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# Spider plots - Advanced sensitivity analysis

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Tornado charts are a great way to identify important input distributions for further inspection. Spider charts are a great option to further measure the influence that key input variables have on the output, as they not only show the effect of each extreme of the input variable, but also reveal non-linearities between model inputs and outputs. Below we explain how spider charts work with different simulation software:

@RISK

Advanced sensitivity analysis proceeds as follows:

• Before starting, set the number of iterations to a fairly low value (e.g. 300)

• Select the input distributions to analyse (performing a crude sensitivity analysis will guide you)

• Specify the cumulative probabilities you wish to test (we habitually use 1%, 5%, 25%, 50%, 75%, 95%, 99%)

• Select the output statistic you wish to measure (mean, a particular percentile, etc)

@RISK then:

• Selects an input distribution;

• Replaces the distribution with one of the percentiles you specified;

• Runs a simulation and records the statistic of the output;

• Selects the next cumulative percentile and runs another simulation;

• Repeats until all percentiles have been run, then put back the @RISK distribution, and move on to the next selected input

Once all inputs have been treated this way, we get a spider plot such as the one below:

Often this type of plot has several horizontal lines for variables that have almost no influence on the output. It makes the graph a lot clearer to delete these.

Now we can very clearly see how the output mean is influenced by each input. The vertical range produced by the "Success" variable shows the range of Net Present Value there would be if the project succeeded or not  (ranging from \$3.5M losses to \$4M gains). The next largest range is for the sales volume, etc. The analysis helps us understand the degree of sensitivity in terms we understand (in this example, predicted monetary gains/losses) rather than correlation coefficients that other sensitivity analysis techniques use.

Crystal Ball

Crystal Ball can create spider plots and tornado charts changing one variable at a time, using the following steps:

• Click "CBTools" >> Tornado Chart;

• Select the forecast or formula cells to target;

• Click "Next"

• Select the assumptions, decision variables and precedents to analyze (performing a crude sensitivity analysis will guide you);

• Click "Next"

• Specify the cumulative probabilities you wish to test in the "Tornado Input" window;

Crystal Ball then:

• Selects an input distribution;

• Replaces the distribution with one of the percentiles you specified;

• Calculates the value of the forecast, using "median" or "existing cell values" (you can specify this);

• Selects the next cumulative percentile and calculates the forecast value again;

• Repeats until all percentiles have been calculated, then put back the Crystal Ball distribution, and move on to the next selected input

Once all inputs have been treated this way, we can plot the following Spider Plot:

Often this type of plot has several horizontal lines for variables that have almost no influence on the output. It makes the graph a lot clearer to delete these.

Now we can very clearly see how the output mean is influenced by each input. The vertical range produced by the Sales price line shows the range of expected profits there would be if the Marketing costs was fixed somewhere between the minimum and maximum (a range of \$5,000). The next largest range is for the Distribution costs (\$3500), etc. The analysis helps us understand the degree of sensitivity in terms we understand rather than correlation coefficients that other sensitivity analysis techniques use.

The Tornado Chart Tool  can also plot a Tornado chart (also using the "Tornado Chart Tool" in Crystal Ball). The numbers on the left and right of the bars represent the most extreme percentile results.

Caveats:

1. Because the Tornado Chart Tool changes one variable at a time (independently of the other), it cannot account for multiple impacts of a variable through correlation and other dependency relationships.

2. The results are depending on the base case used for the variables. Therefore, we recommend that you run the tool more than one time with different base cases

Differences with @RISK:

The steps taken in @RISK advanced sensitivity analysis are fairly similar to those described above, but instead of calculating the forecast, the forecast values are simulated and the analyst can chose what statistic (e.g. the mean) will be reported. Because in this analysis the results are simulated, correlations and other dependency relationships are taken into account, making it a more robust option.

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