# 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 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 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?

## 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.