The problem with TAM

Total Addressable Market (TAM) is a ubiquitous metric in biotech investment pitches, used to quantify the theoretical revenue potential of novel therapies. Its simplicity and apparent rigor make it an appealing tool for startups seeking to attract investors. At its core, TAM promises a snapshot of market opportunity, assuming full market penetration and uniform pricing across a global patient base. However, this allure conceals its significant flaws: oversimplifications that ignore pricing disparities, hurdles imposed by Health Technology Assessment (HTA) bodies, and the volatile, path-dependent nature of biotech markets.

By combining mathematical critiques, such as those from Nassim Nicholas Taleb's theories on fragility and Benoît Mandelbrot's fractal analysis, with real-world policy dynamics, this analysis dissects TAM's shortcomings and proposes more robust alternatives for biotech market forecasting.

The Oversimplifications of TAM in Biotech Markets

TAM Formula:

The basic TAM calculation assumes: $$\text{TAM} = \text{Target Population} \times \text{Treatment Cost per Patient}$$

This formulation operates under several flawed assumptions:

1. Uniform Pricing: Assumes a constant global price for the therapy, ignoring variations due to regional pricing strategies and HTA-imposed limits.
2. Full Market Penetration: Suggests that every eligible patient will access the treatment, disregarding constraints such as reimbursement caps, diagnostic rates, and treatment adoption lags.
3. Homogeneous Dynamics: Treats markets as uniform, ignoring disparities in policy frameworks, healthcare infrastructure, and payer policies.

Example: Oncology Therapy

• Assumed global patient pool: 100,000.
• Treatment cost: $100,000 per patient.

Projected TAM: $$\text{TAM} = 100,000 \times 100,000 = 10 \text{ billion USD}$$

Reality Check:

• NICE (UK) may impose an Incremental Cost-Effectiveness Ratio (ICER) cap of £30,000 per QALY, halving the permissible price.
• IQWiG (Germany) may restrict eligibility to biomarker-positive patients, reducing the market by 60%.
• Delayed HTA approvals in Southern Europe may postpone revenue generation by several years.

Adjusted TAM:

$$\text{Adjusted TAM} = \text{Initial TAM} \times \text{Eligibility Factor} \times \text{Pricing Adjustment}$$

For a therapy with a 30% eligible patient population and a $50,000 average price:

$$\text{Adjusted TAM} = 100,000 \times 0.3 \times 50,000 = 1.5 \text{ billion USD}$$

TAM's Misalignment with Dynamic Market Realities

Flaws in Static Assumptions:

TAM often fails to incorporate:

1. Therapeutic Competition:
   • Emergence of superior therapies (e.g., CAR-T or RNA-based therapies).
   • Entry of generics post-patent expiry.
2. Policy Challenges:
   • EMA approval does not guarantee national reimbursement.
   • Dynamic pricing adjustments (e.g., Germany’s annual AMNOG renegotiations).
3. Population Shifts:
   • Diagnostic advancements may shrink or expand the eligible population.
   • Epidemiological changes (e.g., declining disease incidence).

TAM's Gaussian Assumptions: A Misguided Foundation

Total Addressable Market (TAM) calculations in biotech are ubiquitous yet mathematically naive. They rely on deterministic models and Gaussian assumptions, failing to capture the non-linear, fractal, and fat-tailed nature of real-world market dynamics. This critique explores these shortcomings in greater depth, integrating the theories of Nassim Nicholas Taleb and Benoît Mandelbrot and their relevance to TAM in biotech.

Gaussian Formula

Traditional TAM models implicitly or explicitly assume a Gaussian (normal) distribution for market size and dynamics:

$$ f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}} $$

• f(x): Probability density at point x.
• μ: Mean.
• σ: Standard deviation

Assumption:

• Outcomes cluster around the mean (μ)
• Extreme deviations are rare, predictable, and diminish rapidly (light tails).

Reality in Biotech Markets:

1. Fat Tails: The biotech sector frequently encounters rare but impactful events, such as competition or catastrophic regulatory rejections. These are not captured by Gaussian models.
2. Non-Stationarity: Market conditions evolve dynamically with new therapies, pricing shifts, and changing demographics.

Mandelbrot's Fractals: Self-Similarity and Market Dynamics

Benoît Mandelbrot's fractal theory challenges Gaussian models, emphasizing irregular, self-similar patterns at different scales. This is critical for biotech markets, where small perturbations (e.g., adverse rulings, pricing changes) cascade into larger systemic effects.

Mandelbrot’s Scaling Relation

Market dynamics often follow power-law distributions: $$P(X > x) \sim x^{-\alpha}, \quad \alpha < 2.$$

Where:

• P(X>x): Probability of exceeding threshold x.
• α: Scaling parameter; α<2 implies fat tails.
• Implications for TAM:
• Rare Events Dominate: A single HTA rejection or pricing cap disproportionately affects TAM, far beyond the Gaussian assumption of light tails.

Taleb’s Critique: Fragility and Path Dependence

Path Dependence

Nassim Taleb underscores the importance of sequence-dependent events in complex systems. Biotech markets are highly path-dependent:

• Early success in gaining reimbursement in major markets (e.g., Germany or the UK) creates momentum.
• Failures in these markets can cascade, reducing perceived value and influencing smaller markets.

Dynamic TAM Adjustments

Incorporating path dependence requires a dynamic TAM model:

$$\text{Dynamic TAM} = \text{Initial TAM} \times \text{Eligibility Factor} \times \text{Pricing Adjustment} \times e^{-\lambda t}$$

Where:

• λ: Rate of competitive erosion over time.
• t: Time since market entry.

Taleb’s Insights on Fragility:

• Biotech markets are fragile, with small shocks causing outsized impacts.
• Static TAM models ignore this fragility, leading to inflated projections and investor overconfidence.

Gaussian vs. Power-Law Dynamics in TAM

Gaussian-Based Assumptions in TAM:

• Homogeneous Market Behavior: Assumes uniform pricing and adoption across regions.
• Predictable Variability: Models minor fluctuations around a mean.

Power-Law Dynamics:

Biotech TAM aligns more closely with power-law distributions:

• Heavy Tails: Events like regulatory rejections, blockbuster competitors, or population shifts significantly alter projections.
• Outlier Dominance: A few extreme events dictate market outcomes, defying Gaussian predictions.

TAM as a Static Projection: Misaligned with Real-World Dynamics

Simplistic TAM Formula:

$$\text{TAM} = \text{Target Population} \times \text{Treatment Cost per Patient}$$

Flaws:

1. Uniform Pricing: Ignores regional pricing dynamics and HTA-imposed caps.
2. Full Market Penetration: Overlooks adoption delays and reimbursement restrictions.
3. Fixed Market Conditions: Assumes static populations and competitive landscapes.

6. Real-World Impacts of TAM Oversights

Subpopulation Restrictions

HTA agencies often limit eligibility:

• NICE may approve only biomarker-positive patients.
• IQWiG benchmarks against generics, restricting broad use.

Adjusted TAM:$$\text{Adjusted TAM} = \text{Initial TAM} \times \text{Eligibility Factor}$$

Dynamic Pricing Adjustments

Post-launch pricing renegotiations are common:

$$\text{Dynamic TAM} = \text{Initial TAM} \times \text{Pricing Adjustment} \times e^{-\lambda t}$$

National reimbursement timelines vary:

• EMA approval is insufficient for market entry.
• HTA reviews in France or Italy may delay access by 1–2 years.

Statistical Models for Enhanced TAM Projections

Monte Carlo Simulations

Incorporating stochastic variability:

• Simulate 10,000+ scenarios for pricing, eligibility, and adoption rates.
• Capture uncertainty and fat-tailed risks.

Scenario Planning

Develop TAM under optimistic, realistic, and pessimistic conditions:

• Optimistic: Full eligibility, maximum pricing.
• Pessimistic: Restricted subpopulations, capped pricing, delayed reimbursement.

Conclusion: A Call for Realism in TAM Projections

TAM, while a staple of biotech pitch decks, is deeply flawed as a static projection of market potential. By ignoring HTA-imposed constraints, dynamic pricing adjustments, and the probabilistic nature of biotech markets, it inflates expectations and obscures risks. A shift toward more nuanced, dynamic, and mathematically rigorous models is essential for investors to make informed decisions in this volatile sector.