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Milestone Publications

September 2016: Monte Carlo for the Masses, Sam Savage Analytics Magazine. Showcases the 3.0 SIPmath modeler tools and kicks off the Random Number Initiative.


The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty by Sam Savage, John Wiley, 2009, 2012. Describes the pitfalls of average-case analysis and lays out the necessity of Probability Management. 

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A two-part foundational article on Probability Management was published in OR/MS Today. You can download PDF (Part IPart II) or view online (Part IPart II). (2006)


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Trade-off Analytics: Creating and Exploring the System Tradespace

Edited by Gregory S. Parnell, 2016
Presents an integrated trade-off and risk analysis framework to identify value and risk. Examples from defense and commercial domains illustrate these concepts in the different life cycle stages. Chapter 9, includes an Integrated SIPmath Model by Alexander D. MacCalman, Gregory S. Parnell, and Sam Savage to examine Pareto charts, tornado diagrams and distribution functions to perform sensitivity analysis and identify dominant solutions in near real-time.

Calculating Uncertainty: Probability Management with SIP Math

by John Marc Thibault, 2013. 
This book provides a brief introduction to Probability Management and a tutorial on the theory and practice of SIP math.

Frontiers of Modern Asset Allocation

by Paul Kaplan, Quantitative Research Director at Morningstar Europe, John Wiley, 2012. 
Chapter 25 of the book, entitled Updating Monte Carlo Simulation for the Twenty-First Century, by Paul D. Kaplan and Sam Savage, describes Distribution Strings.


  • Monte Carlo for the Masses by Sam Savage. Showcases the 3.0 SIPmath modeler tools and kicks off the Random Number Initiative, September 2016, Analytics Magazine

  • Poisson Formula Write-up by Dave Empey and Marc Thibault, a technical breakdown of the one-cell Poisson distribution generator built in to the SIPmath™ modeler tools, August 2016

  • Speaking Uncertainty to Power, by Shayne Kavanagh and Sam Savage, details the practice of risk aware forecasting and budgeting for CFO's, including applications by financial officers in the cities of Redmond, Washington and Colorado Springs, Colorado. April 2016

  • Towards a Simulation Network, or, The Medium is the Monte Carlo (With Apologies to Marshall McLuhan), by Sam Savage and Marc Thibault, describes how the SIPmath Standard may foster the creation of networks of simulations that bring stochastic modeling to general management. December, 2015

  • Embracing the Uncertainty of the Iran Nuclear Deal, Sam L. Savage, ProbabilityManagement.org, September 2015 - Dr. Savage addresses the need to avoid average-based thinking in the Iran Nuclear Deal, and recounts a disaster in an earlier Iran saga. The failed Operation Eagle Claw mission to free the US hostages is still presented as a poster child for the Flaw of Averages by the Naval Postgraduate School. A PowerPoint and Excel model accompany the article.

  • MIT Sloan Management Review, December 2014 - Psychologists Robin Hogarth and Emre Soyer present the benefits of interactive simulation and the communication of uncertainty, two of the cornerstones of the discipline of probability management. In “Using Simulated Experience to Make Sense of Big Data,” Hogarth and Soyar cite ProbabilityManagement.org as “a non-profit organization that aims at improving communication of uncertainty,” and applies “simulation-based communication to improve actual managerial decisions and public policies.”

  • Teaching modern portfolio theory to 10-Year-Olds, by Sam Savage, a personal account of the surprising results of teaching portfolio theory to middle schoolers, ORMS Today, October 2014

  • Probability Management 2.0, by Sam Savage and Melissa Kirmse, an overview of the 2nd generation of Probability Management, ORMS Today, October 2014

  • Probability Management in Financial Planning, Sam L.Savage and Shayne Kavanagh, Government Finance Review Magazine, February 2014. Discusses examples of the Flaw of Averages in public finance, and how they may be mitigated through the discipline of Probability Management. Excel sample files may be downloaded from our Models page.

  • The Sequestetron, Sam Savage and Shayne Kavanagh, November/December 2013, Analytics Magazine. Describes the application of Probability Management to municipal finance in the face of uncertain tax revenues.

  • Distribution Processing and the Arithmetic of Uncertainty, Sam Savage, November/December 2012, Analytics Magazine. An introduction to SIPmath in Excel

  • Monetising NOLs: Finding the ‘Flaw of Averages’ and Producing Useful Forecasts, by Michael H. Salama, Tax Management Weekly State Tax Report. (2012)
    Addresses the issue of managing net operating losses under uncertainty.

  • Cost vs. Risk in Defense Portfolios, by Philip Fahringer and Sam Savage, Phalanx. (March 2012)
    Investigates the inherent tradeoffs between cost and military airlift preparedness using libraries of threat scenarios.

  • The Flaw of Averages in U.S.Corporate Income Taxes: An Evaluation From the Taxpayer’S Perspective, by Michael H. Salama, Virginia Tax Review (2011)

  • The Flaw of Averages In Project Management, in PMI Virtual Library, by Philip Fahringer, John Hinton, Marc Thibault and Sam Savage. (2011)
    Explores the use of Stochastic Libraries in simulating project completion.

  • Monte Carlo, A Lightbulb for Illuminating Uncertainty, in Investments & Wealth Monitor, by Paul D. Kaplan and Sam Savage. (2011)
    Discusses the history and future of financial simulation including Distribution Strings.

  • Toward a Consolidated Risk Statement, by Sam Savage and Aaron Brown, appears in the December issue of Risk Professional magazine. (Subscribers to the magazine may view it at their site.) It describes the potential of Distribution Strings to enable the aggregation of risk reports across an organization. (2009)