✔ PASS Search & Retrieval task_065_Q65_search_position_bias_dcg Scaled: 1M+ Records Ordered: No

Discounted Cumulative Gain (DCG) with Search Position Bias Discount

Candidate Latency (1M Rows)

43.14 ms

(1.0x faster than golden)

Golden Latency (1M Rows)

43.50 ms

DuckDB in-memory engine

Underlying Data Volume

1,000,000 rows

11.4 MiB across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 4.9s

✔ Correctness Verified on 1M+ Records

Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap

Business Scenario & Problem

Users are far more likely to click the #1 search result than the #5 result regardless of relevance. Ranking quality is measured via Discounted Cumulative Gain: DCG = SUM(relevance / log2(rank + 1)).

⚡ The Frontier Trap (Why LLMs Fail)

Simple click counts reward poorly placed relevant items unfairly.

Prompt / User Request Given to Model

Users are far more likely to click the #1 search result than the #5 result regardless of relevance. Ranking quality is measured via Discounted Cumulative Gain: DCG = SUM(relevance / log2(rank + 1)).

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: query_id, dcg_at_3.
Row order does not matter.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 11.4 MiB)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 search_impressions 1,000,000 rows 11.4 MiB Data Volume

query_id (INTEGER) rank_position (INTEGER) relevance_label (INTEGER)

Data Preview (showing sample rows from 1,000,000 total rows):

#	query_id	rank_position	relevance_label
1	1	1	2
2	1	2	0
3	1	3	1
4	1	2	1
5	2	3	2
6	3	1	1
7	4	1	1
8	5	1	1
9	6	1	1
10	7	1	1
11	8	2	1
12	9	2	1
13	10	1	1
14	11	2	1
15	12	2	1

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 127.77 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

📊 HASH_GROUP_BY 🔥 88.0% Cost

Latency: 112.47 ms

Rows In/Out: 933,078

Data Vol: 10.68 MB

📐 PROJECTION 9.1%

Latency: 11.64 ms

Rows In/Out: 933,081

Data Vol: 10.68 MB

📁 Projections: ['query_id', '(CAST...

🔍 TABLE_SCAN 2.9%

Latency: 3.66 ms

Rows In/Out: 933,081

Data Vol: 10.68 MB

📁 memory.main.search_impressions

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
HASH_GROUP_BY	88.0%	112.47 ms	933,078	10.68 MB	-	🔥 BOTTLENECK
PROJECTION	9.1%	11.64 ms	933,081	10.68 MB	Projections: ['query_id', '(CAST(relevance_label	Normal
TABLE_SCAN	2.9%	3.66 ms	933,081	10.68 MB	memory.main.search_impressions	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

SELECT query_id,
       sum(relevance_label / log2(rank_position + 1)) AS dcg_at_3
FROM search_impressions
WHERE rank_position <= 3
GROUP BY query_id;

-- Calculate DCG@3 for query 1

SELECT query_id,
       round(sum(relevance_label / log2(rank_position + 1)), 4) AS dcg_at_3
FROM search_impressions
WHERE rank_position <= 3
GROUP BY query_id;

CREATE TABLE search_impressions (query_id INT, rank_position INT, relevance_label INT -- 0=irrelevant, 1=relevant, 2=perfect
);


INSERT INTO search_impressions
VALUES (1, 1, 2),
       -- Rank 1: perfect match
 (1, 2, 0),
 -- Rank 2: bad match
 (1, 3, 1); -- Rank 3: good match

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (933,078 rows × 2 cols)

#	query_id	dcg_at_3
1	245,799	1
2	245,838	1
3	245,839	1
4	245,862	1
5	245,877	0.6309
6	245,906	0.6309
7	245,973	0.6309
8	246,018	0.6309
9	246,022	1
10	246,035	0.6309
11	246,086	0.6309
12	246,126	1
13	246,183	1
14	246,256	1
15	246,266	1
16	246,290	0.6309
17	246,357	0.6309
18	246,393	1
19	246,546	1
20	246,592	1
21	246,600	0.6309
22	246,696	0.6309
23	246,706	0.6309
24	246,713	1
25	246,730	0.6309

Showing first 25 of 933,078 total rows.

Expected Golden Output (933,078 rows × 2 cols)

#	query_id	dcg_at_3
1	245,799	1
2	245,838	1
3	245,839	1
4	245,862	1
5	245,877	0.6309
6	245,906	0.6309
7	245,973	0.6309
8	246,018	0.6309
9	246,022	1
10	246,035	0.6309
11	246,086	0.6309
12	246,126	1
13	246,183	1
14	246,256	1
15	246,266	1
16	246,290	0.6309
17	246,357	0.6309
18	246,393	1
19	246,546	1
20	246,592	1
21	246,600	0.6309
22	246,696	0.6309
23	246,706	0.6309
24	246,713	1
25	246,730	0.6309

Showing first 25 of 933,078 total rows.

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#	query_id	rank_position	relevance_label
1	1	1	2
2	1	2	0
3	1	3	1
4	1	2	1
5	2	3	2
6	3	1	1
7	4	1	1
8	5	1	1
9	6	1	1
10	7	1	1
11	8	2	1
12	9	2	1
13	10	1	1
14	11	2	1
15	12	2	1

#	query_id	rank_position	relevance_label
1	1	1	2
2	1	2	0
3	1	3	1
4	1	2	1
5	2	3	2
6	3	1	1
7	4	1	1
8	5	1	1
9	6	1	1
10	7	1	1
11	8	2	1
12	9	2	1
13	10	1	1
14	11	2	1
15	12	2	1

#	query_id	rank_position	relevance_label
1	1	1	2
2	1	2	0
3	1	3	1
4	1	2	1
5	2	3	2
6	3	1	1
7	4	1	1
8	5	1	1
9	6	1	1
10	7	1	1
11	8	2	1
12	9	2	1
13	10	1	1
14	11	2	1
15	12	2	1