PostgreSQL – Grouping() Equivalent in PostgreSQL

Okay, so here is the query modified to work the way you want:

DECLARE @players table
(
    PlayerID uniqueidentifier NOT NULL PRIMARY KEY,
    PlayerName nvarchar(64) NOT NULL
);

DECLARE @playerScores table
(
    ID bigint NOT NULL IDENTITY PRIMARY KEY,
    PlayerID uniqueidentifier NOT NULL,
    DateCreated datetime NOT NULL,
    Score int NOT NULL,
    TimeTaken bigint NOT NULL,
    PuzzleID int NOT NULL
);

DECLARE @puzzleId int = 0;

SELECT TOP 50
    a.PlayerID,
    p.PlayerName,
    a.Score,
    a.TimeTaken,
    a.PlayedDate
    FROM
    (
        SELECT
            ps.PlayerID,
            ps.Score,
            ps.TimeTaken,
            ps.DateCreated AS PlayedDate,
            ROW_NUMBER()
                OVER
                (
                    PARTITION BY ps.PlayerID
                    ORDER BY ps.Score DESC, ps.TimeTaken, ps.DateCreated
                ) AS RN
            FROM @playerScores ps
            WHERE ps.PuzzleID = @puzzleId
    ) a
    INNER JOIN @players p ON p.PlayerID = a.PlayerID
    WHERE a.RN = 1
    ORDER BY
        a.Score DESC,
        a.TimeTaken,
        a.PlayedDate;

Having written this (note: indexes are not optimized), and looking at the other queries you're going to need to write, what I would actually recommend is to abandon this type of query entirely, and create a denormalized high-score table (rows are unique on the combination of PlayerID, PuzzleID), on which to run aggregates instead.

The reason why is because the GameResult table is going to grow huge in the database, and so it will be less and less efficient to run aggregates on it directly as time passes, and the requirements are incompatible with doing something like creating an indexed view to summarize the information.

Also, if you aren't doing this already, it's highly likely you'll want to use an asynchronous process to compute the "leaderboards" periodically and cache the results, instead of computing them just-in-time. (You could do something like merge the current player's score with the cached leaderboards so the player can see themself on the leaderboards immediately if they got a high score.) See my answer here for some ideas to consider when implementing a caching mechanism.

The query you have

You could simplify your query using a WINDOW clause, but that's just shortening the syntax, not changing the query plan.

SELECT id, trans_ref_no, amount, trans_date, entity_id
     , SUM(amount) OVER w AS trans_total
     , COUNT(*)    OVER w AS trans_count
FROM   transactiondb
WINDOW w AS (PARTITION BY entity_id, date_trunc('month',trans_date)
             ORDER BY trans_date
             ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING);

• Also using the slightly faster count(*), since id is certainly defined NOT NULL?
• And you don't need to ORDER BY entity_id since you already PARTITION BY entity_id

You can simplify further, though:
Don't add ORDER BY to the window definition at all, it's not relevant to your query. Then you don't need to define a custom window frame, either:

SELECT id, trans_ref_no, amount, trans_date, entity_id
     , SUM(amount) OVER w AS trans_total
     , COUNT(*)    OVER w AS trans_count
FROM   transactiondb
WINDOW w AS (PARTITION BY entity_id, date_trunc('month',trans_date);

Simpler, faster, but still just a better version of what you have, with static months.

The query you might want

... is not clearly defined, so I'll build on these assumptions:

Count transactions and amount for every 30-day period within the first and last transaction of any entity_id. Exclude leading and trailing periods without activity, but include all possible 30-day periods within those outer bounds.

SELECT entity_id, trans_date
     , COALESCE(sum(daily_amount) OVER w, 0) AS trans_total
     , COALESCE(sum(daily_count)  OVER w, 0) AS trans_count
FROM  (
   SELECT entity_id
        , generate_series (min(trans_date)::timestamp
                         , GREATEST(min(trans_date), max(trans_date) - 29)::timestamp
                         , interval '1 day')::date AS trans_date
   FROM   transactiondb 
   GROUP  BY 1
   ) x
LEFT JOIN (
   SELECT entity_id, trans_date
        , sum(amount) AS daily_amount, count(*) AS daily_count
   FROM   transactiondb
   GROUP  BY 1, 2
   ) t USING (entity_id, trans_date)
WINDOW w AS (PARTITION BY entity_id ORDER BY trans_date
             ROWS BETWEEN CURRENT ROW AND 29 FOLLOWING);

This lists all 30-day periods for each entity_id with your aggregates and with trans_date being the first day (incl.) of the period. To get values for each individual row join to the base table once more ...

The basic difficulty is the same as discussed here:

• Referencing current row in FILTER clause of window function

The frame definition of a window cannot depend on values of the current row.

And rather call generate_series() with timestamp input:

• Generating time series between two dates in PostgreSQL

The query you actually want

After question update and discussion:
Accumulate rows of the same entity_id in a 30-day window starting at each actual transaction.

Since your data is distributed sparsely, it should be more efficient to run a self-join with a range condition, all the more since Postgres 9.1 does not have LATERAL joins, yet:

SELECT t0.id, t0.amount, t0.trans_date, t0.entity_id
     , sum(t1.amount) AS trans_total, count(*) AS trans_count
FROM   transactiondb t0
JOIN   transactiondb t1 USING (entity_id)
WHERE  t1.trans_date >= t0.trans_date
AND    t1.trans_date <  t0.trans_date + 30  -- exclude upper bound
-- AND    t0.entity_id = 114284  -- or pick a single entity ...
GROUP  BY t0.id  -- is PK!
ORDER  BY t0.trans_date, t0.id

SQL Fiddle.

A rolling window could only make sense (with respect to performance) with data for most days.

This does not aggregate duplicates on (trans_date, entity_id) per day, but all rows of the same day are always included in the 30-day window.

For a big table, a covering index like this could help quite a bit:

CREATE INDEX transactiondb_foo_idx
ON transactiondb (entity_id, trans_date, amount);

The last column amount is only useful if you get index-only scans out of it. Else drop it.

But it's not going to be used while you select the whole table anyway. It would support queries for a small subset.