Overview

Factbase employs a comprehensive suite of research metrics to assess capability across countries, institutions, and individual researchers. This article focuses specifically on research publication and citation metrics. Factbase also incorporates other intelligence dimensions (actors, assets, strategic indicators) which use different measurement frameworks.

Understanding these metrics and how they work together is essential for accurate capability assessment and strategic decision-making.

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Volume Metrics

Volume metrics measure research output – how much research is being produced.

Paper Count (Whole Counting)

Definition: Total number of papers authored or co-authored by an entity, counting each paper once regardless of number of co-authors.

Formula:

Whole_Count = Number of papers with at least one author from entity

**Example**:

Paper with authors from USA, UK, and Germany:

• USA whole count: +1
• UK whole count: +1
• Germany whole count: +1 Global total: 3 (but only 1 actual paper exists)

**Use cases**:
- Research visibility and breadth of involvement
- Network analysis and collaboration mapping
- Individual researcher CVs

**Limitations**:
- Double-counts collaborative papers
- Inflates totals for highly collaborative countries
- Not suitable for international comparisons

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### Fractional Paper Count

**Definition**: Papers attributed proportionally based on author contribution, ensuring global totals equal actual paper counts.

**Formula**:

Fractional_Count = Σ(Authors_from_entity ÷ Total_authors) across all papers

**Example**:

Paper A: 3 USA authors, 2 UK authors (total: 5)

• USA fractional count: 3÷5 = 0.6
• UK fractional count: 2÷5 = 0.4 Global total: 1.0 ✓

**Use cases**:
- National capability assessment
- International rankings and comparisons
- Fair benchmarking across different collaboration patterns

**Advantages**:
- No double-counting
- Fair attribution based on actual contribution
- International standard (OECD, UNESCO endorsed)

**This is Factbase's primary volume metric.**

See: [Understanding Fractional Credit in Research Output Attribution](#) for detailed methodology.

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### Annual Volume Trends

**Definition**: Change in fractional paper count year-over-year.

**Formula**:

Annual_Growth = ((Papers_this_year - Papers_last_year) ÷ Papers_last_year) × 100

**Example**:

Country X in AI:

• 2023: 356.2 fractional papers
• 2024: 398.5 fractional papers
• Growth: ((398.5 - 356.2) ÷ 356.2) × 100 = +11.9%

**Interpretation**:
- Positive growth: Expanding research capacity
- Negative growth: Declining output or strategic pivot
- Compare to global growth rate to assess relative performance

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## Share Metrics

Share metrics measure **relative contribution** – what percentage of global research activity does an entity represent?

### Paper Share

**Definition**: Entity's fractional papers as percentage of global total papers in a topic.

**Formula**:

Paper_Share = (Entity_fractional_papers ÷ Global_total_papers) × 100

**Example**:

Global AI papers (5Y): 8,450 USA fractional papers: 2,847.3

USA paper share: (2,847.3 ÷ 8,450) × 100 = 33.7%

**Interpretation**:
- 33.7% means USA produces roughly one-third of global AI research
- Dominant player: >30%
- Major player: 15-30%
- Significant player: 5-15%
- Niche player: <5%

**Use cases**:
- Market share analysis ("Who dominates this topic?")
- Strategic positioning assessment
- Trend analysis (gaining or losing share?)

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### Citation Share

**Definition**: Entity's fractional citations as percentage of global total citations in a topic.

**Formula**:

Citation_Share = (Entity_fractional_citations ÷ Global_total_citations) × 100

**Example**:

Global AI citations (5Y): 125,000 USA fractional citations: 52,500

USA citation share: (52,500 ÷ 125,000) × 100 = 42.0%

**Interpretation**:
- Citation share > Paper share: Above-average quality
- Citation share = Paper share: Average quality
- Citation share < Paper share: Below-average quality

**Example analysis**:

USA: 33.7% paper share, 42.0% citation share → 42.0 ÷ 33.7 = 1.25× multiplier → Papers receive 25% more citations than volume alone would predict → Quality advantage

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### Share Ratio (Quality Multiplier)

**Definition**: Ratio of citation share to paper share, indicating quality relative to volume.

**Formula**:

Share_Ratio = Citation_Share ÷ Paper_Share

**Interpretation**:

| Share Ratio | Meaning |
|-------------|---------|
| **> 1.3** | High quality relative to volume (quality leader) |
| **1.1 - 1.3** | Above-average quality |
| **0.9 - 1.1** | Average quality (citations match volume) |
| **0.7 - 0.9** | Below-average quality |
| **< 0.7** | Volume over quality (quantity-focused) |

**Example**:

Country A: Share ratio = 1.45 (citations outpace papers by 45%) Country B: Share ratio = 0.82 (citations lag papers by 18%)

Interpretation: Country A achieves more impact per paper than Country B

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## Quality Metrics

Quality metrics measure **research impact** – how influential and well-regarded is the research?

### TMCM (Topic Median Citation Multiple)

**Definition**: Research quality measured as a multiple of the median citations for papers in the same topic and year.

**Formula**:

Paper_TMCM = (Citations to paper) ÷ (Median citations for topic-year)

Entity_TMCM = Σ(Paper_TMCM × Fractional_credit) ÷ Σ(Fractional_credit)

**Example**:

Paper in Quantum Computing (2023):

• Citations: 16
• Topic median: 4
• TMCM: 16 ÷ 4 = 4.0×

Interpretation: Paper received 4× the citations of a typical paper in this topic

**Use cases**:
- Field-normalized quality comparison
- Cross-topic capability assessment
- Trend analysis (improving or declining quality?)

**Advantages**:
- Normalizes for topic citation rates (fair comparison AI vs mathematics)
- Normalizes for publication year (fair comparison 2020 vs 2024)
- Intuitive interpretation (2× = double the typical citations)

See: [Understanding TMCM: Topic Median Citation Multiple](#) for detailed methodology.

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### Periodic TMCM

**Definition**: Average research quality across a time window, calculated by averaging annual TMCM values.

**Standard periods**:
- **3Y**: Recent momentum (last 3 years + current YTD)
- **5Y**: Current capability (last 5 years + current YTD)
- **10Y**: Sustained excellence (last 10 years + current YTD)
- **20Y**: Generational authority (last 20 years + current YTD)

**Formula**:

Period_TMCM = (Σ Annual_TMCM for years in period) ÷ (Number of years)

**Example**:

Country X AI research:

• 3Y TMCM: 3.8× (recent performance)
• 5Y TMCM: 3.4× (current cycle)
• 10Y TMCM: 3.1× (sustained capability)
• 20Y TMCM: 2.4× (generational contribution)

Interpretation: Quality improving (3.8 > 3.4 > 3.1 > 2.4)

See: [Understanding Periodic Research Impact Analysis](#) for detailed methodology.

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### TMCM-Int (International TMCM)

**Definition**: TMCM calculated using only international citations (excluding domestic/self-citations).

**Formula**:

TMCM-Int = (International citations only) ÷ (International median for topic-year)

Where:
- International citations = citations from papers with NO authors from the entity's country
- International median = median calculated using only international citation patterns

**Example**:

Country X paper with 50 total citations:

• 45 international citations (from other countries)
• 5 domestic citations (from Country X)
• International citation rate: 90%

Standard TMCM: 50 ÷ 15 = 3.33× TMCM-Int: 45 ÷ 13 = 3.46×

Interpretation: Strong international recognition (TMCM-Int > TMCM)

**Use cases**:
- Detecting self-citation inflation
- Assessing genuine international impact
- Quality assurance for metrics

**Interpretation**:
- TMCM ≈ TMCM-Int: Clean, genuine quality
- TMCM >> TMCM-Int: High self-citation (potential gaming)
- Domestic citation rate < 15%: Healthy international recognition
- Domestic citation rate > 25%: Concerning self-citation levels

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## Excellence Metrics

Excellence metrics identify **breakthrough research** – papers in the top tier of global performance.

### Percentile Classification

Papers are classified into performance bands based on their TMCM relative to the global distribution:

**Global percentile thresholds** (approximate):

| Percentile | TMCM Threshold | Performance Level |
|------------|----------------|-------------------|
| **Top 1%** | ≥ 20× | Exceptional (breakthrough research) |
| **Top 5%** | ≥ 8× | Excellent (high-impact work) |
| **Top 10%** | ≥ 5× | Very good (strong contribution) |
| **Top 25%** | ≥ 2× | Above average (solid work) |
| **Top 50%** | ≥ 1× | Median or better |
| **Bottom 50%** | < 1× | Below median |

*Note: Exact thresholds vary by topic and year; values shown are representative.*

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### Excellence Share

**Definition**: Percentage of an entity's papers that fall into each excellence band.

**Formula**:

Top_X%_Share = (Fractional papers with TMCM ≥ threshold) ÷ (Total fractional papers) × 100

**Example**:

Country X in Quantum Computing (5Y):

• Total fractional papers: 1,250.7
• Papers with TMCM ≥ 20 (top 1%): 102.5
• Top 1% share: (102.5 ÷ 1,250.7) × 100 = 8.2%

**Interpretation**:
- Expected share if average quality: 1%
- Actual share: 8.2%
- Over-representation: 8.2 ÷ 1 = **8.2× over-represented** in top 1%

**Excellence profile example**:

| Band | Expected | Actual | Over-representation |
|------|----------|--------|---------------------|
| Top 1% | 1% | 8.2% | 8.2× |
| Top 5% | 5% | 18.5% | 3.7× |
| Top 10% | 10% | 32.5% | 3.25× |
| Top 25% | 25% | 58.2% | 2.33× |
| Above median | 50% | 78.5% | 1.57× |

**Interpretation**: Strong concentration in top tiers → genuine research excellence, not just volume.

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### Excellence Count

**Definition**: Absolute number (fractional) of papers in each excellence band.

**Formula**:

Top_X%_Count = Σ(Fractional_credit) for papers with TMCM ≥ threshold

**Use cases**:
- Comparing entities of different sizes
- Assessing total volume of breakthrough research
- Strategic capacity assessment

**Example**:

Country A: Top 1% share = 8%, Top 1% count = 80 papers Country B: Top 1% share = 4%, Top 1% count = 400 papers

Interpretation:

• Country A higher quality (8% vs 4%)
• Country B more breakthrough research (400 vs 80 papers)
• Different strategic profiles

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## Citation Diversity Metrics

Citation diversity metrics assess **geographic spread** of research influence – is impact truly international or concentrated domestically?

### Domestic Citation Rate

**Definition**: Percentage of citations from authors in the same country as the paper's authors.

**Formula**:

Domestic_Rate = (Citations from same country) ÷ (Total citations) × 100

**Example**:

Country X paper with 100 citations:

• 15 from Country X authors
• 85 from international authors

Domestic rate: (15 ÷ 100) × 100 = 15%

**Interpretation**:

| Domestic Rate | Assessment |
|---------------|------------|
| **< 15%** | 🟢 Healthy international recognition |
| **15-25%** | 🟡 Acceptable (monitor for trends) |
| **25-40%** | 🟠 Concerning (possible self-citation inflation) |
| **> 40%** | 🔴 Red flag (likely citation cartel or gaming) |

---

### International Citation Rate

**Definition**: Percentage of citations from authors outside the entity's country.

**Formula**:

International_Rate = 100% - Domestic_Rate

**Example**:

Domestic rate: 15% International rate: 85%

Interpretation: Strong international recognition

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### Citation Network Diversity (Herfindahl Index)

**Definition**: Measure of geographic concentration in citations using the Herfindahl-Hirschman Index (HHI).

**Formula**:

HHI = Σ(Country_citation_share²) for all citing countries

**Example**:

Paper cited by:

• 50% Country A authors
• 30% Country B authors
• 15% Country C authors
• 5% Country D authors

HHI = 0.50² + 0.30² + 0.15² + 0.05² = 0.25 + 0.09 + 0.0225 + 0.0025 = 0.365

**Interpretation**:

| HHI Value | Concentration Level | Assessment |
|-----------|---------------------|------------|
| **< 0.15** | Low concentration | 🟢 Highly diverse international impact |
| **0.15-0.25** | Moderate | 🟢 Good geographic spread |
| **0.25-0.40** | Moderate-high | 🟡 Some concentration (monitor) |
| **> 0.40** | High concentration | 🔴 Concentrated citations (possible gaming) |

**Use cases**:
- Detecting citation cartels
- Assessing genuine international influence
- Quality assurance for impact metrics

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### Citing Countries Count

**Definition**: Number of distinct countries from which citations originate.

**Formula**:

Citing_Countries = Count of unique countries with at least one citing paper

**Example**:

Paper cited by authors from 47 different countries

Interpretation: Broad international recognition

**Benchmarks**:
- 40+ countries: Excellent global reach
- 20-40 countries: Good international visibility
- 10-20 countries: Moderate visibility
- <10 countries: Limited international impact

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## Ranking Metrics

Ranking metrics show **relative position** among peers in a specific topic or overall.

### Topic Rankings

Entities (countries, institutions, authors) are ranked within each topic based on selected metrics.

**Ranking criteria** (user-selectable):
- Fractional paper count (volume leader)
- Paper share (market share leader)
- Mean TMCM (quality leader)
- Citation count (total impact leader)
- Citation share (impact share leader)
- Top 1% share (excellence concentration)

**Example – Top 5 Countries in Artificial Intelligence (5Y, by TMCM)**:

| Rank | Country | TMCM | Paper Share | Citation Share |
|------|---------|------|-------------|----------------|
| 1 | Switzerland | 3.8× | 2.1% | 3.2% |
| 2 | Singapore | 3.6× | 1.8% | 2.5% |
| 3 | United States | 3.4× | 33.7% | 42.0% |
| 4 | United Kingdom | 3.2× | 8.5% | 10.1% |
| 5 | Canada | 3.1× | 4.2% | 5.0% |

**Interpretation**:
- Switzerland/Singapore lead on quality but low volume
- USA leads on volume and total impact (despite #3 TMCM)
- Different strategic profiles

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### Multi-Metric Composite Rankings

**Dominance Index**: Combines volume and quality into single metric.

**Formula**:

Dominance_Index = Paper_Share × (TMCM ÷ 2.0)

**Example**:

USA: 33.7% paper share, TMCM 3.4× Dominance = 0.337 × (3.4 ÷ 2.0) = 0.337 × 1.7 = 0.573 = 57.3%

Interpretation: USA "controls" 57% of effective research capacity (volume boosted by quality multiplier)

**Dominance bands**:
- > 40%: Dominant leader
- 20-40%: Major player
- 10-20%: Significant contributor
- 5-10%: Niche specialist
- < 5%: Emerging or limited presence

---

### Percentile Ranks

**Definition**: Entity's position as a percentile (0-100) among all entities in the topic.

**Formula**:

Percentile_Rank = (Number of entities with lower value ÷ Total entities) × 100

**Example**:

100 countries publish in quantum computing Country X ranks 8th by TMCM

Percentile rank: ((100 - 8) ÷ 100) × 100 = 92nd percentile

Interpretation: Outperforms 92% of countries in this topic

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## Combining Metrics: Research Profiles

**Individual metrics tell part of the story. Comprehensive assessment requires multiple metrics together.**

### Complete Country Profile Template

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ COUNTRY X – ARTIFICIAL INTELLIGENCE – 5Y (2020-2024, 2025 YTD) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

VOLUME Fractional papers: 2,847.3 Whole count papers: 4,125 Paper share: 33.7% (rank #1 globally) Annual growth: +8.2% per year

SHARE ANALYSIS Paper share: 33.7% Citation share: 42.0% Share ratio: 1.25× (quality advantage) Dominance index: 57.3% (dominant leader)

QUALITY (TMCM) 5Y TMCM: 3.4× (rank #3 globally) Median TMCM: 2.8× 3Y TMCM: 3.8× (improving) 10Y TMCM: 3.1× (sustained excellence)

CITATION DIVERSITY Domestic rate: 9.2% (healthy) International rate: 90.8% Citing countries: 67 countries HHI: 0.12 (highly diverse) TMCM-Int: 3.5× (genuine international impact)

EXCELLENCE Top 1%: 8.2% of papers (8.2× over-representation) Top 5%: 18.5% of papers (3.7× over-representation) Top 10%: 32.5% of papers (3.25× over-representation) Top 1% count: 233.5 papers (rank #1 globally)

RANKINGS TMCM rank: #3 of 89 countries Paper share rank: #1 of 89 countries Citation share rank: #1 of 89 countries Top 1% count rank: #1 of 89 countries

TRAJECTORY Quality: Improving (3Y > 5Y > 10Y) Volume: Growing (+8.2% annual) Share: Stable (±2% over 5Y) International impact: Strong and genuine

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ ASSESSMENT: Dominant global leader with quality advantage, strong international recognition, and improving trajectory ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

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## Interpretation Guidelines

### Strategic Questions Each Metric Answers

| Question | Primary Metric | Supporting Metrics |
|----------|----------------|-------------------|
| **Who produces the most research?** | Fractional paper count | Paper share, annual growth |
| **Who dominates this topic?** | Paper share | Citation share, dominance index |
| **Who produces the highest quality?** | Mean TMCM | Top 1% share, TMCM-Int |
| **Is quality improving?** | Periodic TMCM (3Y vs 5Y vs 10Y) | Annual TMCM trends |
| **Who has genuine international impact?** | TMCM-Int | International rate, HHI, citing countries |
| **Who produces breakthrough research?** | Top 1% share, Top 1% count | Excellence profile across bands |
| **Volume or quality leader?** | Share ratio | Paper share vs citation share |
| **Overall capability leader?** | Dominance index | Combined assessment of all metrics |

### Red Flags and Quality Concerns

**Warning signs** when analyzing research metrics:

🚩 **High TMCM with low TMCM-Int** → Self-citation inflation
- Check: Domestic citation rate, HHI
- Action: Discount quality metrics, investigate patterns

🚩 **High volume, low TMCM** → Quantity over quality strategy
- Check: Excellence shares (likely low)
- Interpretation: Broad capability but not leading edge

🚩 **High top 1% share, low top 10% share** → Outlier-driven
- Check: Median TMCM vs mean TMCM (large gap?)
- Interpretation: Few breakthrough papers, otherwise mediocre

🚩 **Declining periodic TMCM** → Quality erosion
- Check: Volume trends (quality vs quantity trade-off?)
- Action: Investigate causes (funding, talent, competition)

🚩 **Domestic citation rate > 30%** → Possible citation cartel
- Check: HHI, citing countries count
- Action: Use TMCM-Int for quality assessment

🚩 **Paper share >> Citation share** → Impact deficit
- Check: Share ratio << 1.0
- Interpretation: High output, low influence

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## Metric Selection Guide

### For Different Use Cases

**National S&T Policy**:
- Primary: Paper share, TMCM (5Y, 10Y), Top 1% share
- Supporting: Annual growth, periodic trends, excellence counts

**Defence/Security Intelligence**:
- Primary: Paper share, Top 1% count, TMCM-Int
- Supporting: Citation diversity, citing countries, trajectory

**University Benchmarking**:
- Primary: Fractional papers, TMCM (5Y), Top 10% share
- Supporting: Citation share, share ratio, rankings

**Researcher Evaluation** (use with caution):
- Primary: Fractional papers, Individual TMCM, Top 1% count
- Supporting: International collaboration rate, h-index
- **Note**: Individual metrics less reliable; designed for aggregate assessment

**Competitive Intelligence**:
- Primary: Paper share trends, TMCM trajectory, dominance index
- Supporting: Share ratio, excellence distribution, growth rates

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## Technical Notes

### Data Updates

All metrics recalculated **quarterly** with:
- New publications added
- Citation counts updated
- Medians recalculated
- Rankings refreshed

### Statistical Confidence

**Minimum thresholds** for reliable metrics:
- Entity TMCM: ≥20 fractional papers recommended
- Excellence shares: ≥50 fractional papers recommended
- Citation diversity: ≥100 total citations recommended

**Low-confidence flags**:
- Metrics based on <20 papers flagged "low sample size"
- Very recent periods (YTD) flagged "preliminary"
- Topics with <50 global papers annually flagged "emerging topic"

### Metric Interdependencies

**Remember**:
- High TMCM ≠ high capability (volume matters)
- High volume ≠ high capability (quality matters)
- Rankings change with metric choice (TMCM vs paper share vs citation share)
- Single metrics mislead; profiles inform

**Always combine**:
- Volume (how much?)
- Quality (how good?)
- Diversity (how widespread?)
- Trajectory (what direction?)

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## Summary

Factbase provides **comprehensive research metrics** across five dimensions:

**1. Volume Metrics**
- Fractional paper count (output quantity)
- Paper share (relative volume)
- Growth rates (trajectory)

**2. Share Metrics**
- Paper share (% of global output)
- Citation share (% of global impact)
- Share ratio (quality multiplier)
- Dominance index (combined capacity)

**3. Quality Metrics**
- TMCM (topic-normalized quality)
- Periodic TMCM (quality over time)
- TMCM-Int (international quality)

**4. Excellence Metrics**
- Excellence shares (% in top tiers)
- Excellence counts (absolute breakthrough research)
- Percentile classifications

**5. Diversity Metrics**
- Domestic/international citation rates
- Citation network diversity (HHI)
- Geographic reach (citing countries)

**6. Rankings**
- Topic rankings by various criteria
- Percentile positions
- Composite scores

**Use these metrics together** to build complete capability profiles that answer strategic questions about research leadership, quality trajectories, and international influence.

**These metrics assess research output only.** For comprehensive capability assessment, combine with Factbase's actor intelligence (key researchers, institutions) and asset intelligence (infrastructure, patents, applications).

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*For detailed methodology on specific metrics, see individual help articles:*
- *[Understanding TMCM: Topic Median Citation Multiple](#)*
- *[Understanding Fractional Credit in Research Output Attribution](#)*
- *[Understanding Periodic Research Impact Analysis](#)*

*For technical specifications, API documentation, or custom metric requests, contact the Factbase team.*