A sensitivity analysis is a method used to determine how changes in variables impact an outcome, based on a given set of assumptions. By creating a model that plays out “what-if” scenarios—how a change in variable affects an output, such as profits—businesses or individuals can see how sensitive their results are to those changes. This helps identify which factors have the greatest impact, empowers companies to make more informed decisions, and mitigates risk.

Imagine that you’re planning a road trip with your friends. Each potential route has fixed characteristics—such as the length of the drive and whether you have to pay tolls—as well as variables that are more, well, variable—such as traffic and the price of gas. To find the optimal route, it would be prudent for your group to tweak these factors to see how they impact the total duration and expenses of the road trip. You might calculate how the cost will change if gas prices go up or how much longer the trip will take if there’s a lot of traffic.

Determining how the outcome may change by adjusting these variable factors is similar to conducting a sensitivity analysis. A sensitivity analysis shows how different values of an independent variable (in this instance, traffic and the price of gas) impact a given dependent variable (the total length and cost of your trip). Although you can’t know for sure what the cost of gas or the volume of traffic will be on the day you actually embark on the trip, you can make some assumptions to arrive at an informed decision on which route to take.¹

Also known as “what-if” analysis, sensitivity analyses allow businesses to predict the outcome of an action when they are not entirely in control of the environment. For example, a clothing store can conduct a sensitivity analysis to help them determine the parameters of a sale. There are multiple variables to consider: what discount they should offer, how much they should spend advertising the sale, and how many customers they think will turn out. By checking how varying these elements impacts their revenue, the store can predict which conditions will lead to the optimal result.¹

Sensitivity analyses allow us to make more informed choices by providing a deeper understanding of the relationship between variables, demonstrating how sensitive the outcome is to each. It can be challenging to factor in the multitude of relevant variables, especially in our rapidly changing environment, but thanks to advanced computing capabilities, a sensitivity analysis gets us a step closer to making accurate predictions.²

Variables: Factors within a model that can change. Independent variables are intentionally manipulated in an experiment or model to observe their impact on dependent variables. In a sensitivity analysis, a business will select a few target variables, such as costs, market conditions, and risk factors, to see how changing these influences an outcome such as profits.¹ 

Output: The result or outcome of a model that changes in response to alterations in independent variables. With sensitivity analyses, the output may be profit margins, production output, or market control.

Financial Modeling: A summary of a company’s past and present expenses and earnings, usually in a spreadsheet, used to predict future financials. In a sensitivity analysis, elements of the financial model, such as the price of resources or sales, can be altered to see how it would impact future financial outcomes. This helps executives make data-informed decisions to ensure the sustained success of the company.⁴ 

Black Box Process: A model where the relationship between variables and an output is complex or unclear. It can be useful to conduct a sensitivity analysis for these models because it is otherwise difficult to predict how a change in a variable will impact the outcome. A “what-if” analysis helps you to see how the outcome will change, even if you don’t understand exactly how the independent variables contribute to it.²

Baseline Scenario: The outcome you predict based on the most likely or common set of assumptions before adaptations are made to the independent variables. For example, for the road trip, you would determine the baseline scenario (length and cost of the trip) by making assumptions about how much traffic there will be and the current cost of gas. You would then use your baseline scenario as a benchmark to compare to what-if scenarios during a sensitivity analysis.⁵

R-squared: A number that represents how much of the output variation can be explained by independent variables. To determine R-squared, you first create a model that incorporates variables you deem relevant to the output to predict the outcome. Next, you compare it to the actual output to see how much variation there was. If the R-squared is 0.85, for example, that means 85% of the outcome can be explained by the variables you included in the model, while 15% fall outside of that. If your R squared is low, that would let you know that there are additional variables that impact the output that you should have considered in your sensitivity analysis.⁶

Sensitivity analyses incorporate probabilities, which originated in the 17th century with the development of probability theory. French mathematicians Pierre de Fermat and Blaise Pascal developed mathematical models to calculate the probabilities of possible outcomes in games of chance.⁷ Their models provided a tool to deal with situations with a degree of uncertainty.

As the applications of probability evolved, people used them to explore how small changes in variables could impact outcomes. Pioneers such as English scientist Francis Galton explored relationships between variables, introducing concepts such as correlation, which measures the strength of the relationship between a variable and an outcome (later leading to the development of R-squared), and regression, a statistical method used to analyze the relationship between independent and dependent variables.⁸

In the 1920s and 1930s, British statistician Ronald Fisher developed standardized methods for conducting experiments in which variables are manipulated to test their effect on an outcome. Experimental design provided a roadmap for people to later conduct sensitivity analyses.⁹

These early economic and statistical foundations laid the groundwork for systematically assessing how changes in variables affect outcomes. It became a more formalized tool in military operations research during World War II.  Important decisions had to be made about military strategy and resource allocation, and the complexity and widespread impact of these large-scale operations meant that military strategists and economists needed a way to predict the effects of even small changes.⁹ For example, analysts studied the deployment of convoy escorts in the Battle of the Atlantic to determine the optimal amount to deploy for the protection of merchant ships without spreading resources too thin. They analyzed how adding a convoy escort would impact survival rates in the Atlantic while also considering where they would have to remove resources from.¹⁰ By modeling various scenarios and assessing the consequences of changing particular variables, they provided recommendations that improved military efficiency and effectiveness.

After sensitivity analyses proved their usefulness for decision-making during World War II, and as computers became more sophisticated, sensitivity analysis was adopted by other fields such as engineering, finance, and environmental modeling. In the 1970s, mathematician Paul Cukier developed the Fourier Amplitude Sensitivity Test (FAST). This model differed from previous sensitivity analysis models that could only test one variable at a time, known as a local sensitivity analysis, whereas FAST was able to factor in multiple variables that could affect the outcome and identify which had the greatest impact.¹¹

As computers became more accessible, sensitivity analysis became more widely used across industries, no longer solely for deciding military strategy or evaluating policy changes. Today, most businesses will leverage sensitivity analyses to better understand the market and how to make optimal decisions. Manufacturers use them to optimize production processes and reduce costs, financial analysts use them to assess investment risks, and marketers use them to predict the outcome of a campaign.

Pierre de Fermat & Blaise Pascal

French mathematicians who are credited with laying the foundation of probability theory in their exploration of games of chance. They developed models to split the pot of winnings for an unfinished game based on the probable outcomes. Their work in probability theory provided a way to quantify uncertainty and understand how variables affect outcomes, which underscores sensitivity analysis. Both mathematicians also contributed to the development of calculus.⁷

Francis Galton

A British scientist and anthropologist, Galton developed the concept of correlation, defining factors as being correlated when a variation in one leads to a variation in the other. Correlation forms the basis for sensitivity analysis, which explores how closely linked variables are to one another. Galton is infamous for his interest in and promotion of eugenics.¹² 

Ronald Fisher

British statistician known as the founder of the modern experiment. Fisher was one of the first researchers to apply statistical procedures to scientific experiments, formalizing experimental design. Fisher actually developed a standardized way to conduct scientific experiments to answer the age-old debate in England of whether milk should go in the cup before or after tea. His boss was adamant she could tell the difference, so he set up an experiment with eight cups of tea (half where the milk was added first, half where it was added after). When his boss was able to accurately identify the cups of tea, Fisher applied statistics to the fun experiment to determine the likelihood that it was just chance. Later in his career, Fisher developed other statistical concepts like the null hypothesis and was also known for being a proponent of eugenics.¹³

Paul F. Cukier

Along with his colleagues, Cukier created one of the first sensitivity analyses that allowed for the manipulation of multiple variables, called the Fourier Amplitude Sensitivity Test (FAST).¹¹ Cukier applied FAST to various fields, including chemistry and engineering, to determine how sensitive outcomes were to multiple variables without having to test each variable independently.¹⁴

Sensitivity analysis helps individuals and businesses understand how different scenarios may impact their decisions and outcomes, enabling them to anticipate challenges and plan accordingly. This foresight allows for better preparedness and strategic adjustments before problems arise, making it a powerful tool for navigating uncertainty.

Make Data-Informed Decisions

Without mathematical models and analyses, businesses would have to operate on a trial-and-error basis. Decisions would be made solely based on assumptions without a clear understanding of their potential impact. Sensitivity analyses allow businesses to understand to what degree deviations from the baseline scenario would impact the outcome, providing data to make informed decisions.

For example, imagine a tech company was preparing to launch a new pair of headphones and was trying to determine how much money to spend on marketing. A sensitivity analysis may show that increasing spending by 10% would likely lead to a 15% increase in profits, giving them assurance that marketing is worth the extra investment. Alternatively, if they learned that increasing marketing spending would have little impact on profits, they could reallocate those resources to other projects. 

Reduce Risk

Although conducting a sensitivity analysis takes time, it can help businesses avoid decisions that would negatively impact them in the long run. As American writer and teacher Dale Carnegie once said, “An hour of planning can save you 10 hours of doing.”¹⁵

As the name suggests, sensitivity analyses are conducted to see how sensitive an outcome is to particular variables. For a business, the hope is that your model or project will be resilient to change, and if not, a sensitivity analysis helps you make decisions to mitigate risks.¹⁶ For example, if a company was building a new school and determined through a sensitivity analysis that an increase in material costs would result in the project going over budget, the manager can focus on acquiring fixed-price contracts to reduce the risk of increased material costs.

Proactive Approach to Change

The only constant in life is change, which, as Alvin Toffler pointed out, makes some people feel like they can’t plan for the future. However, sensitivity analysis allows individuals and businesses to see how changes impact outcomes and, therefore, provides them with the information they need to make decisions and enact changes before unintended outcomes occur.¹⁷

A sensitivity analysis is a proactive risk management tool. For example, imagine you wanted to buy a house and were deciding what mortgage to get. You calculate that if your circumstances stayed exactly the same, you’d be able to afford a 5-year mortgage at 4%. A sensitivity analysis would show you what would happen if your mortgage rate went up by 1% or if you lost your job for a few months. This might reveal that it would be tough to pay your mortgage in either of those scenarios, inspiring you to save up an emergency reserve fund before you buy a house so that you have something to fall back on. Without this proactive approach, you might have proceeded with buying a house and found yourself in a difficult situation if circumstances changed.

While sensitivity analysis can be a powerful tool, it’s not a perfect one. It heavily relies on assumptions, overlooks the relationship between variables, and requires substantial time and resources to implement effectively. 

It’s a Guessing Game

You might have noticed the word “assumptions” is used a few times throughout this article. Although sensitivity analysis helps us predict what could happen in the future and how that will impact our desired outcome, it does so based on assumptions that may never come to fruition. That means a lot of time and effort can be dedicated to considering “what-if” scenarios that never end up happening.¹

It can be very difficult (and sometimes pointless) to predict the future. For example, COVID-19 completely revolutionized the world and the way businesses operate, but no one could have predicted that it would happen or the long-lasting impact it would have. Shortly before the pandemic, a business may have conducted a sensitivity analysis to determine how much money to spend on renting office space, only to encourage all of its employees to work from home a few months later. It may be more important for a company to focus on being resilient and adaptable than spending time assessing the endless possibilities of the future.

Overlooking Interdependencies

Although sensitivity analyses can test the impact of multiple variables on an outcome, thanks to models like FAST, they do not always account for the relationship between different elements. Our world is very complex, with dynamic relationships between variables that are not always captured in sensitivity analysis.¹

For example, a retail company might conduct a sensitivity analysis to see how profits would be impacted by a change in a few key variables: equipment efficiency, material cost, and labor cost. The sensitivity analysis may show that upgrading the equipment would improve profits, allowing the company to produce clothes at a quicker pace, but it may not reveal the full impact, failing to consider how labor costs are affected. It’s likely that upgraded equipment could automate some tasks, reducing labor costs.

Sensitivity analysis can, therefore, create an oversimplified representation of the complex environment, missing the interconnectedness of variables, which aren’t always so independent after all.¹⁸ 

Time & Resource-Intensive

Consider the multitude of variables that can impact a business outcome, such as profits—there’s a lot. A cafe running a sensitivity analysis to evaluate impacts on profits would have to consider supply costs, rental costs, labor costs, customer demand, competition, and more. Just identifying all the variables can be time-intensive, as is collecting all the necessary data.¹

Running a sensitivity analysis is complex and requires significant computational resources. Simulations need to be run on computers with high processing power, which can be costly, especially for organizations with limited resources. As it’s nearly impossible to factor in every variable or imagine all the ‘what-if’ scenarios, smaller businesses may want to run sensitivity analyses that focus on a few key variables they deem most likely to impact the outcome.

Euro Disney’s Mistaken Assumptions

When Euro Disney (now known as Disneyland Paris) was being developed, Disney made some assumptions based on the models of their other Disney park locations. In their other parks, about half of the revenue came from admission ticket sales, while the other half came from merchandise, food, and hotels. They assumed the same would be true for Euro Disney. They predicted 11 million people would visit the park in their first year of operations in 1992 and chose the price of tickets, merchandise, food, and hotel stays accordingly.¹⁹ 

Unfortunately, Disney was wrong. They had incorrectly assumed that patrons would plan multi-day visits, building many luxury hotels within the park to accommodate them, but most people visiting just came for a day excursion. Though Disney predicted that half the revenue would be from sources outside of ticket sales, patrons were also less interested in the merchandise, with Mickey Mouse memorabilia appealing less to French customers who just wanted to spend a day at the park rather than acquire all things Disney.²⁰

Euro Disney found itself taking on debt and facing a huge revenue loss in their first few years of operations. Had they conducted a sensitivity analysis, they may have realized sooner that some variables (such as one-day visits and fewer merchandise sales) would have a big impact on overall revenue and could have adjusted their prices accordingly and avoided a major loss.

Sensitivity Analyses in Clinical Trials

Clinical trials are conducted to see if new drugs or treatments are effective and safe for people to use. If a treatment is found to improve health outcomes with minimal side effects, it gets approved for wider use.

Although clinical trials are rigorous, they are conducted on a subset of a population, making it hard to determine with confidence that the results are generalizable to wider groups. A sensitivity analysis can be useful to see if small changes in variables (e.g., a demographic change in the patient, an altered form of administration, or varying the length of treatment) have a significant impact on the outcome. If the sensitivity analysis reveals that the changes have little impact on the result of treatment, researchers can be more confident that the positive health outcomes will apply to a wider population.²¹

A sensitivity analysis can also help fill in missing data. For example, in a clinical study testing the effectiveness of a treatment for macular edema (eye swelling) that was caused by retinal vein occlusion, not all patients continued the trial, so they had missing data points for their outcomes—they didn’t know if it improved their vision. A sensitivity analysis was conducted, testing different possible values for the missing vision data to see how it affected the overall conclusion about the treatment’s effectiveness. They varied the mean outcome by -20 to 20 to see if they could still say with confidence that the drug was—in most cases—effective, and they found that it was!²²

Webinar: Strengthen Your Strategy with Cyber Scenarios

Sensitivity analysis is all about assessing the potential impact of uncertain variables and assessing the risk of our models by testing how sensitive outcomes are to changing variables. In our digital world, one of those uncertain variables is the risk of a cyberattack. In this webinar panel, The Decision Lab sat down with experts in cybersecurity, behavioral science, and strategic planning to discuss how scenario planning, a concept similar to sensitivity analysis that asks businesses to imagine various potential cyber futures, can help risk-proof your organization. 

Why do we think some things are related when they aren’t?

A sensitivity analysis allows us to see the strength of the relationship between a variable and an outcome and avoid the illusory correlation bias. Often, we believe there’s a correlation between two variables—like wearing a lucky shirt and our favorite sports team winning—when it's simply coincidence. In this article, our co-directors, Dan Pilat and Dr. Sekoul Krastev, explore the illusory correlation bias and provide advice on how to avoid it. 

1. Kenton, W. (2024, June 27). Sensitivity analysis. Investopedia. Retrieved from https://www.investopedia.com/terms/s/sensitivityanalysis.asp
2. Vipond, T. (n.d.). What is sensitivity analysis? Corporate Finance Institute. Retrieved from https://corporatefinanceinstitute.com/resources/financial-modeling/what-is-sensitivity-analysis/
3. Schilling Consulting. (2023, January 25). New tool: Scenario sensitivity analysis. Retrieved from https://www.schilling-consulting.com/new-tool-scenario-sensitivity-analysis/
4. Kopp, C. M. (2024, June 14). Financial modeling. Investopedia. Retrieved from https://www.investopedia.com/terms/f/financialmodeling.asp
5. Gillenwater, M. (2022, March 14). What is a baseline? GHG Management Institute. Retrieved from https://ghginstitute.org/2022/03/14/what-is-a-baseline/
6. Fernando, J. (2024, November 13). R-squared. Investopedia. Retrieved from https://www.investopedia.com/terms/r/r-squared.asp
7. Porter, T. M. (2024, December 4). Probability. Encyclopedia Britannica. Retrieved from https://www.britannica.com/science/probability
8. Fiveable. (2024, July 30). Nash bargaining solution. Retrieved from https://library.fiveable.me/game-theory/unit-9/nash-bargaining-solution/study-guide/uKCTDxb9WEUUOXnL
9. Tarantola, S., Ferretti, F., Lo Piano, S., Kozlova, M., Lachi, A., Rosati, R., Puy, A., Roy, P., Vannucci, G., Kuc-Czarnecka, M., & Saltelli, A. (2024). An annotated timeline of sensitivity analysis. Environmental Modelling & Software, 174, 105977. https://doi.org/10.1016/j.envsoft.2024.105977
10. McCloskey, J. F. (1987). U.S. operations research in World War II. Operations Research, 35(6), 910–925. https://doi.org/10.1287/opre.35.6.910
11. Ryan, E., Wild, O., Voulgarakis, A., & Lee, L. (2018). Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output. Geoscientific Model Development, 11(8), 3131–3146. https://doi.org/10.5194/gmd-11-3131-2018
12. Encyclopedia Britannica. (2024, November 25). Francis Galton. Retrieved from https://www.britannica.com/biography/Francis-Galton
13. Kean, S. (2019, August 6). Ronald Fisher, a bad cup of tea, and the birth of modern statistics. Science History Institute. Retrieved from https://www.sciencehistory.org/stories/magazine/ronald-fisher-a-bad-cup-of-tea-and-the-birth-of-modern-statistics/
14. Cukier, R. I., Fortuin, C. M., Shuler, K. E., Petschek, A. G., & Schaibly, J. H. (1973). Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I. Theory. The Journal of Chemical Physics, 59(8), 3873–3878. https://doi.org/10.1063/1.1680571
15. Funding for Good. (2023, February 27). Inspiring quotes about strategic planning. Retrieved from https://fundingforgood.org/inspiring-quotes-about-strategic-planning/
16. LinkedIn. (n.d.). How can you use sensitivity analysis to evaluate different scenarios? Retrieved from https://www.linkedin.com/advice/3/how-can-you-use-sensitivity-analysis-evaluate-different-1
17. Keita, B. (2024, July 23). What is sensitivity analysis in project management? Invensis Learning. Retrieved from https://www.invensislearning.com/blog/what-is-sensitivity-analysis-in-project-management/
18. FasterCapital. (n.d.). Benefits and limitations of sensitivity analysis. Retrieved from https://fastercapital.com/startup-topic/Benefits-and-Limitations-of-Sensitivity-Analysis.html
19. Patro, S. (2023, October 9). Sensitivity analysis: Assessing the impact of assumptions in financial models. The Wall Street School. Retrieved from https://www.thewallstreetschool.com/blog/sensitivity-analysis-assessing-the-impact-of-assumptions-in-financial-models-2/
20. Francis, A. (n.d.). Case study: Euro Disney failure – Failed Americanism. MBA Knowledge Base. Retrieved from https://www.mbaknol.com/management-case-studies/case-study-euro-disney-failure-failed-americanism/
21. Parpia, S., Morris, T. P., Phillips, M. R., Wykoff, C. C., Steel, D. H., Thabane, L., Bhandari, M., & Chaudhary, V. (2022). Sensitivity analysis in clinical trials: Three criteria for a valid sensitivity analysis. Eye, 36(11), 2073–2074. https://doi.org/10.1038/s41433-022-02182-3
22. Parpia, S., Morris, T. P., Phillips, M. R., et al. (2022). Sensitivity analysis in clinical trials: Three criteria for a valid sensitivity analysis. Eye, 36(11), 2073–2074. https://doi.org/10.1038/s41433-022-02182-3