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April 01, 2024 Feature

Patent Damages Trends: Statistical Approaches to Apportionment

Dan Werner and Joe Milbury

©2024. Published in Landslide, Vol. 16, No. 3, March/April 2024, by the American Bar Association. Reproduced with permission. All rights reserved. This information or any portion thereof may not be copied or disseminated in any form or by any means or stored in an electronic database or retrieval system without the express written consent of the American Bar Association or the copyright holder.

Methodologies for calculating patent damages continue to be shaped by the intellectual property law landscape. In response to court decisions, statistical approaches are increasingly being used for apportionment of damages.

➭ Attend the corresponding webinar, “An Overview of Different Patent Valuation Models and Damages Calculations,” on April 23, 2024, at 1:00 PM (ET).

The patent damages statute states that “[u]pon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.” Reasonable royalty damages aim to determine the monetary amount attributable to a license that would have emerged from a hypothetical negotiation between the patent holder and the alleged infringer. However, determining what constitutes a “reasonable royalty” is often a point of contention between litigating parties.

In products containing multiple elements, courts have established that the damages award should only relate to the patents at issue, meaning that experts must apportion between the patented and unpatented elements if the patented element is not the sole driver of demand. This ensures that the resulting royalty accurately reflects the impact of the invention, since “the trial court must carefully tie proof of damages to the claimed invention’s footprint in the market place.” Consequently, the issue of apportionment and the value of a patented technology is often a focus of the expert analysis, and damages methodologies have evolved in order to meet courts’ requirements in this area.

To meet courts’ requirements, economists and valuation analysts may employ various approaches to measure the value of patented technology and address the issue of apportionment. Economists commonly adopt a framework in which products are regarded as assortments of attributes or product features, with each feature adding incremental value to the overall product. In many situations, this allows for the use of statistical methods to measure the incremental value conferred by each feature, including the patented technology at issue. For example, a statistical analysis of pricing for similar products with and without the patented technology can inform how the patent contributes to the revenue (and profits) of the licensee. This provides relevant information to the hypothetical negotiation framework under the Georgia Pacific factors. Given sufficient data and proper implementation, a regression analysis is one such method of statistical analysis that allows practitioners to measure the incremental price premium attributable to a patented feature. In this way, statistical approaches can help to remove potential subjectivity from apportionment approaches while satisfying Daubert criteria.

This article delves into the statistical methods proposed by both plaintiffs and defendants to address apportionment in recent patent cases. The most suitable approach depends on the unique facts and circumstances of each litigation and may be constrained by the accessibility of specific data and information. Nevertheless, past court decisions offer insights into what courts have accepted as suitable apportionment methodologies for estimating damages in the form of a reasonable royalty.

Overview of Regression Analysis Measuring Incremental Value

Economists frequently employ a statistical methodology known as “regression analysis” to estimate the relationship between a product’s price and multiple features. Regression analysis allows practitioners to measure the incremental influence (or value) of one variable on another, while accounting for a variety of other product attributes. Product attributes typically influence the purchase decisions of consumers. When products have desirable features, they tend to be more in demand and may be sold at higher prices. An additional product feature may add incremental value to the overall product. By applying statistical methods to real-world market data, practitioners can determine how much extra customers pay for specific product features. This provides evidence to understand how important those features are in influencing consumer demand, product prices, and the revenues and profits attributable to a particular feature, which can aid in the determination of a reasonable royalty. In this way, a regression analysis can measure the price premium attributable to a particular product feature, while also accounting for all other key product features that influence pricing.

For example, an economist may be focused on studying the impact of heated seats on the price of an automobile. A simple comparison of automobile prices with and without heated seats may not be sufficient to isolate the price premium due to heated seats because there are also other automobile features that may impact pricing (e.g., vehicle age or the presence of leather seats). By statistically analyzing data on various automobiles with and without heated seats, an economist can use regression analysis to measure the price premium linked only to that feature, while accounting for the influence of other attributes (e.g., vehicle age or leather seats) on an automobile’s price. Thus, in certain circumstances the use of regression analysis offers a significant advantage over simpler methodologies because it allows quantitative insights to be unearthed from complex datasets generated from the interplay of various market factors.

In the above hypothetical example, if the heated seating feature is a technology conferred only by the patent at issue, then a regression analysis can help quantify the incremental value added by the patent at issue. Put differently, the regression analysis can apportion the contested product into its component parts and identify the incremental price (or revenue) attributed to the patent at issue. However, if the measured feature (heated seats in this example) is enabled by multiple patents, then the described regression-based approach can only measure the collective value of such patents. In these situations, further apportionment may be required to properly isolate the incremental value (and resulting reasonable royalty) attributable to the single patent at issue.

The application of regression analysis to investigate prices for products with multiple features is widely accepted in peer-reviewed academic literature by economists (and many other quantitative disciplines). For example, regression analysis has been used to analyze computers, automobiles, grocery products, and housing. It has also been used by government agencies to analyze products and to estimate the incremental pricing impact from particular product attributes.

Experts have employed regression analysis to substantiate their testimony in a wide variety of legal cases, including product defects, price fixing, and intellectual property disputes. Courts regularly admit expert testimony that incorporates properly implemented regression analysis, provided that the analysis is aligned with the specific facts and circumstances of the case. However, expert testimonies relying on regression models may be excluded by courts if the models inadequately account for major factors that are relevant to the case.

Using Regression Analysis in Patent Damages

Regression analysis played an important role in VLSI’s damages model in VLSI Technology v. Intel Corp., a patent case where the jury awarded $2.18 billion in damages before the Federal Circuit vacated the damages verdict and remanded the case for a new trial limited to damages. At trial, VLSI’s technical experts testified that the patents at issue conferred two benefits to the accused Intel microprocessor products: decreased power consumption and increased performance. They further opined that a 1% improvement in either of these attributes could be valued as a 1% increase in processor speed. VLSI’s damages expert utilized regression analysis to estimate the influence of various microprocessor attributes on pricing. After accounting for other attributes, the damages expert specifically quantified the increase in price that resulted from an increase in microprocessor speed. Using the regression results and relying on the opinions of the technical experts, VLSI’s damages expert calculated the increased profits Intel gained from the patents. Finally, damages were calculated by splitting this pool of profits between VLSI and Intel in a hypothetical negotiation.

Although Intel’s complete rebuttal expert testimony during trial is not publicly available, one rebuttal argument made by an Intel licensing expert noted that he was unaware of a hedonic regression analysis ever being used in patent licensing negotiations. Often, the details of regression analyses are criticized by an opposing expert (since the method’s reliability depends on the design and implementation by a damages expert), but that did not appear to be the case here based on the publicly available testimony. Intel appealed the verdict, challenging several aspects of the analysis by VLSI’s experts, and the Federal Circuit noted “a readily identifiable error” in the analysis of VLSI’s technical expert, which did not properly calculate the incremental technical benefit attributable to the patent. Since VLSI’s damages expert relied on that input from the technical expert, the Federal Circuit “[could not] say that this error ‘could not have changed the result,’ namely, the precise amount of damages, so as to render it harmless” and remanded the case for a new trial on damages. However, the Federal Circuit also reported that “Intel, in this court, has not persuasively shown that the regression analysis used to determine price effects of speed improvements is an improper or unreasonable one.”

Given that the Federal Circuit left intact the damages expert’s use of regression analysis, this case provides valuable insights for all parties involved in patent litigation, as regression analysis can be adopted as part of a comprehensive damages model but reliability is important for each step in the overall calculation.

Potential Issue: Variables Not Considered

While a properly designed and implemented regression analysis can measure the incremental value attributable to a patented product feature, excluding important variables in a regression may distort the results and undermine the accuracy of the analysis. This exclusion can create “omitted variable bias.” By neglecting these omitted variables, the regression analysis may fail to capture the true influence of certain features on product pricing, which can lead to flawed conclusions and a failure to accurately capture the impact of a patented feature on pricing. However, the omission of a variable in a regression analysis does not automatically result in bias in the regression results. The inclusion of every theoretically plausible variable in a regression analysis is not required so long as the model incorporates the major determinants of pricing.

Kaist v. Samsung provides an example of the issue of omitted variable bias arising in patent litigation involving microprocessors. To calculate damages, Kaist’s damages expert relied on the opinion of another expert who asserted that the patented invention had led to a substantial increase in processor speed compared to alternative technologies. Kaist’s damages expert then used “regression analysis to measure the relationship between changes in processor speed and the price of Samsung’s devices.” Samsung criticized the implementation of the regression analysis, claiming that the analysis omitted device features that biased the damages calculations. Samsung noted that the plaintiff’s expert included “only nine device features out of hundreds,” and damages decreased by approximately one-third after inclusion of an additional feature that was ignored in Kaist’s model.

In this case, the court noted that Samsung’s omitted variable criticism was “a compelling counter-position to [Kaist’s expert’s] position, but amounts to a disagreement between experts as to what variables should be considered.” As a result, the court denied Samsung’s motion to exclude Kaist’s damages expert’s testimony, viewing this as a divergence of opinions between experts that speaks to the weight of the testimony on damages, rather than a fundamental flaw that prevents the admissibility of the testimony on damages.

The court ruled similarly in AVM v. Intel, when AVM’s expert used regression analysis to measure the impact of a specific feature on the price of the product, and Intel sought to exclude the expert for omitting variables, among other alleged shortcomings. However, in other non-patent cases where the price premium of a contested feature was analyzed, regression models have been excluded by courts in part based on the variables that were not considered in the analysis. Thus, when regression analysis is used in litigation, it is important for both plaintiffs and defendants to consider which features are key determinants of the product pricing and therefore should be included in the model, and whether the exclusion of certain features may undermine the analysis.

Potential Issue: Further Apportionment Required

When multiple patents contribute to a measured feature in the data, a regression-based approach may only be able to capture the combined value of these patents. Consequently, to determine a reasonable royalty specific to the single patent at issue, additional apportionment might be necessary to accurately isolate the incremental value of the patent.

In the U.S. International Trade Commission case of Certain Memory Modules & Components Thereof & Products Containing Same, regression analysis was used to determine fair, reasonable, and nondiscriminatory (FRAND) royalties for standard essential patents (SEPs). In this matter, the dispute over damages centered around Netlist’s obligation to license its patents on FRAND terms, with the opposing party setting forth a FRAND defense and arguing that Netlist’s licensing offer did not meet the requirements.

Netlist relied on expert testimony using regression analysis to support its claim that its licensing offers to the opposing party were FRAND. The expert’s analysis estimated the value of the disputed memory modules by examining the price premium paid in the market compared to modules with the next best standard. The expert opined that the regression analysis measured the incremental value of the technologies in question (separate from the value of standardization itself) and attributed that value to SEPs within the standard. However, because the measured feature was enabled by multiple patents, the regression-based approached only measured the collective value of such patents, and further apportionment was necessary. Therefore, the expert’s analysis also included an incremental cost deduction and the use of forward citation analysis to perform further apportionment to the patents at issue. Although criticized by an opposing expert, this approach was accepted, with the judge ruling against the opposing side’s FRAND defense. Thus, this case provides an example where regression analysis assisted in the calculation of apportioned reasonable royalty damages but where further apportionment was necessary after performing the regression analysis.

Stragent, LLC v. Intel Corp. provides another example of using regression analysis while also highlighting the importance of apportionment. In this matter, Stragent alleged that Intel infringed on three of its network processor patents. The plaintiff’s damages expert used regression analysis to value Intel’s network processors, finding the value of the “reliability, availability, and service” (RAS) component of the accused products. The infringed patents were used in only one of 19 features of the RAS component, so further apportionment was required. To distribute the value of the patent damages to the one feature, the plaintiff’s expert assumed that each RAS feature contributed equally to the RAS component’s value (i.e., the value of the infringed patents was assumed to be 1/19 of the value of the RAS component). In Intel’s motion to exclude the plaintiff’s expert testimony, Intel argued that attributing 1/19 of the combined value of the RAS features to the accused feature was arbitrary and made without factual support. While not debating the merits of the hedonic regression directly, and even though the plaintiff’s expert argued that this allocation was “quite conservatively low,” the court described the plaintiff’s expert methodology as “arbitrary” with no basis in the facts of the case. Thus, the court excluded the plaintiff’s expert testimony on damages.


The determination of damages in patent infringement cases is a complex process that aims to calculate a reasonable royalty based on the hypothetical negotiation between the patent holder and the infringer. Properly implemented statistical analysis provides one methodology that can value the contribution of patented technologies, satisfy courts’ apportionment directive, and properly calculate damages that are tied to the “footprint” of the invention at issue. Regression analysis is widely accepted in academia, has been used extensively by damages experts outside of intellectual property cases, and is now being increasingly used to assist in calculating patent damages. However, its successful implementation requires careful consideration of relevant factors and the unique circumstances of each case. The choice of methodology depends on the specific facts of each litigation and may be constrained by the availability of certain information. However, previous court rulings can offer useful insights into what types of statistical analyses have been admitted. These rulings shed light on situations where specific damages methodologies have been accepted and caution against potential shortcomings.

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    Dan Werner

    NERA Economic Consulting

    Dan Werner, PhD, CPA, is a damages expert and director at NERA Economic Consulting.

    Joe Milbury

    NERA Economic Consulting

    Joe Milbury is a consultant at NERA Economic Consulting.


    The views expressed in this article are those of the authors alone and not necessarily those of NERA Economic Consulting. This article is for general information purposes and is not intended to be, and should not be taken as, legal advice or expert opinion.