Quantitative Valuation Models for Physical AI / Embodied Robotics Companies

1. Model Framework Overview

Physical AI and embodied robotics represent one of the most capital-intensive and technologically complex frontiers in artificial intelligence. Unlike software companies, these firms must solve problems in hardware, perception, dexterity, safety, and real-world deployment simultaneously. This makes traditional valuation methods insufficient on their own, because most companies in this space are pre-revenue or early-commercial, meaning revenue-based multiples and discounted cash flow models cannot be applied in a straightforward way.

To address this, we propose a hybrid quantitative valuation framework that combines traditional financial metrics with Physical AI-specific technical and operational signals. The goal is to explain why certain companies command significantly higher valuations than others, even when they are at similar funding stages or have similar amounts of capital raised.

What Are We Trying to Explain?

Because most of these companies are pre-revenue, we treat post-money valuation at the last funding round (or the latest estimated valuation) as the primary dependent variable. In simpler terms, we are trying to answer a single question: what drives one robotics company to be valued at $39 billion while another, with comparable funding, is valued at $2 billion?

The Four Pillars of the Model

The model breaks valuation drivers into four interconnected categories:

1. Technical performance of foundation models. This measures how capable a company's underlying AI model actually is. In Physical AI, the dominant paradigm is the Vision-Language-Action (VLA) model, which takes visual and language inputs and produces robotic actions. Companies with models that score higher on standardized manipulation and generalization benchmarks should, in theory, command higher valuations because their technology is closer to being deployable at scale.

2. Capital efficiency and deployment traction. This captures how well a company turns capital into real-world progress. It includes total funding raised, but more importantly, it includes deployment metrics: how many robots are actually in the field, how many pilot programs are running, and how many commercial contracts have been signed. A company that has raised less but deployed more may be more valuable than one that has raised more but deployed nothing.

3. IP strength and ecosystem signals. Patents, strategic partnerships, and the quality of investors all signal whether a company has defensible technology and credible support. A startup backed by NVIDIA Ventures, Sequoia, or Lux Capital carries an implicit endorsement that affects how the market prices its equity.

4. Macro tailwinds. Broader market conditions matter. If the total addressable market for humanoid robotics is projected to reach $38 billion by 2035 (per Goldman Sachs), that growth expectation lifts all companies in the sector. Conversely, a high interest rate environment depresses valuations by increasing the cost of capital and reducing the present value of future cash flows.

Core Hypothesis

In the 2025 to 2026 Physical AI wave, technical model performance and real-world deployment metrics explain a significant portion of valuation premiums beyond traditional funding stage or investor quality.

This means that if you control for how much money a company has raised and who invested, the companies with better models and more robots in the field should still be valued higher. Testing this hypothesis is the central purpose of the framework.

2. The Dependent Variable: What We Are Valuing

Before building any model, we need to define precisely what we are trying to predict. In public markets, this is straightforward: you use stock price, market capitalization, or enterprise value. In private markets, especially in an emerging sector like Physical AI, it is much harder.

Primary Measure: Log of Post-Money Valuation

We use the natural logarithm of post-money valuation at the last funding round as the primary dependent variable. Taking the logarithm is a standard technique in econometrics that serves two purposes. First, it compresses the wide range of valuations (from $2 billion to $39 billion in our dataset) into a more manageable scale. Second, it allows us to interpret our regression coefficients as percentage changes rather than dollar amounts, which makes the results easier to understand and compare across variables.

When a company has not raised a round recently, we use the latest reported or estimated valuation from secondary market transactions or PitchBook estimates.

Why Not Revenue?

Most Physical AI companies have little to no revenue. Figure AI, despite a $39 billion valuation, is primarily selling pilot deployments rather than shipping products at scale. Skild AI raised $1.4 billion at a $14 billion valuation based almost entirely on the promise of its general-purpose robot brain, not on current sales. Using revenue would exclude the most important companies from the analysis.

Alternative Proxies for Robustness

To ensure our findings are not artifacts of a single valuation measure, we run the model against three alternative dependent variables:

• Total capital raised to date. This captures investor conviction but may overstate the value of companies that have raised many small rounds versus fewer large ones.
• Implied valuation from secondary transactions. When employees or early investors sell shares on secondary markets, the transaction price implies a valuation. This is useful because it reflects what buyers are actually willing to pay, not just what primary investors negotiated.
• PitchBook estimated valuations. For companies without recent rounds, PitchBook provides modeled estimates based on comparable companies and sector multiples.

Data sources: Crunchbase, PitchBook, company press releases, Bloomberg, and TechCrunch deal coverage from 2025 through mid 2026.

3. Key Predictor Variables: Breaking Down What Drives Value

The strength of any quantitative model lies in choosing the right independent variables. We group our predictors into five categories, each explained below.

Category 1: Technical Performance

This is the most novel and important part of the framework. In software AI, model quality is often measured by benchmark scores on language or coding tasks. In Physical AI, the equivalent is performance on manipulation and generalization benchmarks, which test whether a robot can perform physical tasks (like picking up objects, opening drawers, or assembling parts) and whether it can generalize those skills to new objects and environments it has never seen before.

We use three specific predictors:

Model benchmark score. The average normalized success rate across standardized tasks. For example, if a company's VLA model successfully completes 72% of tasks in a standardized benchmark suite while a competitor completes 55%, that difference should be reflected in valuation. Sources include arXiv papers, company technical blogs (such as pi.website for Physical Intelligence), OpenVLA and Octo comparison tables, and the Stanford AI Index 2026.

Training data volume. How many hours of teleoperated robot data the company has collected. Physical Intelligence's pi0 model was trained on over 10,000 hours of teleoperation data, which is one reason it is considered a leading generalist policy. More data generally means a more capable model, though the relationship is not linear.

Model architecture advantage. Whether the company uses a more advanced architecture, such as flow-matching or continuous action spaces, compared to older autoregressive approaches. We score this as a binary or ordinal variable based on published technical reports.

Category 2: Capital and Traction

Total funding raised is the cumulative capital a company has brought in across all rounds. While more funding does not guarantee a higher valuation (it depends on equity sold), it is a strong signal of investor confidence and resource availability.

Deployment traction is the variable we expect to have the strongest effect on valuation. It measures how many robots are actually in commercial or pilot deployment, how many pilot hours have been logged, and how many commercial contracts have been signed. Examples include Figure AI's BMW partnership, Agility Robotics' deployments with Amazon and GXO, and Apptronik's work with Mercedes-Benz. A company with robots in real factories is fundamentally different from one with only lab demos, and the market prices that difference heavily.

Category 3: IP Strength

Patent count and quality measures both the number of patents filed or granted and the number of forward citations those patents receive. A patent that is cited by many subsequent patents is more valuable than one that is never cited, because it indicates the invention is foundational. Sources include the USPTO, Google Patents, and Derwent innovation databases.

Category 4: Ecosystem Signals

Tier-1 investor count tallies how many top-tier venture capital firms have invested. We define tier-1 as firms like Andreessen Horowitz (a16z), Sequoia, Lux Capital, Khosla Ventures, and NVIDIA Ventures. Having multiple tier-1 investors signals that sophisticated, well-connected parties have done due diligence and committed capital, which reduces information asymmetry for other investors.

Strategic partnerships counts partnerships with large technology companies or major manufacturers. These are valuable because they provide distribution channels, manufacturing expertise, and validation. A partnership with BMW or Amazon is worth more than a partnership with a mid-size logistics company.

Category 5: Stage, Size, and Macro

Company age and funding stage controls for the natural progression of valuations. A Series C company will typically have a higher valuation than a Seed company, but the marginal effect diminishes over time. We measure this as months since founding plus a categorical variable for funding stage.

Robotics market growth captures the broader market expectation. We use total addressable market (TAM) forecasts from the IFR World Robotics Report and Goldman Sachs projections. When the projected market is growing faster, all companies in the sector benefit.

Interest rate environment uses the Federal Funds Rate or the 10-year Treasury yield, lagged by one quarter, as a macroeconomic control. Higher rates reduce the present value of distant future cash flows, which is particularly punishing for pre-revenue companies whose value is entirely based on future expectations.

4. Core Companies in the Dataset

The chart above shows estimated valuations for the five companies that form our initial panel. Each one represents a different strategic approach to Physical AI, which is what makes them useful for comparison.

Figure AI ($39B, September 2025)

Figure AI is the highest-valued company in the dataset and the most deployment-focused. Its partnership with BMW to deploy humanoid robots on automotive assembly lines is one of the few cases of Physical AI robots working in a production environment at scale. Figure has also secured funding from NVIDIA, Microsoft, and OpenAI, giving it an exceptionally strong ecosystem score.

Skild AI ($14B, January 2026)

Skild AI raised $1.4 billion in January 2026 at a valuation exceeding $14 billion. Its strategy is to build a single general-purpose "brain" that can control any robot for any task, rather than building a specific robot body. This is a bet on the model layer rather than the hardware layer, which makes its valuation more sensitive to technical performance metrics than to deployment metrics.

Physical Intelligence ($11B, 2025)

Physical Intelligence (known as pi) developed the pi0 family of VLA models, which are widely considered among the most capable generalist robot policies. Its valuation reflects strong technical performance scores but limited deployment compared to Figure. The company has been in talks for further funding at $11 billion or more, showing how quickly valuations can move in this sector.

Apptronik ($5B implied, February 2026)

Apptronik raised a $520 million extension in February 2026, bringing total funding to over $935 million, with an implied valuation around $5 billion. The company has partnerships with Mercedes-Benz and NASA, which strengthens both its deployment traction and ecosystem scores. It represents a mid-tier valuation that balances technical promise with real-world deployment.

Agility Robotics ($2.1B, 2025)

Agility Robotics is the maker of Digit, a bipedal robot designed for warehouse logistics. Its deployments with Amazon and GXO make it one of the few companies with robots in commercial operation. Despite this, its valuation is lower than Figure's, which suggests that the market may be weighting the automotive manufacturing use case more heavily than logistics, or that Figure's stronger investor base is driving a premium.

Expanding the Panel

As more data becomes available, we plan to add Covariant, Neura Robotics, 1X Technologies, and a Tesla Optimus segment proxy. Tesla is a particularly interesting case because it is a public company, which means its financials are transparent, but the Optimus program is embedded within the broader automotive business, making it difficult to isolate the robotics segment's contribution to overall valuation.

Data collection approach: Start with Crunchbase filters for Robotics and Physical AI, then manually verify each company's latest funding round via their official site and recent press announcements.

5. Methodological Basis: Three Approaches for Robustness

No single statistical method is sufficient for a dataset this small and this noisy. We recommend running all three of the following approaches and comparing results. When all three point in the same direction, we can be more confident in our conclusions.

Approach 1: Panel Data Regression (Main Specification)

This is the core of the framework. A panel regression allows us to control for both company-specific characteristics and time-specific effects, isolating the relationship between each predictor and valuation.

The main equation is:

log(Valuation) = beta_0 + beta_1(BenchmarkScore) + beta_2(DeploymentTraction) + beta_3(TotalFunding) + beta_4(Patents) + beta_5(InvestorTier) + controls + error

Here is what each part means in plain language:

• beta_0 is the intercept, representing the baseline log valuation when all predictors are zero.
• beta_1 through beta_5 are the coefficients we are trying to estimate. Each one tells us how much a one-unit increase in that variable changes the log valuation, holding all other variables constant.
• controls include company age, funding stage, and macro variables like interest rates.
• error captures everything we cannot measure or predict.

We use fixed effects for company and time, which means we control for unobserved characteristics that are constant within a company (like its founding team's quality) and unobserved shocks that affect all companies in a given quarter (like a sudden change in AI sentiment).

Approach 2: Machine Learning Ensemble

Regression assumes a linear relationship between variables and valuation. In reality, the relationship may be non-linear: for example, training data volume might have diminishing returns after a certain point, or deployment traction might only matter above a minimum threshold.

We use XGBoost or Random Forest models, which can capture these non-linear patterns automatically. The primary output of this approach is feature importance, which ranks which variables matter most for predicting valuation.

To make the results interpretable, we use SHAP values (SHapley Additive exPlanations). SHAP tells us not just which features matter, but for each individual company, how much each feature contributed to its predicted valuation. For example, SHAP might show that Figure AI's high valuation is driven 40% by deployment traction, 25% by investor quality, 20% by benchmark scores, and 15% by other factors. This level of detail is highly valued by venture capital investors because it explains not just the "what" but the "why."

Approach 3: Valuation Multiples and Comparables

When companies begin generating revenue, we can supplement the regression with traditional multiples analysis:

• EV/Revenue or EV/EBITDA for companies with meaningful sales. The current median EV/EBITDA multiple for robotics and AI companies is approximately 16.8x as of late 2025.
• Funding round multiples and implied step-up analysis for pre-revenue companies. This examines how much a company's valuation increased between rounds relative to the capital raised and milestones achieved.

This approach is less statistically rigorous than the first two, but it provides a sanity check. If the regression model predicts a company should be valued at $10 billion but comparable companies are trading at multiples that imply $20 billion, that gap is worth investigating.

Software stack: Python with pandas for data management, statsmodels for regression, scikit-learn and xgboost for machine learning, and shap for interpretability. R is an acceptable alternative.

6. Additional Data and Proxies

Beyond the core predictor variables, several supplementary data sources can strengthen the model.

Compute and Training Cost Estimates

The cost of training a large VLA model is a proxy for its sophistication. If a company reports spending $50 million on a single training run, that signals a more ambitious model than one trained on a small cluster. We estimate these costs by scraping or deriving them from technical papers and announcements, using public GPU pricing and reported training durations as inputs.

Hype and Sentiment Analysis

Market sentiment can drive valuations independently of fundamentals, especially in a hyped sector like Physical AI. We use Natural Language Processing (NLP) to measure sentiment from X (formerly Twitter) and news articles. Specifically, we use models like FinBERT or Hugging Face transformers to classify each mention of a company or the term "Physical AI" as positive, neutral, or negative. The aggregated sentiment score for a given quarter can then be included as a predictor variable.

Market Forecasts

We incorporate forward-looking market projections from authoritative sources:

• IFR World Robotics Report for annual installation data and growth rates by region and application.
• Goldman Sachs humanoid market projections for long-term TAM estimates.
• Morgan Stanley estimates for the humanoid robot market potentially surpassing $5 trillion by 2050.

These forecasts serve as macro-level controls that capture the overall growth expectation for the sector.

Public Company Anchors

While most Physical AI companies are private, a few public companies provide useful reference points:

• Tesla (Optimus) is the most significant. While Optimus is not a standalone business, Tesla mentions it in earnings calls and investor presentations, which creates a sentiment signal. We use the frequency and tone of Optimus mentions as a proxy for public market interest in Physical AI.
• UBTECH is publicly listed in China and provides a valuation reference for humanoid robotics in Asian markets, where much of the manufacturing activity is concentrated.

7. Challenges and Mitigations

No quantitative model is perfect, and a thesis without an honest discussion of its limitations is not rigorous. Here are the five most significant challenges we face and how we address each one.

Challenge 1: Private Company Valuations Are Opaque

Private companies are not required to disclose their valuations, and when they do, the numbers can be misleading. A valuation announced in a press release may include aggressive assumptions, preferred shares with liquidation preferences, or strategic investor discounts.

Mitigation: We triangulate across multiple sources. We use the last round post-money as the baseline, then cross-reference with PitchBook estimates and secondary market transaction prices. When sources disagree significantly, we use the median and note the range.

Challenge 2: Limited Standardized Benchmarks

There is no universally accepted benchmark for VLA model performance. Each company reports on different tasks, in different environments, with different success criteria. This makes direct comparison difficult.

Mitigation: We normalize scores wherever possible by mapping each company's reported results onto a common scale. Where normalization is not possible, we create a composite "Physical AI Capability Index" that combines multiple signals (benchmark scores, training data volume, architecture type) into a single comparable number. The index is transparent and reproducible, with weights determined by the regression model itself.

Challenge 3: Few Companies Have Revenue

Most companies in the dataset are pre-revenue, which means traditional valuation multiples cannot be applied.

Mitigation: We focus on pre-revenue signals that correlate with future revenue potential. Deployment traction is the strongest such signal because it indicates that a company has a product good enough for a customer to pay for, even if the revenue is currently small. Model performance is the second strongest, because it predicts whether the company can improve its product fast enough to capture market share.

Challenge 4: Rapidly Changing Landscape

The Physical AI sector evolves on a quarterly basis. New models, new funding rounds, and new partnerships are announced constantly, which means any snapshot can become outdated quickly.

Mitigation: We use quarterly snapshots from Q1 2025 through Q2 2026 and always note the data vintage. The panel structure of the regression helps here because it allows us to observe how relationships change over time, rather than relying on a single point-in-time cross section.

Challenge 5: Selection Bias

Our dataset only includes companies that have raised significant funding. Companies that failed early, or that are still in stealth, are not represented. This means our findings may not generalize to the broader population of robotics startups.

Mitigation: We acknowledge this limitation explicitly in all findings. Where possible, we compare our sample to the broader robotics startup population from Crunchbase to assess whether funded companies differ systematically from unfunded ones. If they do, we note the direction and magnitude of the bias.