Cryst al Ball2000.2User ManualThis manual, and the software described in it, are fur nished under license and may only be used or copied in accordance with the ter ms of the license agreement. Information in this document is provided for infor mational purposes only, is subject to change without notice, and does not represent a commitment as to merchantability or fitness for a par ticular pur pose by Decisioneering, Inc.No par t of this manual may be reproduced or transmitted in any for m or by any means, electronic or mechanical, including photocopying and recording, for any purpose without the express wr itten permission of Decisioneer ing, Inc.Written, designed, and published in the United States of America.To purchase additional copies of this document, contact the Technical Ser vices or Sales Depar tment at the address below:Decisioneering, Inc.1515 Arapahoe St., Suite 1311Denver, Color ado, USA 80202Phone: (303) 534-1515 Toll-free sales: 1-800-289-2550 Fax: (303) 534-4818 1988-2001, Decisioneer ing, Inc.OptQuest is a registered tr ademark of Optimization Technologies, Inc.Cr ystal Ball is a registered tr ademar k of Decisioneer ing, Inc.Other product names mentioned herein may be trademar ks and/or registered trademar ks of the respective holders.Cryst al Ball User Manual iiiCont ent sInt roduct ion Welcome to Crystal Ball 2000.2............................................... 11Who should use this program ............................................. 11What you will need .............................................................. 12How this manual is organized ............................................. 12Whats new in Crystal Ball 2000.2 .............................................. 13Chart modifications ............................................................ 14Constant distribution .......................................................... 14Excel charts ......................................................................... 14Forecast filtering ................................................................. 14CB Tools updates ................................................................ 15Locked worksheets .............................................................. 15Report in an existing worksheet ......................................... 15Preserving cell values upon calculation error ..................... 15Sample size limited removed .............................................. 15Statistics Preferences moved ............................................... 16Windows 2000 compatibility ............................................... 16Additional resources ................................................................... 16Technical support ............................................................... 16Consulting referral service .................................................. 16Conventions used in this manual ............................................... 17Chapt er 1: Get t ing St art ed Wit h Cryst al BallWhat Crystal Ball does................................................................ 21Starting the first tutorial ............................................................. 21Running the simulation ...................................................... 23Determining profit .............................................................. 24How Crystal Ball uses Monte Carlo simulation .......................... 25Starting the second tutorial ........................................................ 26Defining assumptions .......................................................... 27Defining forecasts ................................................................ 41Running a simulation .......................................................... 44Interpreting the results ....................................................... 46Summary ............................................................................. 50Closing Crystal Ball .................................................................... 51Chapt er 2: Underst anding t he TerminologyModel building and risk analysis overview................................. 55What is a model? ................................................................. 55Risk ...................................................................................... 57Risk analysis ........................................................................ 57Monte Carlo simulation ...................................................... 58Certainty .............................................................................. 59Understanding probability distributions.................................... 60iv Cryst al Ball User Manual4Cont ent sSelecting a probability distribution ............................................ 64Most commonly used distributions ............................................ 65Uniform distribution .......................................................... 65Normal distribution ............................................................ 67Calculating standard deviation .......................................... 69Triangular distribution ....................................................... 70Other commonly used distributions .......................................... 72Binomial distribution ......................................................... 72Poisson distribution ............................................................ 74Geometric distribution ....................................................... 76Hypergeometric distribution .............................................. 78Lognormal distribution ...................................................... 81Exponential distribution ..................................................... 84Weibull distribution (also Rayleigh distribution) ............... 86Beta distribution ................................................................. 88Custom distribution ............................................................ 90Important custom distribution notes ............................... 100Less commonly used distribution types ................................... 100Gamma distribution (also Erlang and chi-square) ........... 101Pareto distribution ............................................................ 105Extreme value distribution ............................................... 106Negative binomial distribution ......................................... 108Truncating distributions ................................................... 110Comparing the distributions ............................................ 111Sampling methods ................................................................... 113Monte Carlo ...................................................................... 113Latin hypercube ................................................................ 114Confidence intervals................................................................. 115Understanding other statistical terms ..................................... 116Forecast Statistics window terms ....................................... 116Additional statistical terms....................................................... 121Correlation coefficient ...................................................... 122Rank correlation ............................................................... 123Certainty ........................................................................... 124Percentile .......................................................................... 125Chapt er 3: Set t ing Up and Running a Simulat ionThe Crystal Ball toolbar ........................................................... 129Starting Crystal Ball manually ................................................. 129Other methods of starting manually ................................ 130Defining cells: an overview....................................................... 130Defining assumptions .............................................................. 131Identifying a distribution type .......................................... 131Entering an assumption ................................................... 133Cryst al Ball User Manual vCont ent sEntering cell references .................................................... 135Alternate parameter sets ................................................... 136Distribution preferences ................................................... 138Fitting distributions to data ...................................................... 138How distribution fitting works .......................................... 138Specifying correlations between assumptions .......................... 145Freezing assumptions ............................................................... 150Defining decision variables....................................................... 151Define Decision Variable dialog ........................................ 152Defining forecasts ..................................................................... 153Define Forecast dialog ...................................................... 154Editing Crystal Ball data .......................................................... 158Selecting and reviewing your data............................................ 159Setting cell preferences............................................................ 162Setting run preferences ............................................................ 163Trials preferences ............................................................. 164Sampling preferences ....................................................... 166Speed preferences ............................................................. 168Macros preferences ........................................................... 169Options preferences .......................................................... 171Turbo preferences ............................................................. 172Running the simulation............................................................ 173How Crystal Ball uses Monte Carlo simulation ................ 173Simulation overview .......................................................... 174Running/Stopping/Continuing/ Re setting ........................ 176Closing forecasts ............................................................... 177Managing windows ........................................................... 177Responding to problems with correlated assumptions .... 178Saving and restoring a simulation............................................ 179Saving a Crystal Ball simulation ........................................ 179Restoring a Crystal Ball simulation ................................... 181Saving your models................................................................... 182Closing Crystal Ball .................................................................. 182Chapt er 4: Int erpret ing t he Result sUnderstanding the forecast chart............................................. 185Determining the certainty level ................................................ 187Focusing on the display range.................................................. 191Defining the display range using standard deviation ....... 192Defining the display range using fixed endpoints ............ 192Defining the display range using certainty grabbers ........ 194Changing the axis values to actual values ......................... 194Customizing the forecast chart ................................................. 194Changing the chart type ................................................... 195vi Cryst al Ball User Manual4Cont ent sChanging the distribution type ........................................ 197Changing groups .............................................................. 198Showing grid lines ............................................................ 199Using the mean line ......................................................... 200Formatting forecast charts ................................................ 200Interpreting the statistics ......................................................... 202Statistics view .................................................................... 202Percentiles view ................................................................. 203Understanding and using the overlay chart ............................ 204Creating the overlay chart ................................................ 205Customizing the overlay chart .......................................... 207Using distribution fitting with the overlay chart .............. 210Other overlay chart features ............................................. 212Understanding and using the trend chart ............................... 213Understanding the trend chart ........................................ 213Creating the trend chart ................................................... 214Customizing the trend chart ............................................. 215Changing the certainty bands .......................................... 216Changing the placement of the certainty bands .............. 217Changing the forecast axis ............................................... 218Changing the value axis ................................................... 219Changing the grid lines .................................................... 220Adding a title .................................................................... 220Understanding sensitivity and using the sensitivity chart........ 221Understanding the sensitivity chart ................................. 222Creating the sensitivity chart ............................................ 223How Crystal Ball calculates sensitivity .............................. 225Caveats .............................................................................. 226Customizing the sensitivity chart ...................................... 227Changing chart patterns and colors......................................... 231Pasting charts to Excel ............................................................. 232Creating reports ....................................................................... 232Report sections ................................................................. 234Selecting forecasts ............................................................. 235Selecting assumptions ....................................................... 236Percentiles ......................................................................... 236Disposition ........................................................................ 237Charts ................................................................................ 237Extracting data ......................................................................... 238Chapt er 5: Maximizing Your Use of Cryst al BallCrystal Ball tips ........................................................................ 243Simulation accuracy .......................................................... 243Simulation speed .............................................................. 247Cryst al Ball User Manual viiCont ent sMemory use ....................................................................... 250Correlated assumptions .................................................... 251Sensitivity analysis ............................................................. 251Excel tips................................................................................... 251Customizing report and data layouts ................................ 251Chapt er 6: Cryst al Ball ToolsOverview................................................................................... 255Batch Fit tool ............................................................................ 255Batch Fit example ............................................................. 256Batch Fit dialogs ............................................................... 260Correlation Matrix tool ............................................................ 264Correlations ....................................................................... 264Correlation matrix ............................................................ 264Correlation Matrix example ............................................. 265Correlation Matrix dialogs ................................................ 268Tornado Chart tool .................................................................. 272Tornado chart .................................................................... 273Spider chart........................................................................ 274Tornado Chart example ................................................... 275Caveats .............................................................................. 277Tornado Chart dialogs ...................................................... 278Bootstrap tool ........................................................................... 283Bootstrap example ............................................................ 285Bootstrap dialogs .............................................................. 290Decision Table tool ................................................................... 293Decision Table example .................................................... 294Decision Table dialogs ...................................................... 297Scenario Analysis tool ............................................................... 300Scenario Analysis example ................................................ 300Scenario Analysis dialogs .................................................. 304Two-dimensional Simulation tool ............................................ 306Two-dimensional Simulation example ............................. 307Second-order assumptions ................................................ 312Two-dimensional Simulation dialogs ................................ 314Appendix A: Error RecoveryCrystal Ball error messages ...................................................... 321Appendix B: Equat ions and Met hodsFormulas for probability distributions...................................... 335Beta distribution ............................................................... 335Binomial distribution ........................................................ 336Exponential distribution ................................................... 336viii Cryst al Ball User Manual4Cont ent sExtreme value distribution ............................................... 336Gamma distribution .......................................................... 337Geometric distribution ..................................................... 337Hypergeometric distribution ............................................ 338Logistic distribution .......................................................... 338Lognormal distribution .................................................... 339Negative binomial distribution ......................................... 339Normal distribution .......................................................... 340Pareto distribution ............................................................ 340Poisson distribution .......................................................... 340Triangular distribution ..................................................... 341Uniform distribution ........................................................ 341Weibull distribution .......................................................... 342Custom distribution .......................................................... 342Additional comments ........................................................ 342Distribution fitting methods ............................................. 343Precision control formulas ....................................................... 343Mean confidence interval ................................................. 344Standard deviation confidence interval ............................ 344Percentiles confidence interval ......................................... 344Formulas for other statistical terms ......................................... 344Random number generator ..................................................... 348Appendix C: Keyboard CommandsCommand key combinations.................................................... 351Cell, Run, and CBTools menu commands ....................... 351Forecast windows commands ............................................ 352Hot keys.................................................................................... 353Forecast chart hot keys ..................................................... 353Overlay/Comparison chart hot keys ................................. 354Trend chart hot keys ........................................................ 354Sensitivity chart hot keys .................................................. 355Appendix D: Index of CommandsCrystal Ball menus.................................................................... 359The Cell menu .................................................................. 359The Run menu .................................................................. 360The CBTools menu .......................................................... 361Forecast menus......................................................................... 362Edit ................................................................................... 362Preferences ....................................................................... 363View ................................................................................... 363Run ................................................................................... 364Help .................................................................................. 364Cryst al Ball User Manual ixCont ent sOverlay menus .......................................................................... 365Edit .................................................................................... 365Preferences ........................................................................ 365View ................................................................................... 365Run .................................................................................... 366Help .................................................................................. 366Trend menus ............................................................................ 367Edit .................................................................................... 367Preferences ........................................................................ 367View ................................................................................... 368Run .................................................................................... 368Help .................................................................................. 368Sensitivity menus ...................................................................... 369Edit .................................................................................... 369Preferences ........................................................................ 369View ................................................................................... 369Run .................................................................................... 370Help .................................................................................. 370Appendix E: Def ault Names and Dist ribut ion Paramet ersNaming defaults ....................................................................... 373Distribution parameter defaults ............................................... 373Beta ................................................................................... 373Binomial ............................................................................ 374Custom .............................................................................. 374Exponential ....................................................................... 374Extreme value ................................................................... 374Gamma .............................................................................. 374Geometric .......................................................................... 375Hypergeometric ................................................................ 375Logistic .............................................................................. 375Lognormal ......................................................................... 376Negative binomial ............................................................. 376Normal .............................................................................. 376Pareto ................................................................................ 377Poisson .............................................................................. 377Triangular ......................................................................... 377Uniform ............................................................................. 377Weibull .............................................................................. 378Bibliography ......................................................................... 379Glossary................................................................................. 387x Cryst al Ball User Manual4Cont ent sIndex....................................................................................... 397Cryst al Ball User Manual 111Welcome t o Cryst al Ball 2000.2Welcome to Crystal Ball 2000.2!Crystal Ball is a user-friendly, graphically oriented forecasting and risk analysis program that takes the uncertainty out of decision-making.Through the power of simulation, Crystal Ball becomes an effective tool in the hands of the decision-maker. You can answer questions such as, Will we stay under budget if we build this facility? or, What are the chances this project will finish on time? or, How likely are we to achieve this level of profitability? With Crystal Ball, you will become a more confident, efficient, and accurate decision-maker.Crystal Ball is easy to learn and easy to use. Unlike other forecasting and risk analysis programs, you do not have to learn unfamiliar formats or special modeling languages. To get started, all you have to do is create a spreadsheet. From there, this manual guides you step by step, explaining Crystal Ball terms, procedures, and results.And you do get results from Crystal Ball. Through a technique known as Monte Carlo simulation, Crystal Ball forecasts the entire range of results possible for a given situation. It also shows you confidence levels, so you will know the likelihood of any specific event taking place.Who should use t his programCrystal Ball is for the decision-maker, from the businessperson analyzing the potential for new markets to the scientist evaluating experiments and hypotheses. Crystal Ball is easy to learn and easy to use, and has been developed with a wide range of spreadsheet uses and users in mind.You dont need highly advanced statistical or computer knowledge to use Crystal Ball to its full potential. All you need is a basic working knowledge of your personal computer and the ability to create a spreadsheet model.Int roduct ion Welcome to Crystal Ball 2000.212 Cryst al Ball User ManualIWhat you will needTo run Crystal Ball, you will need the following: Microsoft Excel 95 (or later) Windows 95, Windows 98, Windows 2000, or Windows NT 4.0 Personal computer with Pentium microprocessor and at least 16 MB RAM Hard disk drive with at least 16 MB free 2X CD-ROM drive or faster VGA or SVGA graphics card or compatible video graphics adapter and monitorRecommended system r equir ements Pentium II, 200 MHz or faster 24 MB RAM or moreHow t his manual is organizedThis manual includes the following: Chapter 1 - Getting Star ted With Cr ystal BallThis chapter contains two tutorials designed to give you a quick overview of Crystal Balls features and show you how to use them. Read this chapter if you need a basic understanding of Cr ystal Ball. Chapter 2 - Under standing the Ter minology This chapter contains a thorough description of risk analysis, the seventeen probability distributions, and other statistical terms used in Crystal Ball. Read this chapter carefully if your statistical knowledge is limited or if you need a review. Chapter 3 - Setting Up and Running a Simulation This chapter provides step-by-step instructions for setting up and running a simulation in Crystal Ball. Chapter 4 - I nter pr eting the Results This chapter explains how to use Crystal Balls powerful features to interpret the results of a simulation. Chapter 5 - Maximizing Your Use of Cr ystal Ball This chapter describes different aspects that enhance the performance of the programs features.Cryst al Ball User Manual 131 Chapter 6 - Cr ystal Ball ToolsThis chapter describes tools that extend the functionality of Crystal Ball, such as the Tornado Chart and Decision Table tools. Appendices A - Er ror RecoveryA list of the most important Crystal Ball er ror messages with directions for er ror recovery. B- Equations and MethodsA list of the mathematical formulas used in calculating the distributions and the descriptive statistics. It also describes the type of random number generator used in Crystal Ball. This appendix is designed for the statistically sophisticated user. C- Keyboard CommandsA list of the commands you can execute directly from the keyboard. D- Index of CommandsA brief description of Crystal Balls pull-down menus. E- Default Names and Distribution ParametersA brief description of Crystal Balls default values. Bibliogr aphyA list of related publications, including statistics textbooks. Glossar yA compilation of terms specific to Crystal Ball and other statistical terms used in this manual. I ndexAn alphabetical list of subjects and cor responding page numbers.What s new in Cryst al Ball 2000.2If you are already familiar with Crystal Ball, read this section for an overview of Crystal Ball 2000.2s new features.Int roduct ion Whats new in Crystal Ball 2000.214 Cryst al Ball User ManualIChart modif icat ionsThere are changes to the following charts:Forecast chartThe Forecast chart now identifies the number of trials displayed, not the number of outliers excluded from the display.Sensit ivit y chartYou can now view the contribution to variance in positive and negative directions (two-way contribution). New buttons let you select which assumptions and forecasts to view. The chart also has menu options: Edit, Preferences, View, Run, and Help.Trend chartThe Trend chart now starts off blank when you open it after a simulation. New buttons let you select which forecasts to view. The chart also has menu options: Edit, Preferences, View, Run, and Help.Const ant dist ribut ionIf you have cell references defining a continuous distribution and all the referenced values are the same, you no longer get an er ror message when running a simulation. (You do see the er ror message when viewing the distribution.) Excel chart sYou can now generate Excel charts in your reports. You can also create Excel charts from any Crystal Ball charts (forecast, overlay, trend, and sensitivity) by selecting Edit > Paste To Excel from the chart windows menu.Excel charts let you manipulate the appearance of the chart using native Excel functionality. For example, you can change the chart size, axis labels, text color, and font.Cryst al Ball User Manual 151Forecast f ilt eringThis option lets you remove specific values from a single forecast or from all forecasts in a simulation. You can filter out the values that fall inside a specified range or those that fall outside the range.CB Tools updat esThe CB Tools menu now has three sections: OptQuest and CB Predictor (if you have installed the Professional edition) The model setup tools: Batch Fit, Cor relation Matrix, and Tornado Chart The analysis tools: Bootstrap, Decision Analysis, Scenario Analysis, and Two-dimensional SimulationThese new divisions better emphasize the different uses of the specific tools.You can now compute the cor relations automatically between multiple series of data in the Batch Fit tool.Locked worksheet sYou no longer receive an er ror message if there are no Crystal Ball assumptions or forecasts on locked worksheets in an open workbook.Report locat ionThis option lets you create a Crystal Ball report in a new worksheet of an existing workbook or in a new workbook as before.Preserving cell values upon calculat ion errorIf a calculation er ror occurs during a simulation, so that you can find the er ror, Crystal Ball doesnt restore the cell values.Int roduct ion Additional resources16 Cryst al Ball User ManualISample size limit increasedThe limit on the sample size for Latin hypercube sampling and cor relation calculation has been increased to 30,000.St at ist ics Pref erences movedThe Statistics Preferences are no longer available on the forecast chart. The Base Statistics On option is now in the Display Range preferences. The Reverse Percentiles option is now in Run Preferences. Additionally, the Center On Median Or Mean option with certainty bands is now always set to Median.Windows 2000 compat ibilit yThis version of Crystal Ball is fully functional in Windows 2000.Addit ional resourcesDecisioneering, Inc. offers these additional resources to increase the effectiveness with which you can use our product.Technical supportDecisioneering, Inc. offers free technical support for 90 days. If you have a technical support question or would like to comment on Crystal Ball, there are a number of ways to reach technical support described in the README file in your Crystal Ball installation folder.Consult ing ref erral serviceDecisioneering, Inc. provides refer rals to individuals and companies alike. The primary focus of this service is to provide a clearinghouse for consultants in specific industries who can provide specialized services to the Crystal Ball user community.If you wish to learn more about this refer ral service, call 800-289-2550 Monday through Friday, between 8:00 A.M. and 5:00 P.M. Mountain Standard Time or see our Web site at:www.decisioneering.com.Cryst al Ball User Manual 171Convent ions used in t his manualThis manual uses the following conventions:Text separated by > symbols means that you select menu options in the sequence shown, starting from the left. The following example means that you select the Exit option from the File menu:1. Select File > Exit.Steps with attached icons mean that you can click on the icon instead of manually selecting the menu options in the text. For example:2. Select Cell > Define Assumption. Notes provide additional information, expanding on the text. There are four categories of notes:Crystal Ball Note: Notes that provide additional directions or information about using Crystal Ball.Excel Note: Notes that provide additional information about using the program with Microsoft Excel.OptQuest Note: Notes that provide additional directions or information about using OptQuest.Statistical Note: Notes that provide additional information about statistics.Words in angle brackets represent keys on the keyboard, such as < Ctr l> or < Retur n> . Press the key; don t type the letters, words, or brackets.Sometimes you have to press two or more keys simultaneously. For example, < Ctr l> -c means that you hold down the < Ctr l> key and type c. Capitalization is important; < Ctr l> -c and < Ctr l> -C are two different key sequences.A key sequence without hyphens means you type the sequence in the order shown but not simultaneously. For example, < Ctr l> -q N means that you press the < Ctr l> key and type q Int roduct ion Conventions used in this manual18 Cryst al Ball User ManualIsimultaneously, and then type N. Screen capt ure not esAll the screen captures in this document were taken in Excel 2000 for Windows 2000 Professional, using a seed value of 999. Due to round-off differences between various system configurations, you might obtain slightly different calculated results than those shown in the examples.Chapt er 1Getting Started With Crystal BallI n this chapter What Crystal Ball does Futura Apartments spreadsheet tutorial How Crystal Ball uses Monte Carlo simulation Vision Research spreadsheet tutorial Defining assumptions Selecting and defining distributions Defining forecasts Running a simulation Interpreting the resultsIn this chapter are two tutorials, one short, one long, providing an overview of Crystal Balls features. The first tutorial, the Futura Apartments spreadsheet, simulates profit/loss projections from apartment rentals. This tutor ial is ready to run so you can quickly see how Crystal Ball works. If you wor k regularly with statistics and forecasting techniques, this might be all the introduction you need before running your own spreadsheets with Crystal Ball.The second tutorial, the Vision Research spreadsheet, gives you a chance to enter data and set up a complete simulation for a major corporate expenditure decision.Now, spend a few moments learning how Crystal Ball can help you make better decisions under conditions of uncertainty.Cryst al Ball User Manual 211What Cryst al Ball doesCrystal Ball extends the forecasting capability of your spr eadsheet model and provides the infor mation you need to become a more accur ate, efficient, and confident decision maker. As a spreadsheet user, you know that spreadsheets have two major limitations: You can change only one spreadsheet cell at a time. As a result, exploring the entire range of possible outcomes is next to impossible; you cannot realistically determine the amount of risk that is impacting your bottom line. What-if analysis always results in single-point estimates which do not indicate the likelihood of achieving any particular outcome. While single-point estimates might tell you what is possible, they do not tell you what is probable.Cr ystal Ball overcomes both of these limitations: You can describe a range of possible values for each uncertain cell in your spreadsheet. Everything you know about each assumption is expressed all at once. Using a process called Monte Car lo simulation, Crystal Ball displays results in a forecast chart that shows the entire range of possible outcomes and the likelihood of achieving each of them.St art ing t he f irst t ut orialThe best way to quickly under stand this process is to star t Cr ystal Ball and wor k on the fir st tutor ial: the Futur a Apar tments spreadsheet.1. Star t Cr ystal Ball.Crystal Ball Note: For directions on starting Crystal Ball, see Starting Crystal Ball manually on page 129.Glossary Term:spreadsheet modelAny spreadsheet t hat represent s an act ual or hypot het ical syst em or set of relat ionships.Glossary Term:assumpt ionAn est imat ed value or input t o a spreadsheet model.Glossary Term:Mont e Carlo simulat ionA syst em which uses random numbers t o measure t he ef f ect s of uncert aint y in a spreadsheet model.Chapt er 1 Getting Started With Crystal Ball22 Cryst al Ball User Manual 2. Open the Futur a Apar tments wor kbook fr om the Cr ystal Ball Examples folder . You can find this folder by selecting Star t > Pr ogr ams > Cr ystal Ball > Examples. The Futura Apartments worksheet appears, as in Figure 1.1.Figur e 1.1 Futur a Apar tments wor ksheetIn this example, you are a potential purchaser of the Futur a Apar tments complex. You have researched the situation and created the above wor ksheet to help you make a knowledgeable decision. Your work has led you to make the following assumptions: $500 per month is the going rent for the area. The number of units rented during any given month will be somewhere between 30 and 40. Operating costs will average around $15,000 per month for the entire complex, but might vary slightly from month to month.Based on these assumptions, you want to know how profitable the complex will be for various combinations of rented units and oper ating costs. This would be difficult to determine using a spreadsheet alone. As useful as spreadsheets are, you cannot reduce the last two assumptions to single values as required by the spreadsheet format. If you tr ied all the combinations, you would need to spend a great deal of time wor king through what-Cryst al Ball User Manual 231if scenarios, entering single values and recording the results. Even then, you would likely be left with a mountain of data instead of the over all profit and loss picture. With Crystal Ball, this kind of analysis is easy.Running t he simulat ionUse the following steps to run the simulation:1. Select Run > Run.Crystal Ball runs a simulation for the situation in the Futura Apartments workbook and displays a for ecast chart as it creates it.After the simulation has run for at least 500 tr ials, as displayed on your spreadsheet status bar:2. I n the for ecast window, select Run > Stop.Excel Note: If the forecast window disappears behind Excels window during a simulation, you can bring it back to the front by pressing -.The forecast window appears, as in Figure 1.2.Figur e 1.2 Futur a Apar tments pr ofit/loss for ecastGlossary Term:f orecast A st at ist ical summary of t he simulat ion result s in a spreadsheet model, displayed graphically or numerically.Glossary Term:t rial, also it erat ionA t hree-st ep process in which Cryst al Ball generat es random numbers f or assumpt ion cells, recalculat es t he spreadsheet models, and displays t he result s in a f orecast chart .Chapt er 1 Getting Started With Crystal Ball24 Cryst al Ball User Manual The forecast chart reveals the total range of profit and loss outcomes predicted for the Futur a Apar tments situation. Each bar on the char t represents the likelihood, or probability, of ear ning a given income. The cluster of columns near the center indicates that the most likely income level is between $250 and $4,750 per month. Crystal Ball also forecasts that the worst case is a $2,000 loss and the best case is near ly a $7,000 gain.Det ermining prof itNow you can use Cr ystal Ball to deter mine the statistical likelihood of making a profit and what is the most likely range.To have Crystal Ball determine a statistical likelihood:1. Pr ess < Tab> twice or select the left field in the for ecast window.2. Type 0 in the field.3. Pr ess < Enter > .The value in the Certainty field changes to reflect the probability of an income level ranging from $0 to positive infinitythe probability of making a profit. With this information, you are in a much better position to make a decision on whether to purchase the Futura Apartments. As shown in Figure 1.3, there is roughly a 90% chance that you will make a profit.Figur e 1.3 Chance of pr ofitGlossary Term:probabilit y(Classical Theory) The likelihood of an event occurring.Cryst al Ball User Manual 251Note that there is also a small chance of losing as much as $2000 per month.How Cryst al Ball uses Mont e Carlo simulat ionMost real-world problems involving elements of uncertainty are too complex to solve analytically. There are simply too many combinations of input values to calculate ever y possible result. Monte Carlo simulation is an efficient technique that requires only a r andom number table or a r andom number gener ator on a computer.Crystal Ball Note: For information on the random number generator that Crystal Ball uses, see Random number generator on page 351.This is an iterative process that continues until either: The simulation reaches a stopping criterion You stop the simulation manuallyThe final forecast chart reflects the combined uncertainty of the assumption cells on the models output. Keep in mind that Monte Carlo simulation can only approximate a real-wor ld situation. When you build and simulate your own spreadsheet models, you need to carefully examine the nature of the problem and continually refine the models until they approximate your situation as closely as possible.Crystal Ball also provides statistics that describe the forecast results. For more information on statistics and forecast results, see Chapter 2, Understanding the Ter minology, and Chapter 4, Inter preting the Results.Closing t he f irst t ut orialTo close the fir st tutor ial:1. Select Run > Reset.A dialog appears, confirming the reset.2. Click on OK.The simulation resets and the forecast window disappears.3. Close the Futur a Apar tments wor kbook.Glossary Term:random numberA mat hemat ically select ed value which is generat ed (by a f ormula or select ed f rom a t able) t o conf orm t o a probabilit y dist ribut ion.Glossary Term:random number generat orA met hod implement ed in a comput er program t hat is capable of producing a series of independent , random numbers.Generate random numbers for assumption cellsCalculate entirespreadsheetDisplay results in a forecast chartChapt er 1 Getting Started With Crystal Ball26 Cryst al Ball User Manual St art ing t he second t ut orialThe remainder of this chapter contains a tutor ial for the Vision Research spreadsheet. This tutorial provides a more realistic situation to let you examine Crystal Balls features in greater depth. However, if you feel comfortable running Cr ystal Ball now, you can tur n to Chapter 2, Under standing the Terminology, for some background on Crystal Ball terminology. Then you can read Chapter 3, Setting Up and Running a Simulation, to start analyzing your own spreadsheets.As you work through this tutorial, dont wor r y about making mistakes; recover y is as easy as backing up and repeating the steps. If you need additional help, see Er ror Recovery on page 321, or the Cr ystal Ball online help. The Vision Research spreadsheet models a business situation filled with uncer tainty. Vision Research has completed preliminar y development of a new dr ug, code-named Clear View, that cor rects near sightedness. This revolutionar y new product could be completely developed and tested in time for release next year if the FDA approves the product. Although the drug works well for some patients, the over all success rate is marginal, and Vision Research is uncer tain whether the FDA will approve the product.Vision Research can use Crystal Ball to help decide whether to scr ap the project or to proceed to develop and mar ket this potentially profitable new dr ug. The ClearView project is a multimillion-dollar risk. Crystal Ball is a powerful decision-support program designed to take the myster y out of decisions like this.To see how Crystal Ball works in a typical business decision:1. Open the Vision Resear ch wor kbook fr om the Cr ystal Ball Examples folder . You can find this folder by selecting (in Windows) Star t > Pr ogr ams > Cr ystal Ball > Examples. The Vision Research workbook for the ClearView project appears, as in Figure 1.4.Take a look at the Vision Research workbook. This spreadsheet models the problem that Vision Research is trying to solve.Cryst al Ball User Manual 271Figur e 1.4 Vision Resear chs Clear View pr oject wor kbookDef ining assumpt ionsIn Cr ystal Ball, you define an assumption for a value cell by choosing a pr obability distr ibution that describes the uncertainty of the data in the cell. To accomplish this, you select from the 17 distribution types in the Distribution Gallery (see Figure 1.5).How do you know which distribution type to choose? This por tion of the tutor ial will help you under stand how to select a distribution type based on the answer you are looking for. In the following examples, you select the assumption cells in the Vision Research spreadsheet and choose the probability distributions that most accurately describe the uncertainties of the ClearView project.This tutorial explains the reasons for choosing a particular distribution for each assumption. Detailed descriptions of how to select distributions are in Chapter 2, Under standing the Terminology, and Chapter 3, Setting Up and Running a Simulation.Glossary Term:probabilit y dist ribut ionA set of all possible event s and t heir associat ed probabilit ies.Chapt er 1 Getting Started With Crystal Ball28 Cryst al Ball User Manual Def ining t est ing cost s: t he unif orm dist ribut ionSo far, Vision Research has spent $10,000,000 developing ClearView and expects to spend an additional $3,000,000 to $5,000,000 to test it based on the cost of previous tests. For this variable, testing costs, Vision Research thinks that any value between $3,000,000 and $5,000,000 has an equal chance of being the actual cost of testing.Using Crystal Ball, Vision Research chooses the uniform distribution to describe the testing costs. The uniform distribution describes a situation where all values between the minimum and maximum values are equally likely to occur, so this distribution best describes the companys best guess for the cost of testing ClearView.Once you choose the cor rect distribution type, you are ready to define the assumption cell.To define the assumption cell for testing costs:1. Click on cell C5.2. Select Cell > Define Assumption.The Distribution Gallery dialog appears.Figur e 1.5 Distr ibution Galler y dialog3. Click on the Unifor m distr ibution.Cryst al Ball User Manual 2914. Click on OK.The Uniform Distribution dialog appears.Figur e 1.6 Unifor m distr ibution for C5Since cell C5 already has a name next to it on the wor ksheet, that name appear s in the Assumption Name field. Use this name, rather than typing a new one. Also, notice that Crystal Ball assigns default values to the distribution. For more infor mation on the method Crystal Ball uses to assign these default values to each distr ibution, see Appendix E, Default Names and Distribution Parameters.The uniform distr ibution has two par ameter s: minimum and maximum. Vision Research expects to spend a minimum of $3,000,000 and a maximum of $5,000,000 on testing. Use these values in place of the defaults to specify the par ameters of the unifor m distribution in Cr ystal Ball, as descr ibed in the following steps:5. Type 3 in the Min field (r emember that the number s on the wor ksheet r epr esent millions of dollar s).This represents $3,000,000, the minimum amount Vision Research estimates for testing costs.6. Pr ess < Tab> .Chapt er 1 Getting Started With Crystal Ball30 Cryst al Ball User Manual 7. Type 5 in the Max field.This represents $5,000,000, the maximum estimate for testing costs.8. Click on Enter .The distribution changes to reflect the values you entered, as shown in Figure 1.7.Figur e 1.7 Changed distr ibution valuesWith the values from Steps 5 and 7 entered cor rectly, your distribution looks like Figure 1.7. If not, repeat those steps. Later, when you run the simulation, Crystal Ball generates random values for cell C5 that are evenly spread between 3 and 5 million dollars.9. Click on OK to r etur n to the wor ksheet.The assumption cell is now green.Def ining market ing cost s: t he t riangular dist ribut ionVision Research plans to spend a sizeable amount marketing ClearView if the FDA approves it. They expect to hire a large sales force and kick off an extensive advertising campaign to educate the public about this exciting new product. Including sales commissions and advertising costs, Vision Research expects to spend between $12,000,000 and $18,000,000, most likely $16,000,000.Cryst al Ball User Manual 311Vision Research chooses the tr iangular distribution to describe marketing costs because the tr iangular distribution describes a situation where you can estimate the minimum, maximum, and most likely values to occur.To define the assumption cell for marketing costs:1. Click on cell C6.2. Select Cell > Define Assumption.The Distribution Gallery dialog appears.3. Click on the Tr iangular distr ibution.4. Click on OK.The Triangular Distribution dialog appears for cell C6.Figur e 1.8 Tr iangular distr ibution for cell C6Now specify the parameters for the triangular distribution. As you can see in Figure 1.8, the parameters for the triangular distribution are different from those specified earlier for the uniform distribution. The triangular distribution has three parameters: minimum, likeliest, and maximum. The following steps explain how to enter the parameters of the triangular distribution.Chapt er 1 Getting Started With Crystal Ball32 Cryst al Ball User Manual 5. Type 12 in the Min field.This represents $12,000,000, the minimum amount Vision Research estimates for marketing costs.6. Pr ess < Tab> to access the Likeliest field. I f it doesnt contain the value 16, type 16.This represents $16,000,000, the most likely amount for marketing costs.7. Pr ess < Tab> and type 18 in the Max field.This represents $18,000,000, the maximum estimate for marketing costs.8. Click on Enter .The distribution changes to reflect the values you entered.Figur e 1.9 Distr ibution changed for new valuesWhen you run the simulation, Crystal Ball generates random values that fall around 16, with fewer values near 12 and 18.9. Click on OK to r etur n to the wor ksheet.Cryst al Ball User Manual 331Def ining pat ient s cured: t he binomial dist ribut ionBefore the FDA will approve Clear View, Vision Research must conduct a controlled test on a sample of 100 patients for one year. Vision Research expects that the FDA will grant an approval if Clear View completely cor rects the near sightedness of 20 or more of these patients without any significant side-effects. In other words, 20% or more of the patients tested must show cor rected vision after taking ClearView for one year. Vision Research is ver y encouraged by their preliminar y testing, which shows a success rate of around 25%.For this variable, patients cured, Vision Research knows only that their preliminar y testing shows a cure r ate of 25%. Will Clear View meet the FDA standards? Using Cr ystal Ball, Vision Research chooses the binomial distr ibution to descr ibe the uncer tainties in this situation because the binomial distr ibution describes the random number of successes (25) in a fixed number of trials (100).To define the assumption cell for patients cured, use the following steps.1. Click on cell C10.2. Select Cell > Define Assumption.The Distribution Gallery appears.3. Click on the Binomial distr ibution.4. Click on OK.The Binomial Distribution dialog appears (notice that the default value for the probability parameter is 0.5 or 50%).Chapt er 1 Getting Started With Crystal Ball34 Cryst al Ball User Manual Figur e 1.10 Binomial Distr ibution dialogThe binomial distribution has two parameters: probability (Prob) and trials. You know that Vision Research experienced a 25% success rate during preliminary testing, so use the value 0.25 for the probability parameter to show the likelihood or success.Crystal Ball Note: You can express probabilities either as decimal fractions between 0 and 1, such as 0.03, or as whole numbers followed by the percent sign, such as 3%.You also know the FDA expects Vision Research to test 100 people, so use the value 100 for the trials parameter. The following steps explain how to enter these parameter s in the Binomial Distribution dialog.5. Type 0.25 in the Pr ob field.This represents the 25% likelihood, or probability, of successfully cor recting nearsightedness.6. I f the Tr ials field doesnt contain the value 100, pr ess < Tab> .7. Type 100 in the Tr ials field.This represents the 100 patients in the FDA test.Cryst al Ball User Manual 3518. Click on Enter .The distribution changes to reflect the values you entered.Figur e 1.11 Changed binomial distr ibutionWhen you run the simulation, Crystal Ball generates random integers between 0 and 100, simulating the number of patients that would be cured in the FDA test.9. Click on OK to r etur n to the wor ksheet.Growt h rat e: t he cust om dist ribut ionVision Research has determined that near sightedness afflicts nearly 40,000,000 people in the United States, and an additional 0% to 5% of these people will develop this condition during the year in which ClearView is tested.However, the mar keting depar tment has lear ned that a 25% chance exists that a competing product will be released on the mar ket soon. This product would decrease Clear Views potential mar ket by 5% to 15%.This var iable, growth r ate of near sightedness, cannot be described by any of the standard probability distributions. Since the uncertainties in this situation require a unique approach, Vision Research chooses Crystal Balls custom distribution to define the growth rate. For the most part, the custom distribution is used to describe situations that other distribution types cannot.Chapt er 1 Getting Started With Crystal Ball36 Cryst al Ball User Manual The method for specifying par ameter s in the custom distribution is quite unlike the other distribution types, so follow the directions carefully. If you make a mistake, click on Gallery to retur n to the distr ibution galler y, then star t again at step 3.Use the custom distr ibution to plot both the potential increase and decrease of ClearViews market.To define the assumption cell for the growth rate of nearsightedness:1. Click on cell C15.2. Select Cell > Define Assumption.The Distribution Gallery dialog appears.3. Click on the Custom distr ibution.4. Click on OK.The Custom Distribution dialog appears. Notice that in Figure 1.12 that the chart area remains empty until you enter the values for the distribution.Figur e 1.12 Custom Distr ibution dialogThe area remains empt y unt il you ent er values.Cryst al Ball User Manual 371To enter the fir st r ange of values:5. Type 0% in the Value field.This represents a 0% increase in the potential market.6. Pr ess < Tab> .7. Type 5% in the Value2 field.This represents a 5% increase in the potential market.8. Pr ess < Tab> .9. Type 75% in the Pr ob field.This represents the 75% chance that Vision Researchs competitor will not enter the market and reduce Vision Researchs share.10. Click on Enter .A uniform distribution for the range 0% to 5% appears.Figur e 1.13 Unifor m distr ibution r angeTo enter a second range of values:11. Type -15% in the Value field.This represents a 15% decrease in the potential market.12. Pr ess < Tab> .Unif orm dist ribut ion f or t he f irst range of values.Chapt er 1 Getting Started With Crystal Ball38 Cryst al Ball User Manual 13. Type -5% in the Value2 field.This represents a 5% decrease in the potential market.14. Pr ess < Tab> .15. Type 25% in the Pr obability field.This represents the 25% chance that Vision Researchs competitor will enter the market place and decrease Vision Researchs share by 5% to 15%.16. Click on Enter .A uniform distribution for the range -15% to -5% appears. Both ranges now appear in the Custom Distribution dialog.Figur e 1.14 Customized unifor m distr ibutionIn Chapter 2, Understanding the Ter minology, you lear n to use the data button, a special feature on the Custom Distr ibution dialog. You can use the Data button to pull number s from specified cell r anges on the worksheet r ather than typing them in the Custom Distribution dialog. When you r un the simulation, Crystal Ball gener ates r andom values within the r anges you specified.17. Click on OK to r etur n to the wor ksheet.Cryst al Ball displays bot h ranges.Cryst al Ball User Manual 391Def ining market penet rat ion: t he normal dist ribut ionThe mar keting department estimates that Vision Researchs eventual share of the total mar ket for the product will be nor mally distr ibuted around a mean value of 8% with a standar d deviation of 2%. Normally distributed means that Vision Research expects to see the familiar bell-shaped cur ve with about 68% of all possible values for market penetr ation falling between one standard deviation below the mean value and one standard deviation above the mean value, or between 6% and 10%.The low mean value of 8% is a conser vative estimate that takes into account the side effects of the dr ug that were noted dur ing preliminary testing. In addition, the marketing department estimates a minimum mar ket of 5%, given the interest shown in the product during preliminary testing.Vision Research chooses the normal distribution to describe the var iable mar ket penetr ation.To define the assumption cell for market penetration:1. Click on cell C19.2. Select Cell > Define Assumption.The Distribution Gallery dialog appears.3. Click on the Nor mal distr ibution.4. Click on OK.The Normal Distribution dialog appears.Glossary Term:st andard deviat ionThe square root of t he variance f or a dist ribut ion. A measurement of t he dispersion of values around t he mean.Glossary Term:mean or mean valueThe f amiliar arit hmet ic average of a set of numerical observat ions (t he sum of t he observat ions divided by t he number of observat ions).Chapt er 1 Getting Started With Crystal Ball40 Cryst al Ball User Manual Figur e 1.15 Nor mal distr ibution for cell C19Now specify the par ameter s for the nor mal distribution: the mean and the standard deviation.5. I f the Mean field doesnt contain 8.00%, type 8% in the Mean field.This represents an estimated average for market penetration of 8%.6. Pr ess < Tab> .7. Type 2% in the StdDev field.This represents an estimated 2% standard deviation from the mean.8. Click on Enter .The normal distribution scales to fit the chart area, so the shape of the distribution does not change. However, the percent range at the bottom of the chart does change.9. Pr ess < Tab> twice.10. Type 5% in the left tr uncation gr abber field.This represents 5%, the minimum market for the product.Cryst al Ball User Manual 41111. Click on Enter .The distribution changes to reflect the values you entered.Figur e 1.16 Changed distr ibution for the new valuesWhen you r un the simulation, Crystal Ball gener ates r andom values that follow a nor mal distr ibution around the mean value of 8%, and with no values generated below the 5% minimum limit.12. Click on OK to r etur n to the wor ksheet.Def ining f orecast sNow that you have defined the assumption cells in your model, you are ready to define the forecast cells. Forecast cells contain formulas that refer to one or more assumption cells.The president of Vision Research would like to know both the likelihood of achieving a profit on the product and the most likely profit, regardless of cost. These forecasts appear in the gross profit (cell C21) and net profit (cell C23) for the ClearView project.Chapt er 1 Getting Started With Crystal Ball42 Cryst al Ball User Manual Calculat ing gross prof itCr ystal Ball can generate more than one forecast dur ing a simulation. In this case, you can define both the gross profit and net profit formulas as forecast cells. Fir st, look at the contents of the cell for gross profit.1. Click on cell C21.The cell contents appear in the formula bar near the top of your worksheet. The contents are C16*C19*C20. Crystal Ball uses this formula to calculate gross profit by multiplying Persons With Nearsightedness After One Year (C16) by Market Penetration (C19) by Profit Per Customer (C20).Now that you under stand the gross profit for mula, you are ready to define the for ecast for mula cell for gross profit.To define the forecast cell for gross profit:2. Select Cell > Define For ecast.The Define Forecast dialog appears. You can enter a name for the forecast. Since the forecast cell has a name next to it on the worksheet, that name appears in the dialog by default.Figur e 1.17 Define For ecast dialog - Gr oss Pr ofit I f Appr ovedUse the forecast name that appears, rather than typing a new name.Since the spreadsheet model involves millions of dollars, indicate that in this dialog.3. Pr ess < Tab> .4. Type Millions in the Units field.5. Click on OK to r etur n to the wor ksheet.Glossary Term:f orecast f ormulaA f ormula t hat has been def ined as a f orecast cell.Cryst al Ball User Manual 431Calculat ing net prof itBefore defining the forecast cell formula for net profit, look at the contents of the cell for net profit:1. Click on cell C23.The contents appear in the formula bar above the worksheet. The contents are IF(C11, C21-C7, -C4-C5).The formula translates as follows:If the FDA approves the drug (C11 is true), then calculate net profit by subtracting total costs (C7) from gross profit (C21). However, if the FDA does not approve the drug, (C11 is false), then calculate net profit by deducting both development costs (C4) and testing costs (C5) incur red to date.To define the forecast cell for net profit:2. Select Cell > Define For ecast.The Define Forecast dialog appears, as in Figure 1.18.Figur e 1.18 Define For ecast dialog - Net Pr ofitAgain, use the forecast name that appears in the Forecast Name field and specify millions in the Units field.3. Pr ess < Tab> .4. Type Millions in the Units field.5. Click on OK to r etur n to the wor ksheet.You have defined assumptions and forecast cells for the Vision Research spreadsheet, and are now ready to run a simulation.Chapt er 1 Getting Started With Crystal Ball44 Cryst al Ball User Manual Running a simulat ionWhen you run a simulation in Crystal Ball, you have the freedom to stop and then continue the simulation at any time. The Run, Stop, and Continue commands appear on the Run menu as you need them. For example, when you are r unning a simulation, the Stop command appear s at the top of the menu. If you stop the simulation, the Continue command takes its place. Practice using these commands when you r un the simulation for the Clear View project. Before you begin the simulation, specify the number of tr ials and initial seed value so your simulation will look like the forecast char ts in this tutor ial. See Chapter 4, Interpreting the Results for more information on tr ials and seed values.To specify the number of trials and initial seed value:1. Select Run > Run Pr efer ences > Tr ials.The Run Preferences Trials dialog appears.2. I n the Maximum Number Of Tr ials field, type 500.3. Click on Sampling.4. Click the Use Same Sequence Of Random Number s option.5. I n the I nitial Seed Value field, type 999.6. Click on OK.In the next few sections, pr actice a few basic routines.Run, St op, and Cont inueTo practice using the Run, Stop, and Continue commands:1. Select Run > Run.The Net Profit forecast window appears, neatly stacked on top of the Gross Profit forecast window. As the simulation proceeds, the forecast charts reflect the changing values in the forecast cells.2. Select Run > Stop.Crystal Ball Note: You can also stop the simulation by pressing -u,o.Glossary Term:seed valueThe f irst number in a sequence of random numbers. A given seed value produces t he same sequence of random numbers every t ime you run a simulat ion.Cryst al Ball User Manual 4513. I n the fr ont for ecast window, select Run > Continue.Crystal Ball Note: Each forecast window has its own menu bar.The simulation continues.Crystal Ball Note: You can also continue the simulation by pressing -u,u.View t he f orecast chart sYou might not see two complete forecast char ts at the same time. However, there are several ways to bring individual forecast windows to the front of the window stack. The easiest way is to click on the forecast window if it is visible.1. Click on the Gr oss Pr ofit I f Appr oved for ecast window.The Gross Profit chart appears, as in Figure 1.19.Figur e 1.19 Gr oss Pr ofit I f Appr oved for ecast2. Select Run > For ecast Windows. 3. Click on Open All For ecasts to move the Net Pr ofit for ecast window to the fr ont again.While the simulation is r unning, a frequency distribution for each forecast appear s to reflect the changing values in the forecast cell. The frequency distribution appears as columns.Chapt er 1 Getting Started With Crystal Ball46 Cryst al Ball User Manual 4. Continue to r un the simulation until it stops at 500 tr ials.Figur e 1.20 Net Pr ofit for ecastA frequency distribution shows the number or frequency of values occur r ing in a given group interval. In Figure 1.20, the frequency distribution on the Net Profit forecast chart shows a frequency of 17 for the group inter val that contains the most values. That means 17 values occur red in the group interval.Chapter 3, Setting Up and Running a Simulation and Chapter 4, Interpreting the Results describe the forecast chart in more detail. For now, remember that the forecast char t gr aphs the forecast results and shows how the forecast values are distributed. As the simulation progresses, Crystal Ball continues to update the frequency distr ibution for each forecast cell, and the forecast results become more accurate.Int erpret ing t he result sNow that you have run the simulation, you are ready to interpret the forecast results in more depth. The president of Vision Research faces a difficult decision: should the company scrap the Clear View project or proceed to develop and mar ket this revolutionar y new dr ug? To examine this question in more detail, you need to look at the forecast chart in more detail.Cryst al Ball User Manual 471Excel Note: Crystal Ball windows are separate from Excel windows. If Crystal Balls windows disappear from your screen, they are usually simply behind the main Excel window. To bring them to the front, click on the Crystal Ball icon in the Windows taskbar or press -.Underst anding t he f orecast chartCrystal Ball forecasts the entire range of results for the Vision Research project. However, the forecast charts show only the display r ange that, by default, is set to exclude the most extreme values (outlier s). Chapter 4, Inter preting the Results describes how to change the display range to examine specific sections of the forecast in greater detail.In Figure 1.21, the display range includes the values from minus $14.7 to $34.4, as shown on the Net Profit forecast char t.The forecast chart also shows the certainty range for the forecast. By default, the cer tainty range includes all values from negative infinity to positive infinity.Cr ystal Ball compares the number of values in the cer tainty r ange with the number of values in the entire r ange to calculate the cer tainty level. The example above shows a cer tainty level of 100%, since the initial certainty range includes all possible values. Remember that the cer tainty level is an approximation, since the spreadsheet model can only approximate the elements of the real wor ld.In the upper left corner of the forecast chart, Cr ystal Ball shows the total number of tr ials that were run for this forecast. In the upper right cor ner, the number of tr ials shown in the char t appear s.Det ermining t he cert aint y levelNow the Vision Research president wants to know how certain Vision Research can be of achieving a profit and what are the chances of a loss. Chapt er 1 Getting Started With Crystal Ball48 Cryst al Ball User Manual To deter mine the cer tainty level of a specific value r ange:1. I n the Net Pr ofit for ecast char t, pr ess < Tab> twice.2. Type 0 in the r ange minimum field.3. Pr ess < Enter > .Crystal Ball moves the left certainty grabber to the break-even value of $0.0 and recalculates the certainty level.Figur e 1.21 Net Pr ofit for ecast$0 minimumAnalyzing the Net Profit forecast chart again, you can see that the value range between the certainty grabbers shows a certainty level of 79.8%. That means that Vision Research can be 79.8% certain of achieving a net profit. You can therefore calculate a 20.2% chance of suffering a net loss (100% minus 79.8%).Now the president of Vision Research would like to know the certainty of achieving a minimum profit of $2,000,000. With Crystal Ball, you can easily answer this question.4. Type 2 in the r ange minimum field.5. Pr ess < Enter > .A Figure 1.22 shows, Crystal Ball moves the left certainty grabber to $2.0 and recalculates the certainty level.Lef t cert aint y grabberRange minimum f ieldCert aint y levelCryst al Ball User Manual 491Figur e 1.22 Recalculated cer tainty levelVision Research can be 73.6% certain of achieving a minimum net profit of $2,000,000.Vision Research is very encouraged by the forecast result. The president now wants to know how certain Vision Research can be of achieving a minimum net profit of $4,000,000. If Cr ystal Ball shows that Vision Research can be at least two-thirds certain of a $4,000,000 net profit, the president is ready to go ahead with the Clear View project. Again, Cr ystal Ball can easily answer this question.6. Type 4 in the r ange minimum field.7. Pr ess < Enter > .Crystal Ball moves the left certainty grabber to $4.0 and recalculates the certainty level.Chapt er 1 Getting Started With Crystal Ball50 Cryst al Ball User Manual Figur e 1.23 Net Pr ofit for ecast$4.0 minimumThe Net Profit forecast chart in Figure 1.23 shows a certainty level of 66%. With a two-thirds certainty of a minimum net profit of $4,000,000, Vision Research decides to go ahead with the Clear View project and proceed to develop and mar ket this revolutionary new dr ug.The president of Vision Research also is interested in the most likely profit regardless of cost. You now can analyze the gross profit forecast chart as you did the net profit char t.SummaryIn this tutor ial, you explored only a few questions that Vision Research might ask as they analyze the results of the simulation. As you read through this manual, you will lear n to explore the forecast results in more depth. For example, you can customize the forecast char ts, create overlay char ts, create trend char ts, analyze the sensitivity of the model, inter pret the descriptive statistics, and pr int comprehensive reports for any simulation. Cr ystal Ball provides these features so that you can quantify the risk inherent in your assumptions.Cryst al Ball User Manual 511Crystal Ball keeps your assumption and forecast definitions (but not the forecast values) with the spreadsheet. When you save your spreadsheet, the definitions are saved with it. To learn about saving forecast results, see Saving and restoring a simulation on page 179.Closing Cryst al BallTo close Crystal Ball without exiting Excel, in Excel, select Run > Close Crystal Ball.A dialog appear s asking you to confir m the decision. Click on OK to close Crystal Ball and remove the Cell, Run, and CBTools menus and the Crystal Ball toolbar from Excel. The Vision Research spreadsheet remains open in Excel.Crystal Ball Note: Crystal Ball also closes automatically when you exit Excel.Chapt er 1 Getting Started With Crystal Ball52 Cryst al Ball User Manual Chapt er 2Understanding the TerminologyI n this chapter Model building and risk analysis Understanding probability distributions What is probability? Selecting a probability distribution Most commonly used distributions Other commonly used distributions Less commonly used distributions Understanding other statistical termsThis chapter explains probability and probability distributions. Your understanding of both probability and probability distributions will let you select the right probability distribution for your spreadsheet model. The fir st section descr ibes in detail the seventeen distr ibution types Crystal Ball uses and demonstrates using real-world examples. The last section of the chapter explains statistical terms used to describe forecast results.Cryst al Ball User Manual 551Model building and risk analysis overviewTo use Cr ystal Ball, you need to fir st build a model, and then Crystal Ball will help you perform a risk analysis. However, if youre a first-time user, you might not be familiar with or know what is meant by models or r isk analysis. Or, if you do know, you might want a better understanding of how Crystal Ball performs a r isk analysis.What is a model?Crystal Ball works with spreadsheet models, specifically Excel spreadsheet models. Your spreadsheet might already contain a model, depending on what type of infor mation you have in your spreadsheet and how you use it.Dat a vs. analysisIf you only use spreadsheets to hold datasales data, inventor y data, account data, etc.then you dont have a model. Even if you have for mulas that total or subtotal the data, you might not have a model that is useful for simulation.A model is a spreadsheet that has taken the leap from being a data organizer to an analysis tool. A model represents a process with combinations of data, var iables, for mulas, and functions. As you add cells that help you better understand and analyze your data, your data spreadsheet becomes a spreadsheet model.Tradit ional spreadsheet analysisSo now you have a model, or you have created your first model. For each value in your model, ask yourself, How certain am I of this value? Will it var y? Is this a best estimate or a known fact? You might notice that your model has some values in it that you are unsure of. Perhaps you dont have the actual data yet (this months sales figures) or the value varies unpredictably (individual item cost). This lack of knowledge about particular values or the knowledge that some values might always vary contr ibutes to the models uncertainty.Chapt er 2 Understanding the Terminology56 Cryst al Ball User Manual Tr aditional spreadsheet analysis tr ies to capture this uncertainty in one of three ways: Point estimates Range estimates What-if scenariosPoint est imat esPoint estimates are when you use what you think are the most likely values (technically refer red to as the mode) for the uncer tain variables. These estimates are the easiest, but can return very misleading results. For example, tr y crossing a river with an aver age depth of three feet. Or, if it takes you an aver age of 25 minutes to get to the air por t, leave 25 minutes before your flight takes off. You will miss your plane 50% of the time.Range est imat esRange estimates typically calculate three scenar ios: the best case, the worst case, and the most likely case. These types of estimates can show you the r ange of outcomes, but not the probability of any of these outcomes.What -if scenariosWhat-if scenar ios are usually based on the r ange estimates, and calculate as many scenar ios as you can think of. What is the worst case? What if sales are best case but expenses are the worst case? What if sales are aver age, but expenses are the best case? What if sales are average, expenses are aver age, but sales for the next month are flat? As you can see, this is extremely time consuming, and results in lots of data, but still doesnt give you the probability of achieving different outcomes.Cryst al Ball User Manual 571RiskUncertainty, like that descr ibed above, can often indicate risk, which is the possibility of loss, damage, or any other undesirable event and the severity associated with the event. For example, if sales for next month are above a cer tain amount (a desir able event), then order s will reduce the inventory. If the reduction in inventory is large enough, there will be a delay in shipping order s (an undesirable event). If a delay in shipping means losing orders (sever ity), then that possibility presents a risk.There are two points to keep in mind when analyzing r isk: Where is the risk? How significant is the risk?Almost any change, good or bad, poses some risk. Your own analysis will usually reveal numerous potential risk areas: overtime costs, inventory shortages, future sales, geological survey results, personnel fluctuations, unpredictable demand, changing labor costs, government approvals, potential merger s, pending legislation. Once you identify your risks, a model can help you quantify them. Quantifying r isk means deter mining the chances that the r isk will occur and the cost if it does, to help you decide whether a risk is worth taking. For example, if there is a 25% chance of running over schedule, costing you $100 out of your own pocket, that might be a risk you are willing to take. But if you have a 5% chance of running over schedule, knowing that there is a $10,000 penalty, you might be less willing to take that risk. Risk analysisYou can perform risk analysis in several ways, but one method involves building a spreadsheet model. A good spreadsheet model can be very helpful in identifying where your risk might be, since cells with formulas and cell references identify causal relationships among variables. One of the drawbacks of conventional spreadsheet models, however, is that you can only enter one value in a cell at a time. Why would you want to put more than one value in a cell, you ask? Remember those uncer tain values that you could represent either with point estimates, r ange estimates, or what-if scenarios? A spreadsheet will not let you put in a range or Chapt er 2 Understanding the Terminology58 Cryst al Ball User Manual multiple values; it allows only one value at a time. So, calculating the r ange requires you to replace the uncer tain value sever al times to see what effect the minimum, most likely, and maximum values have.Calculating more realistic what-if scenarios is the same, except it requires you to change your spreadsheet even more. And dont forget to keep tr ack of all the results somewhere, or you will have to repeat the scenario!This is where Crystal Ball comes in. Crystal Ball helps you define those uncertain var iables in a whole new way: by defining the cell with a r ange or a set of values. For example, you can define your business phone bill for future months as any value between $2500 and $3750, instead of using a single-point estimate of $3000. Cr ystal Ball then uses the defined range in a simulation.In addition, Crystal Ball keeps tr ack of the results of each scenario for you. Mont e Carlo simulat ionSimulation is any analytical method that is meant to imitate a real-life system, especially when other analyses are too mathematically complex or too difficult to reproduce. Spreadsheet risk analysis uses both a spreadsheet model and simulation to analyze the effect of varying inputs on outputs of the modeled system. One type of spreadsheet simulation is Monte Carlo simulation, which randomly generates values for uncer tain variables over and over to simulate a model. Hist oryMonte Carlo simulation was named for Monte Carlo, Monaco, where the pr imary attr actions are casinos containing games of chance. Games of chance such as roulette wheels, dice, and slot machines exhibit r andom behavior. The random behavior in games of chance is similar to how Monte Carlo simulation selects variable values at random to simulate a model. When you roll a die, you know that either a 1, 2, 3, 4, 5, or 6 will come up, but you dont know which for any particular tr ial. It is the same with the variables that have a known r ange of values but an uncer tain value for any par ticular time or event (e.g., interest rates, staffing needs, stock prices, inventory, phone calls per minute). Cryst al Ball User Manual 591For each variable, you define the possible values with a probability distribution. The type of distribution you select depends on the conditions sur rounding the var iable. For example, some common distribution types are:During a simulation, the value to use for each variable is selected r andomly from the defined possibilities.DiscussionA simulation calculates numerous scenarios of a model by repeatedly picking values from the probability distribution for the uncertain variables and using those values for the cell. Commonly, a Crystal Ball simulation calculates hundreds or thousands of scenar ios in just a few seconds. Since all those scenar ios produce associated results, Crystal Ball also keeps tr ack of the forecasts for each scenario. Forecasts are cells (usually with formulas of functions) that you define as important outputs of the model. These usually are cells such as totals, net profit, or gross expenses. For each forecast, Cr ystal Ball remember s the cell value for all the tr ials (scenar ios). Dur ing the simulation, you can watch a histogram of the results, which shows how they stabilize toward a smooth frequency distribution as the simulation progresses. After hundreds or thousands of tr ials, you can view sets of values, the statistics of the results (such as the mean forecast value), and the cer tainty of any par ticular value.Cert aint yThe forecast results show you not only the different result values for each forecast, but also the probability of any value. Crystal Ball normalizes these probabilities to calculate another important number : the certainty. The certainty is the percent chance that a par ticular forecast value will fall within a specified r ange. Chapt er 2 Understanding the Terminology60 Cryst al Ball User Manual For example, the chance of any forecast value falling between -Infinity and + Infinity is always 100%. However, the chance of that same forecast being at least zero (which you might want to calculate to make sure that you make a profit) might be only 45%. For any range you define, Crystal Ball calculates the resulting cer tainty. This way, not only do you know that your company has a chance to make a profit, but you can also quantify that chance by saying that the company has a 45% chance of making a profit on a venture (a venture you might, therefore, decide to skip). Benef it s of risk analysisFinding the certainty of achieving a particular result is often the goal of a model analysis. Risk analysis takes a model and sees what effect changing different values has on the bottom line. Risk analysis can: Help end analysis paralysis and contribute to better decision-making by quickly examining all possible scenarios Identify which variables most affect the forecast Expose the uncertainty in a model, leading to a better communication of riskUnderst anding probabilit y dist ribut ionsTo begin to under stand probability, consider this example: You want to look at the distr ibution of non-exempt wages within one department of a large company. First, you gather raw data, in this case the wages of each non-exempt employee in the department. Second, you organize the data into a meaningful for mat and plot the data as a frequency distr ibution on a char t. To create a frequency distribution, you divide the wages into group intervals and list these intervals on the charts horizontal axis. Then you list the number or frequency of employees in each inter val on the char ts ver tical axis. Now you can easily see the distr ibution of non-exempt wages within the depar tment.Cryst al Ball User Manual 611A glance at the char t illustr ated in Figure 2.1 reveals that most of the employees (approximately 60 out of a total of 180) earn from $7 to $9 per hour.Figur e 2.1 Raw data for pr obabilityYou can chart this data as a probability distr ibution. A probability distribution shows the number of employees in each inter val as a fr action of the total number of employees. To create a probability distribution, you divide the number of employees in each interval by the total number of employees and list the results on the charts vertical axis.The chart illustrated in Figure 2.2 shows you the number of employees in each wage group as a fraction of all employees; you can estimate the likelihood or probability that an employee drawn at random from the whole group earns a wage within a given interval. For example, assuming the same conditions exist at the time the sample was taken, the probability is 0.33 (a 1 in 3 chance) that an employee dr awn at r andom from the whole group earns between $8 and $8.50 an hour. Number of Employees605040302010Hourly Wage Ranges in Dollars 7.00 7.50 8.00 8.50 9.00Chapt er 2 Understanding the Terminology62 Cryst al Ball User Manual Figur e 2.2 Pr obability distr ibution of wagesCompare the probability distr ibution in the example above to the probability distributions in Crystal Ball as shown in Figure 2.3.Figur e 2.3 Distr ibution Galler y dialogThe probability distr ibution in the example in Figure 2.2 has a shape similar to many of the distributions in the Distribution Gallery. This process of plotting data as a frequency distribution and conver ting it to a probability distribution provides one Probabilit y0.33Hourly Wage Ranges in Dollars 7.00 7.50 8.00 8.50 9.00Cryst al Ball User Manual 631star ting point for selecting a Crystal Ball distribution. Select the distr ibutions in the gallery that appear similar to your probability distribution, then read about those distributions in this chapter to find the cor rect distr ibution.For information about the similarities between distributions, see Comparing the distributions on page 112. For a complete discussion of probability distributions, refer to the sources listed in the bibliogr aphy.Notice that the Distribution Gallery shows whether the probability distributions are discrete or continuous. Discrete probability distributions describe distinct values, usually integers, with no intermediate values and are shown as a series of vertical bars, such as in the binomial distribution in the example above. A discrete distribution, for example, might descr ibe the number of heads in four flips of a coin as 0, 1, 2, 3, or 4.Continuous probability distributions, such as the normal distr ibution, descr ibe values over a r ange or scale and are shown as so