the year to find the rows to apply the YTD calculation on. In our samples, this could all be solved using the SalesMonth column.

Again, it are the JOIN-solution and subquery-solution that used it in their condition, whereas the window function-solution uses it in its ORDER BY-clause.

In this case, the fix is more straighforward then with the year: instead of the month column, these solutions can simply use the date or date/time column directly. No conversion or datepart extraction is required.

Lowest granularity

The granularity is of special concern to the UNION-solution. The solution relies on an exhaustive and static enumeration of all possible future dates within the year. Already at the month level, this already required a lot of manual code.

Below the month, the next level would be day. While it would in theory be possible to extend the solution to that level, it is already bordering the impractible at the month level.

The Key

The key definition affects both the JOIN-solution and the UNION-solution, as that both require a GROUP BY over the key.

Year-to-Date on Synapse Analytics 4: Using UNION and GROUP BY

For one of our Just-BI customers we implemented a Year-to-Date calculation in a Azure Synapse Backend. We encountered a couple of approaches and in this series I'd like to share some sample code, and discuss some of the merits and benefits of each approach.

TL;DR: A Year-to-Date solution based on a SUM() window function is simple to code and maintain as well as efficient to execute. This as compared to a number of alternative implementations, namely a self-JOIN (combined with a GROUP BY), a subquery, and a UNION (also combined with a GROUP BY).

Note: this is the 4th post in a series.

• For sample data and setup, please see the 1st post in this series.
• For a solution based on a self-JOIN and GROUP BY, please find the 2nd post in this series.
• For a solution based on a subquery, please find the 3rd post in this series.

(While our use case deals with Azure Synapse, most of the code will be directly compatible with other SQL Engines and RDBMS-es.)

Using a UNION

We mentioned how the solution with the JOIN relates each row of the main set with a subset of "extra" rows over which the YTD value is calculated by aggregating over the key of the main set using a GROUP BY.

It may not be immediately obvious, but we can also use the SQL UNION (or rather, UNION ALL) operator to generate such a related subset. Just like with the JOIN-solution, this can then be aggregated using GROUP BY. An example will help to explain this:

select      SalesYear
,           SalesMonth
,           sum(SumOfSalesAmount)      as SumOfSalesAmount
,           sum(YtdOfSumOfSalesAmount) as YtdOfSumOfSalesAmount
from (
    select  SalesYear
    ,       SalesMonth
    ,       SumOfSalesAmount
    ,       SumOfSalesAmount           as YtdOfSumOfSalesAmount
    from    SalesYearMonth
    union all
    -- JANUARY
    select  SalesYear
    ,       SalesMonth + 1            -- february
    ,       null
    ,       SumOfSalesAmount
    from    SalesYearMonth
    where   SalesMonth = 1
    union all
    select  SalesYear
    ,       SalesMonth + 2            -- march
    ,       null
    ,       SumOfSalesAmount
    from    SalesYearMonth
    where   SalesMonth = 1
    union all
    
    ... and so on, all for JANUARY ...

    union all
    select  SalesYear
    ,       SalesMonth + 11            -- december
    ,       null
    ,       SumOfSalesAmount
    from    SalesYearMonth
    where   SalesMonth = 1
    union all
    -- FEBRUARY
    select  SalesYear
    ,       SalesMonth + 1            -- march
    ,       null
    ,       SumOfSalesAmount
    from    SalesYearMonth
    where   SalesMonth = 2
    union all
    
    ... and so on, for the rest of FEBRUARY, 
        and then again for MARCH, APRIl, MAY, JUNE, JULY, AUGUST, SEPTEMBER, OCTOBER...   

    -- NOVEMBER
    select  SalesYear
    ,       SalesMonth + 1            -- december
    ,       null
    ,       SumOfSalesAmount
    from    SalesYearMonth
    where   SalesMonth = 11
) Sales
group by    SalesYear
,           SalesMonth

Duplicating metric-data so it contributes to the following months

In the top of the UNION we simply provide the entire resultset from SalesYearMonth, reporting the SumOfSalesAmount-metric as is, but also copying it to YtdSumOfSalesAmount. The other parts of the UNION are used to selectively duplicate the data for the SumOfSalesAmount-metric into the YtdSumOfSalesAmount, so that its data contributes to the YtdSumOfSalesAmount for all following months.

We start by grabbing january's data by applying the condition that demands that the SalesMonth equals 1:

-- JANUARY
select  SalesYear
,       SalesMonth + 1            -- february
,       null
,       SumOfSalesAmount
from    SalesYearMonth
where   SalesMonth = 1
union all
... repeat to duplicate january's data into february, march, and so on all the way up to december...

. This is done for a total of 11 times, each time adding 1, 2, 3 and so on - all the way up to 11 - to the SalesMonth attribute. This ensures january's data, as captured by the condition in the WHERE clause, is reported also in february (SalesMonth + 1), march (SalesMonth + 2), and so on, all the way up to december (SalesMonth + 11).

After the string of UNIONs for january appear more parts to duplicate the data also for february and all following months: -- FEBRUARY select SalesYear , SalesMonth + 1 -- march , null , SumOfSalesAmount from SalesYearMonth where SalesMonth = 02 union all ... repeat to duplicate february's data into march, april, and so on all the way up to december... . Again, february's data is selected by applying the condition

where   SalesMonth = 2

, and this happens now 10 times, again adding a number to the SalesMonth so it is duplicated to march, april, may, all the way up to december - in other words, all months following february.

What we thus did for january and februry is repeated for march, april, and so on for all months up to november. November is the last month we need to do this for: November's data still needs to be copied to december, but as december is the last month, that data only needs to be counted in december itself.

While it may seem wasteful to duplicate all this data, it really is not that different in that respect from the other solutions we've seen so far. It's just that now it's really in your face, because there is a pretty direct correspondence between the SQL code and the data sets that are being handled. The JOIN and subquery solutions hande similar amounts of data, it's just achieved with way less code, and in a far more implicit manner.

Original metric is retained

Note that the original metric also computes correctly, because the parts of the union only duplicate the data to the YTD column. The union parts that duplicate the data to the subsequent months select a NULL for the original metric. So the data for the original metric is never duplicated, and thus retains its normal value.

Drawbacks to the UNION-solution

The main drawback to the UNION-solution is its maintainability. A lot of code is required, far more than for any of the methods we have seen so far. Despite the indiviual patterns are simple (condition to get one month, adding a number to project that data to a future month), it is suprisingly easy to make a little mistake somewhere

We just argued that this solution is not so much different from the JOIN solution, but that remark only pertains to how the calculation is performed. The JOIN-solution generates the data it operates upon dynamically and declaratively; the UNION solution does this statically and explicitly. This is also why it is impossible to generalize ths approach for any arbitrary JOIN: YTD is a special case, because we know exactly how often we should duplicate the data as this is dictated by the cyclical structure of our calendar.

Next installment: Solution 4 - window functions

In the next installment we will present and discuss a solution based on a window functions.

Year-to-Date on Synapse Analytics 3: Using a Subquery

For one of our Just-BI customers we implemented a Year-to-Date calculation in a Azure Synapse Backend. We encountered a couple of approaches and in this series I'd like to share some sample code, and discuss some of the merits and benefits of each approach.

TL;DR: A Year-to-Date solution based on a SUM() window function is simple to code and maintain as well as efficient to execute. This as compared to a number of alternative implementations, namely a self-JOIN (combined with a GROUP BY), a subquery, and a UNION (also combined with a GROUP BY).

Note: this is the 3rd post in a series.

• For sample data and setup, please see the 1st post in this series.
• For a solution based on a self-JOIN and GROUP BY, please find the 2nd post in this series.

(While our use case deals with Azure Synapse, most of the code will be directly compatible with other SQL Engines and RDBMS-es.)

Using a subquery

We can also think of YTD calculation as a separate query that we perform for each row of the SalesYearMonth table. While this does imply a row-by-row approach, we can still translate this easily to pure SQL by creating an expression in the SELECT-list, which uses a subquery to calculate the YTD value for the current row:

select      SalesOriginal.SalesYear
,           SalesOriginal.SalesMonth
,           SalesOriginal.SalesAmount
,           (
                select sum(SalesYtd.SalesAmount)
                from   SalesYearMonth as SalesYtd
                where  SalesYtd.SalesYear   = SalesOriginal.SalesYear
                and    SalesYtd.SalesMonth <= SalesOriginal.SalesMonth
            ) as SalesYtd
from        SalesYearMonth as SalesOriginal

There's a similarity with the JOIN-solution, in that we use the SalesYearMonth table twice, but in different roles. In the JOIN-solution both appeared on one side of the JOIN keyword and we used the aliases OriginalSales and YtdSales to be able to keep them apart. In the subquery approach, the distinction between these two different instances of the SalesYearMonth table is more explicit: the main instance of the SalesYearMonth table occurs in the FROM-clause, and the one for the YTD calculation occurs in the SELECT-list.

Also similar to the JOIN solution is the condition to tie the set for the YTD calculation to the main query using the SalesYear and SalesMonth columns. Such a subquery is referred to as a correlated subquery.

As for any differences with the JOIN solution: In the condition, the only difference is the left/right placement of SalesOriginal and SalesYtd, which is chosen only by order of appearance in the query but functionally completely equivalent. The most striking difference between the JOIN solution and the subquery is the absence of the GROUP BY-list in the latter.

Drawbacks of the subquery

As we had much to complain about the GROUP BY-list in the JOIN solution, it might seem that the subquery solution is somehow "better". However, a solution with a correlated subquery in general tends to be slower than a JOIN solution. Whether this is actually the case depends on on many variables and you'd really have to check it against your SQL engine and datasets.

Another drawback of the subquery solution becomes clear when we want to calculate the YTD for multiple measures. Our example only has one SalesAmount measure, but in this same context we can easily imagine that we also want to know about price, discount amounts, tax amounts, shipping costs, and so on.

In the JOIN solution, we would simply add any extra measures to the select list, using MAX() (or MIN() or AVG()) to obtain the original value, and SUM() to calculate its respective YTD value: As long as it's over the same set, the JOIN, its condition, and even the GROUP BY-list would remain the same, no matter for how many different measures we would add a YTD calculation.

This is very different in the subquery case. Each measure for which you need a YTD calculation would get its own subquery. Even though the condition would be the same for each such YTD calculation, you would still need to repeat the subquery code - one for each YTD measure.

Next installment: Solution 3 - using a UNION

In the next installment we will present and discuss a solution based on a UNION and a GROUP BY.

Year-to-Date on Synapse Analytics 2: Using a self-JOIN and GROUP BY

For one of our Just-BI customers we implemented a Year-to-Date calculation in a Azure Synapse Backend. We encountered a couple of approaches and in this series I'd like to share some sample code, and discuss some of the merits and benefits of each approach.

TL;DR: A Year-to-Date solution based on a SUM() window function is simple to code and maintain as well as efficient to execute. This as compared to a number of alternative implementations, namely a self-JOIN (combined with a GROUP BY), a subquery, and a UNION (also combined with a GROUP BY).

Note: this is the 2nd post in a series. For sample data and setup, please see the first post in this series. (While our use case deals with Azure Synapse, most of the code will be directly compatible with other SQL Engines and RDBMS-es.)

Using a self-JOIN

The recipe for the set-oriented approach can be directly translated to SQL:

select      SalesOriginal.SalesYear
,           SalesOriginal.SalesMonth
,           max(SalesOriginal.SalesAmount) as SalesAmount
,           sum(SalesYtd.SalesAmount)      as SalesYtd
from        SalesYearMonth as SalesOriginal
inner join  SalesYearMonth as SalesYtd
on          SalesOriginal.SalesYear  = SalesYtd.SalesYear
and         SalesOriginal.SalesMonth >= SalesYtd.SalesMonth
group by    SalesOriginal.SalesYear
,           SalesOriginal.SalesMonth

The self-JOIN

In our discussion of the set-oriented approach we mentioned combining the rows from the table with each other to produce all different combinations. In the code sample about, the JOIN-clause takes care of that aspect.

As you can see, the SalesYearMonth table appears twice: on the left hand and on the right hand of the JOIN-keyword, but using different aliases: SalesOriginal and SalesYtd. It is a so-called self-join.

Even though both aliases refer to an instance of the same SalesYearMonth base table, each has a very different role. We can think of the one with the SalesOriginal alias as really the SalesYearMonth table itself. The SalesYtd alias refers to an instance of the SalesYearMonth table that, for any given row from SalesOriginal, represents a subset of rows that chronologically precedes the row from SalesOriginal.

The ON-clause that follows controls which combinations should be retained: for each particular row of SalesOriginal we only want to consider rows from SalesYtd from the same year, which is why the first predicate in the ON-clause is:

SalesOriginal.SalesYear  = SalesYtd.SalesYear

Within that year, we only want to consider rows that precede it chronologically, and that explains the second predicate:

SalesOriginal.SalesMonth >= SalesYtd.SalesMonth

GROUP BY and SUM()

It is is important to realize the JOIN is only half of the solution.

While the JOIN takes care of gathering and combining all related rows necessary to compute the YTD value, the actual calculation is done by the SUM() function in the SELECT-list, and the GROUP BY defines which rows should be taken together to be summed.

In summary:

• the JOIN generates new rows by combining rows from its left-hand table with the rows from its right-hand table, bound by the condition in the ON-clause.
• The GROUP BY partitions the rows into subsets having the same combinations of values for SalesYear and SalesMonth.
• The SUM() aggregates the rows in each SalesYear, SalesMonth partition, turning its associated set of rows into one single row, while adding the values of the SalesAmount column together.

Note that the columns in the GROUP BY list are qualified by the SalesOriginal alias - and not SalesYtd. Also note that the GROUP BY columns form the key of the original SalesYearMonth table - together they uniquely identify a single row from the SalesYearMonth table. This is not a coincidence: it expresses precisely that SalesOriginal really has the role of being just itself - the SalesYearMonth table.

What about the other columns?

The GROUP BY affects treatment of the non-key columns as well. In this overly simple example, we had only one other column - OriginalSales.SalesAmount.

(Note that this is different from YtdSales.SalesAmount, which we aggregated using SUM() to calculate the YTD value)

Since OriginalSales.SalesAmount comes from the SalesOriginal instance of the SalesYearMonth table, we can reason that after the GROUP BY on the key columns SalesYear and SalesMonth, there must be exactly one SalesAmount value for each distinct combination of SalesYear and SalesMonth. In other words, SalesAmount is functionally dependent on SalesYear and SalesMonth.

Some SQL engines are smart enough to realize this and will let you refer to any expression that is functionally dependent upon the expressions in the GROUP BY-list in the SELECT-list. Unfortunately, Synapse and MS SQL Server are not among these and if we try we will get an Error:

Msg 8120, Level 16, State 1, Line 11
Column 'Sales.SalesAmount' is invalid in the select list because it is not contained in either an aggregate function or the GROUP BY clause.

The error message suggets we can do two things to solve it:

• either we aggregate by wrapping the SalesOriginal.SalesAmount-expression into some aggregate function
• or we expand the GROUP BY-list and add the SalesOriginal.SalesAmount-expression there.

To me, neither feels quite right.

SalesAmount is clearly intended as a measure, and it feels weird to treat them the same as the attributes SalesYear and SalesMonth. So adding it to the GROUP BY-list feels like the wrong choice. Besides, it also makes the code less maintainable, as each such column will now appear twice: once in the SELECT-list, where we need it no matter what, and once again in the GROUP BY-list, just to satisfy the SQL engine.

So, if we don't want to put it in the GROUP BY-list, we are going to need to wrap it in an aggregate function. We just mentioned that SalesAmount is a measure and therefore that does not sound unreasonable. However, we have to be careful which one we choose.

One would normally use SalesAmount as an additive measure and be able to use SUM() for that. But here, in this context, SUM() is definitily the wrong choice!

All we want to do is to "get" back" whatever value we had for SalesAmount, in other words, unaffected by the whole routine of join-and-then-aggregate, which we did only to calculate the YTD value. The "extra" rows generated by the JOIN are only needed to do the YTD calculation and should not affect any of the other measures. Using SUM() would simply add the SalesAmount just as many times as there are preceding rows in the current year, which simply does not have any meaningful application.

What we want instead is to report back the original SalesAmount for any given SalesYear, SalesMonth combination. We just reasoned that there will be just one distinct SalesOriginal.SalesAmount value for any combination of values in SalesOriginal.SalesYear, SalesOriginal.SalesMonth, and it would be great if we had an aggregate function that would simply pick the SalesOriginal.SalesAmount value from any of those rows. To the best of my knowledge, no such aggregate function exists in MS SQL Server or Synapse Analytics.

We can use MAX() or MIN(), or even AVG(). While this would all work and deliver the intended result, it still feels wrong as it seems wasteful to ask the SQL engine to do some calculation on a set of values while it could pick just any value.

Next installment: Solution 2 - using a subquery

In the next installment we will present and discuss a solution based on a subquery.

Year-to-Date on Synapse Analytics 1: Background

For one of our Just-BI customers we implemented a Year-to-Date calculation in a Azure Synapse Backend. We encountered a couple of approaches and in this series I'd like to share some sample code, and discuss some of the merits and benefits of each approach.

(While our use case deals with Azure Synapse, most of the code will be directly compatible with other SQL Engines and RDBMS-es.)

TL;DR: A Year-to-Date solution based on a SUM() window function is simple to code and maintain as well as efficient to execute. This as compared to a number of alternative implementations, namely a self-JOIN (combined with a GROUP BY), a subquery, and a UNION (also combined with a GROUP BY).

In this Installment

• A definition of what Year-to-Date (YTD) is
• Some background on why we are interested in calculating the YTD using Synapse Analytics / MS SQL Server
• How to calculate YTD using an iterative and a set-oriented approach
• A sample table and dataset which will be used in the next installments to demonstrate our sample code.

Context

Our customer is using an Azure Data Lake to store data from all kinds of source systems, including its SAP ERP system. Azure Synapse Analytics sits on top of the Data Lake and is used as analytics workhorse, but also to integrate various data sets present in the data lake. Front-end BI tools, such as Microsoft PowerBI, can then connect to Synapse and import or query the data from there.

In many cases, the datamarts presented by Synapse are pretty straightforward. Calculations and derived measures needed to build dashboards and data visualizations can typically be developed rather quickly inside the Power BI data model. Once the front-end development has stabilized, one can consider to refactor the solution and move parts away from the front-end and push them down to the backend for performance or maintainability.

(There are all kinds of opinions regarding data architecture and on when to put what where. We do not pretend to have the final answer to that, but the current workflow allows us to very quickly deliver solutions that can be used and verified by the users. At present I do not think we could achieve the same productivity if we would demand that everything be designed and built on the backend right from the get go.)

So, today we were refactoring some of the logic in a PowerBI model, including a Year-to-Date calculation. The solution we ended up implementing to solve it seems to work rather nicely so I figured to share it.

Year-to-Date value

What's a year to date (YTD) value? Basically it's the cumulative value over a metric in time, which resets once a year. In other words, the year to date value is the per-year total of the value achieved up to the current date.

This is best explained with an example. Consider the following dataset:

Date	Value	YTD Value
2012-01-10	35,401.14	35,401.14
2012-01-20	15,012.18	50,413.32
2012-02-01	25,543.71	75,957.03
2012-02-10	32,115.41	108,072.43
2012-02-20	17,688.07	125,760.50
2012-03-01	10,556.53	136,317.03
...	...	...
2013-01-01	19,623.90	19,623.90
2013-01-10	8,351.18	27,975.08
2013-01-20	20,287.65	48,262.73
2013-02-01	33,055.69	81,318.42

In the table above we have dates from two years - 2012 and 2013 - and for each date a Value.

For the first date encountered within a year, the YTD Value is equal to the Value itself; For each subsequent Date, the YTD Value is maintained as a running total of the values that appeared at the earlier dates.

So, 2012-01-10 is the first date we encounter in 2012 and therefore its YTD Value is equal to the Value at that date (35,401.14). The next date is 2012-01-20 and its Value is 15,012.18; therefore its YTD Value is 50,413.32, which is 15,012.18 + 35,401.14. The accumulation continues until we reach the last date of 2012.

At 2013-01-01 the first date of the next year, the YTD Value resets again to be equal to the Value, and then in the subsequent dates of 2013, the YTD Value again accumulates the current Value by adding it to the preceding YTD-value.

How to use YTD

You can use YTD values to analyze how well actual trends are developing over time as compared to a planning or predicition. By comparing the calculated YTD of a measure to a projected value (for example, a sales target), we can see how far off we are at any point in time.

If you gather these comparisons for a couple of moments in time, you can get a sense of the pace in which the actual situation is deviating from on converging to the target or the projected situation. These insights allow you to intervene in some way: maybe you need to adjust your planning, or change your expectations. Or maybe you need to adjust your efforts in order to more closely approximate your target.

Thinking about YTD as iteration

From the way we explained what a year-to-date value is, you might think about it as an actual "rolling sum". By that I mean, you might think about it as an iterative problem, that you solve by going through the rows, one by one. In pseudocode, such a solution would do something like:

    declare year, ytd
  
    loop through rows:
    
        if year equals row.year then 
        
          assign ytd + row.value to ytd
          
        else
        
          assign row.value to ytd
          assign row.year to year
          
        end if
        
    end loop through rows

While this approach would apparently give you the desired result, it does not help you to solve the problem in SQL directly. Pure SQL does not let you iterate rows like that, and it also does not let you work with variables like that.

Even with the iterative approach there is a hidden problem: the reset of the ytd variable and the update of the year variable that occurs whenever the row.year is different from the current value of the year variable will only work properly if the rows of one particular year are next to each other (like when the rows are ordered by year prior to iteration). The same applies within the year: the rows need to be sorted in chronological order, as the YTD value should reflect how much of the value was accumulated at that date within that year.

It may seem like a waste of time to think about an approach that is of no use to solving the problem. But this simple iterative approach provides a very simple recipe for quickly checking whether an actual solution behaves as expected. We'll use it later to veryify some results.

A set-oriented approach

To implement it in SQL we have to think in a set-oriented way. Conceptually, we can think about it as if we combine each row in the set with all of the other rows, forming a cartesian product, and then retain only those combinations that have identical values for year, but a smaller or equal value for the month.

This way, each row will combine with itself, and with all the other rows that chronologically precede it within the same year. The YTD value is then obtained by aggregating the rows over year and month value, summing the value to become the YTD value.

Sample Data

To play around a bit with the problem in SQL, let's set up a simple table:

create table SalesYearMonth (
  SalesYear   int
, SalesMonth  int
, SalesAmount decimal(20,2)
, primary key(SalesYear, SalesMonth)
);

And, here's some data:

insert into SalesYearMonth (
  SalesYear
, SalesMonth
, SalesAmount
) values (
 (2011,5,503805.92)
,(2011,6,458910.82)
,(2011,7,2044600.00)
,(2011,8,2495816.73)
,(2011,9,502073.85)
,(2011,10,4588761.82)
,(2011,11,737839.82)
,(2011,12,1309863.25)
,(2012,1,3970627.28)
,(2012,2,1475426.91)
,(2012,3,2975748.24)
,(2012,4,1634600.80)
,(2012,5,3074602.81)
,(2012,6,4099354.36)
,(2012,7,3417953.87)
,(2012,8,2175637.22)
,(2012,9,3454151.94)
,(2012,10,2544091.11)
,(2012,11,1872701.98)
,(2012,12,2829404.82)
,(2013,1,2087872.46)
,(2013,2,2316922.15)
,(2013,3,3412068.97)
,(2013,4,2532265.91)
,(2013,5,3245623.76)
,(2013,6,5081069.13)
,(2013,7,4896353.74)
,(2013,8,3333964.07)
,(2013,9,4532908.71)
,(2013,10,4795813.29)
,(2013,11,3312130.25)
,(2013,12,4075486.63)
,(2014,1,4289817.95)
,(2014,2,1337725.04)
,(2014,3,7217531.09)
,(2014,4,1797173.92)
,(2014,5,5366674.97)
,(2014,6,49005.84);

This setup is slightly different from the original problem statement. Instead of a column with DATE data type, we have separate SalesYear and SalesMonth columns. This is fine - it doesn't change the problem or the solution in any way.

In fact, this setup allows us to think about the essential elements of the problem without having to worry about the details of getting to that point. Once we done that, we can apply the approach to a more realistic case.

Next installment: Solution 1 - a self-JOIN

In the next installment we will present and discuss a solution based on a self-JOIN and a GROUP BY.