# RESEARCH ARTICLES | RISK + CRYSTAL BALL + ANALYTICS

## Correlation of Duke Basketball Scores, in ModelRisk (7/8)

Correlation behavior in ModelRisk is enforced with the use of copulas. Copulas offer more flexibility in accurately simulating real data scatter-plot patterns than do single-value correlation coefficients. While this advantage is clear for financial and insurance applications, its implementation in an MCA spreadsheet simulator can make the difference between universal adoption and rejection by a majority of the intended user group. Let us now use ModelRisk (MR) to enforce the correlation behavior between Duke Basketball offense scores and their opponents' scores, based on the '09/'10 historical data.

## Correlation of Duke Basketball Scores, in Crystal Ball (6/8)

In our quest to simulate future Duke Basketball scores, we have taken past historical data of individual games during the '09/'10 season and fitted probability distributions to that data. Two PDFs are generated; one for Duke's scores (offense) and one for their opponents' scores (defense). We have used both Crystal Ball and ModelRisk to perform this task. Is there something missing in our PDF formulations?

## Correlation and Impact on Monte Carlo Analysis Results (5/8)

All the top dogs in the Monte Carlo Analysis spreadsheet universe have distribution-fitting capabilities. Their interfaces have common elements, of course, since they rely on (for the most part) the same PDFs in their arsenal of distribution-fitters. There are important differences, to be sure. It is hoped this comparison will illustrate pros and cons from a practical standpoint. Before going over our scorecard between Crystal Ball and ModelRisk, there is one more very important capability category begging for review: Correlation.

## Discrete Distribution Fitting to Duke Basketball Scores, in ModelRisk (4/8)

Let the battle begin anew. We continue our journey in uncertainty modeling, having understood how to fit distributions to data using Crystal Ball (CB). How does that experience compare to what ModelRisk (MR) has to offer?

Open the Duke 09_10 Scores spreadsheet with ModelRisk loaded in the Excel environment. We will first create the MR Objects representing the fitted PDFs. (Just as with the CB exercise, it is good practice to examine a variety of best-fitting distributions, rather than blindly accepting the top dog.) Then, in distinctly separate cells, we will create the VoseSimulate functions that behave as sampled values from the PDFs modeled by the MR Objects.

## Distributions in ModelRisk as Objects (3/8)

As with Crystal Ball, ModelRisk has the ability to fit distributions to historical data. The analyst looking to describe the variation of a Monte Carlo Analysis input can use "fitting" windows to select data and manipulate other options. How does the ModelRisk (MR) fitting experience stack up against the Crystal Ball (CB) methods and options? There are some important differences one should understand about MR before fitting PDFs to the Duke 09_10 Scores spreadsheet.