Companion Models to Published Articles and Presentations

The best way to learn about probability management is to explore interactively.
NOTE: to experiment with the models below, you will need to enable content, if asked, and make sure that Excel is in Automatic Calculation mode.

Datasaurus Arithmetic

Based on the Datasaurus data set of Alberto Cairo, which was based in turn on DrawMyData by Robert Grant. This model shows that SIPmath lets you do arithmetic with the most bizarre distributions imaginable.

Download Model (.xlsx)

Figure 3.png

None of My Successes Have Been Planned and None of My Plans Have Been Successful: Simulating Rags to Riches and Vice Versa

Blog Post by Sam Savage

Download Model

Three Italian physicists created a simulation that shows how chance drives the disparity in the distributions of talent and wealth. Inspired by the physicists, this SIPmath model explores similar principles. The model shows that chance plays a role, but that disparity in income can arise without it. 


The Sum of the Sandbags Doesn't Equal the Sandbag of the Sum: How Probability Management Helps Solve Age-Old Problems in Budgeting and Forecasting

Article: How to Profit from Probability Management by Matthew Raphaelson and Sam Savage, in Banking Strategies, Bankers Administration Institute 

SandbagCalc.xlsx   Demonstrates basic sandbag math

Demonstrates basic sandbag math

BAI_Model.xlsx   Banking example with revenues and expenses

Banking example with revenues and expenses


Rolling Up Operational Risk

Rolling up operational risk at PG&E by Jordan Alen, Christine Cowsert Chapman, Melissa Kirmse, Farshad Miraftab, & Sam L. Savage

From from OR/MS Today, December 2016, Volume 43, Number 6. 

Asset Level Model (.xlsx)
Consolidated Risk (.xlsx)

Operation Eagle Claw

Operation Eagle Claw was a failed special operations mission designed to rescue 52 Americans who had been taken hostage by Iranian revolutionaries in Tehran in November 1979. The Naval Postgraduate School uses it a case study in Flaw-of-Average based decision modeling. This is described in PowerPoint deck, and Helicopter.xlsx, which lets you experiment with the reliability and number of aircraft sent, then instantly simulates 10,000 missions to determine the chances of completion.


Eagle Claw Simulation (.xlsx)


SIPmath™ Flood Model

By Sam Savage, August 2015. 

This is an active SIPmath™ simulation of the example in Figures 1.5 and 37.3 of Dr. Savage's book, The Flaw of Averages: Why we Underestimate Risk in the Face of Uncertainty. It demonstrates that the average damage from flooding is greater than the damage associated with the average crest.

Model (.xlsx)

Probability Management in Financial Planning

By Sam Savage and Shayne Kavanagh, Government Finance Review Magazine, February 2014. 

These SIPmath™ models demonstrate the examples of scheduling, surplus and deficit, and reserves. The Dice calculator is available below.


Schedule (.xlsx)
Surplus Deficit (.xlsx)
Reserves (.xlsx)

Files from Dr. Savage's Stanford Webinar

The three SIPmath™ models included here demonstrate why so many things are Behind Schedule, Beyond Budget, and Below Projection. This is explained by the Flaw of Averages, a systematic set of errors that occur when single "average" estimates are substituted for uncertainties.

Behind Schedule (.xlsx)
Below Projection (.xlsx)
Beyond Budget (.xlsx)


SIPmath Dice Calculator

Here is a SIPmath™ calculator that simulates 10,000 rolls of a pair of dice before your finger leaves the key. Experiment with the formula in D10 to see the distributions of outcomes of different calculations based on the dice.

Model (.xlsx)

Shortfall Model

As described in “The 'Sequestetron'“ by Sam Savage and Shayne Kavanagh, Analytics Magazine, November/December 2013, and presented at the 107th annual meeting of the GFOA in San Francisco, June 2013.


Model (.xlsx)

Cost vs. Risk in Defense Portfolios

by Philip Fahringer and Sam Savage, Phalanx. (March 2012).

Article (.pdf)

Model (.xlsm)

Cost vs Risk GIF 0.5.gif

The Flaw of Averages In Project Management in PMI Virtual Library

by Philip Fahringer, John Hinton, Marc Thibault and Sam Savage (2011).

Article (.pdf)

Model (.xlsx)


Further examples

The models below accompanied the original articles on Probability Management in OR/MS Today. They were created before the SIPmath standard, and were tedious to create, requiring thousands of formulas. You need to enable macros to access the clickable scatter plot in the first model.

Probability Management, Sam Savage, Stefan Scholtes & Daniel Zweidler, OR/MS Today, Part 2, February, 2006

Probability Management, Sam Savage, Stefan Scholtes & Daniel Zweidler, OR/MS Today, Part 1, February, 2006