Written by Tom Hagy


Experienced statistical modeling expert Dr. G. William Kennedy says the analytical tools he uses can be “extremely powerful” in establishing or disproving liability or determining damages if applied by a properly trained expert.   However, he says, in the hands of a novice they can be dangerous. 


Dr. Kennedy, Ph.D. and CPA/ABV with Anders Minkler & Diehl, LLP in St. Louis spoke on a live recording for Mealey’s Litigation Conferences and Business Valuation Resources LLC entitled “Compelling Statistical Evidence: Mining, Modeling, and Presenting Quantitative Financial Evidence to Juries.” 


If paired with a well-trained professional, Kennedy is extremely confident in the accuracy of the tools he discussed on the recording.  “Most of the methods I am relying on are in the textbooks and offer a great deal of certainty,” Kennedy said.  “The benefit of these statistical tools, the benefit to the bar, is that they all meet the criteria established under Daubert.”   He said he has told juries he is 99.999% confident in his estimations.


Once you have gathered the data Kennedy recommends that you draw a simple plot, which, he says, “helps avoid traps of using data that may have errors or need serious diagnostic work, or that the conclusions you are drawing are really not valid.” 


Then begin performing analysis.  “This process is iterative,” he says.  “There is not a eureka moment.”  The answers should be very clear at this point and you should only modify the analysis if necessary.  “I don’t mean to get to the answer counsel wants.  I mean if there are errors in the modeling, in the data, etcetera.  Anything that would make us go back and make corrections to make sure the results are credible.”  It is a quality control process, he said, that once complete offers data that are ready for forecasting.


These kinds of tools and techniques might be used in a productive way in litigation settings, both for damages and liability estimations. 


There are several statistical tools one can use in establishing liability or in damages quantification:  statistical sampling, correlation analysis, analysis of variance, time-series analysis, regression analysis, event studies and Monte Carlo simulation.  


Statistical sampling.  Take a sample but make sure it is representative of the population.  You can use it where the total population isn’t available or if it is impractical to obtain.  In a recent case where insurance allocation was based on addresses, he said he had to use sampling because it was impossible to get information on all of the locations.


Correlation analysis.  This looks at the relationship of two variables, for example height and weight, analysis of which would show that the taller a person is the more he will weigh.   This analysis will show the strength and direction of that correlation.  Correlation analysis is an effective tool to use in lost profits cases, he said, because it can test whether a factor is significant to a company’s sales and profitability.


Analysis of variance.  This not a method Kennedy uses a lot because it is imbedded in other tools like regression analysis.  He used it in a damages-for-lost-profits case where the question was whether national publicity about a product was the cause of the damages.  “We tested whether after the event the sales month to month changed and if there was an adverse reaction by consumers to the product problem.   If so there would be an increased volatility.  We tested this in various ways.  We compared that to the immediate period after the event and news publicity and came to an objective and quantifiable conclusion as to whether sales volatility increased.  In this case we actually were working on a liability determination.”  


Time series analysis.  This is a method that includes a regression-based calculation displaying a single series of dates.  A popular example is in graphical updates on the stock market.  What this analysis shows is whether the variable movements have a pattern.  This is one tool that can help forecast future sales, observe seasonality, or allow adjustments for seasonal or cyclical trends.   


Regression analysis.  This is broader than time series analysis, although it can be based on time.  Regression analysis permits two or more variables.  You can have variables X or Y or a number of variables.  In statistical analysis X tends to be time, but in regression X can be anything, like height or weight.  A business model might be that company’s sales move in sync with overall retail sales or with macroeconomic or internal factors.  Regression analysis can be used with cross sections of data.  It is important when diagnosing errors in data to know whether something is cross sectional or time sensitive.  Examples are lost profit calculations, which are influenced by a multitude of internal and external factors, “a situation well suited for regression analysis,” Kennedy explained. 


Event studies.  Event studies have been used in securities fraud cases, subprime lending cases, and in accounting liability action.  Conducting event studies is similar to constructing market models where you regress a company’s returns against market indices and come up with relationship about how stock prices might be performing across time against particular indices.  An event is something defined by the pleadings in the case, a particular adverse behavior by a board of directors or management, or an external event on a particular date.   In a classic event study you go back to pre-event time windows, look at daily returns against market indices or, in a more refined model, at daily stock returns or industry indices.  Then you test around the event window:  was there a change in the relationship between your company’s stock price and the overall market?  If so, how much?  You then need to quantify the change around the event date.  You can use this model to answer questions like:  what would the stock price have been had the event not occurred? 


Monte Carlo simulation.  How do you get around issues of quantifying uncertainty of an unestablished business where there is no commercialization yet?  The Monte Carlo simulation is a good tool for this, he said.  It is good for construing something as simple as “price x quantity” in software commercially available.  You can specify a range of prices and ranges of quantities and specify how you think the prices will likely stack – at higher or lower ranges.  Allowing you to show the variables will behave the Monte Carlo simulation will let you run and re-run the model, change the numbers and track the answer.  It allows you to do this thousands of times, he said, taking forecasting uncertainty out of the analysis.  “I use it almost every time I conduct an IP valuation.”


When presenting analysis based on Monte Carlo, Kennedy quotes authorities that have commented on the simulation.  The Litigation Services Handbook has many flattering things to say about Monte Carlo tool, calling it “The most flexible method of calculating an expectation when there are multiple potential outcomes or when the outcomes depend to varying degrees on the different inputs.”  The ABA treatise Fundamentals of Intellectual Property Valuation, a primer for identifying and determining value, also has good things to say about Monte Carlo simulations, he said.


Kennedy summarized by saying that statistical models are a very powerful way to present damages or proof or lack of liability; that because of the complex nature of the tools the expert should be thoroughly trained and knowledgeable of the tools; that attorneys should know the limitations of the tools; and, even though the tools are complex, experts and attorneys must present them to the trier of fact in a way that is easy to understand. 


Dr. Kennedy presented along with Jeffrey Dorman, Esq. with Freeborn & Peters, LLP of Chicago.  To receive more information about how to receive a copy of the recording, the materials and transcript of the presentation, contact Customer Service at (888) BUS-VALU, (503) 291-7963 or write to me directly at tom.hagy@bvresources.com.  I also own a phone and know how to use it:  610-312-4754.