SQL moving aggregate SUM without partial results - sql

Question

Assume I have this schema (tested on postgresql) where the 'Scorelines' relation contains results of sport matches. (kickoff is a TIMESTAMP but replaced by INT for readability)
SQLFiddle here: http://sqlfiddle.com/#!12/52475/3
CREATE TABLE Scorelines (
team TEXT,
kickoff INT,
scored INT,
conceded INT
);
Now I want to produce another column 'three_matches_scored' that contains the sum of the points scored
over the 3 preceding game (determined by kickoff) of the same team. I have this:
SELECT team, kickoff, scored, conceded, SUM(scored) OVER three_matches AS three_matches_scored
FROM Scorelines
WINDOW three_matches AS
(PARTITION BY team ORDER BY kickoff
ROWS BETWEEN 3 PRECEDING AND 1 PRECEDING)
ORDER BY kickoff;
This works beautifully so far, except that I get values starting from the second game. Example:
| TEAM | KICKOFF | SCORED | CONCEDED | THREE_MATCHES_SCORED |
|------|---------|--------|----------|----------------------|
| A | 1 | 1 | 0 | (null) |
| B | 2 | 1 | 1 | (null) |
| A | 3 | 1 | 1 | 1 |
| A | 4 | 3 | 0 | 2 |
| B | 4 | 1 | 4 | 1 |
| A | 6 | 0 | 2 | 5 |
| B | 6 | 4 | 2 | 2 |
| B | 8 | 1 | 2 | 6 |
| B | 10 | 1 | 1 | 6 |
| A | 11 | 2 | 1 | 4 |
I want the column 'three_matches_scored' to be (null) for the first 3 games because there are no 3 results to sum up. How can I achieve this?
I'd prefer simple understandable solutions, performance is not critical for this particular case.
My only idea right now, is to define a stored function SUM3, that results in (null) with less than 3 values to add up. But I never defined a function in SQL and can't seem to figure it out.

Answer 1

You can use a case statement to null the rows where there are less than 3 games:
SELECT team, kickoff, scored, conceded,
CASE WHEN COUNT(scored) OVER three_matches = 3
THEN SUM(scored) OVER three_matches
ELSE NULL
END AS three_matches_scored
FROM Scorelines
WINDOW three_matches AS
(PARTITION BY team ORDER BY kickoff
ROWS BETWEEN 3 PRECEDING AND 1 PRECEDING)
ORDER BY kickoff;
Output:
team | kickoff | scored | conceded | three_matches_scored
------+---------+--------+----------+----------------------
A | 1 | 1 | 0 |
B | 2 | 1 | 1 |
A | 3 | 1 | 1 |
A | 4 | 3 | 0 |
B | 4 | 1 | 4 |
A | 6 | 0 | 2 | 5
B | 6 | 4 | 2 |
B | 8 | 1 | 2 | 6
B | 10 | 1 | 1 | 6
A | 11 | 2 | 1 | 4
(10 rows)

Answer 2

See harmics answer above.
(my first solution, just for reference)
Solution with user defined aggregate:
CREATE TYPE intermediate_sum AS (
sum INT,
count INT
);
CREATE FUNCTION sum_sfunc(intermediate_sum, INTEGER) RETURNS intermediate_sum AS
$$ SELECT $2 + $1.sum AS sum, $1.count - 1 AS count $$ LANGUAGE SQL;
CREATE FUNCTION sum_ffunc(intermediate_sum) RETURNS INTEGER AS
$$ SELECT (CASE WHEN $1.count > 1 THEN null
WHEN $1.count = 0 THEN $1.sum
END)
$$ LANGUAGE SQL;
CREATE AGGREGATE sum3(INTEGER) (
sfunc = sum_sfunc,
finalfunc = sum_ffunc,
stype = intermediate_sum,
initcond = '(0,3)'
);
The aggregate SUM3 wants at least 3 values, otherwise it returns (null). One can define other aggreates like SUM4 by changing the initcond, for example to '(0,4)'.