This series of articles will give you an overview of how to manage spreadsheet risk. These articles are written by Myles Arnott from Excel Audit
- Part 1: An Introduction to managing spreadsheet risk
- Part 2: How companies can manage their spreadsheet risk
- Part 3: Excel’s auditing functions
- Part 4: Using external software packages to manage your spreadsheet risk
In the first two articles in this series we highlighted the risks that poorly managed spreadsheet solutions can introduce to a business and outlined the steps companies can take to manage this risk. This article works through the application of some of Excel’s built in auditing functions:
- Error checking (Background and stepping through each error)
- Trace Error
- Circular Reference
- Go To Special
Let’s have a look at an example spreadsheet that is riddled with issues.
The spreadsheet contains four tabs: a simple front page; an Example tab with the report that we wish to audit; a Resolved tab with the corrected report; and a Notes tab which details all of the issues contained within the spreadsheet (if you print the Resolved tab, all of the comments will also be printed for your reference).
If you are up for a challenge you could download the file and work through the report in the Example tab to see how many of the errors you can find yourself.
First off let’s identify the obvious issues
Circular reference
On opening the file you are presented with this warning message:
Click OK to continue opening the file. Here is how the report looks:
Excel helpfully gives you the location of the first circular reference (Q30) in the bottom left corner of the screen:
An alternative approach to locating circular references is to select Error Checking > Circular References on the Formulas tab of the Ribbon:
By clicking into the formula on cell Q30 you will see that the formula is =AVERAGE(M30:N30,P30:Q30). This average formula is including the cell Q30, hence the circular reference.
[Related: Understanding & Using Excel Circular References]
#REF error
The next obvious issue is that cells I13, J13, J33, S13, S18 & S33 contain the #REF error. The #REF error is a warning that the formula contains an invalid cell reference (this usually happens when the user deletes a cell/row/column/worksheet that is being referenced by a formula).
To trace the cell originating this error select any cell containing the error (I chose S33 as this would appear to be the main report total), and select Error Checking > Trace Error on the Formulas tab of the Ribbon:
This highlights that cell I13 is the source of the error:
Cell I13 contains the formula =3109+#REF!. To remove the error simply remove the +#REF! within the formula.
It is also however important to try to understand what cell was referenced by the formula originally. The best way to do this would be to talk to the user/previous user (if they are still there) and look back through archived versions of the report (if they exist).
Now that the obvious issues have been identified we are now going to employ some of Excel’s other auditing tools to see if there are any hidden errors.
[Related: Understanding & fixing Excel Formula Errors]
Excel’s error checking function
I’m sure that you will have noticed the small green triangles in the top left hand corner of some of the cells. This is Excel’s background error checking function warning you that these cells break one of the predetermined rules.
Firstly let’s have a look at the errors that are being checked for. To open the Error Checking options select File > Options> Formulas (2010) or Office button> Excel options>Formulas (2007).
Below is the default set up:
When reviewing a spreadsheet for errors it is always worth a quick check to ensure that the above is set up as you would like it to be. I always also tick the “Formulas referring to empty cells” rule.
Click OK to return to the spreadsheet.
The most systematic way to walk through all of the issues identified by the error checking function is to run Error Checking on the Formulas tab of the Ribbon:
This launches the Error checking dialogue box and allows you to review each error in turn:
I will leave you to run through the errors one by one to see what Excel picks up.
Please note that this is not a fool proof check as it is simply checking against the predefined rules. This function will not highlight cells that comply with the rules but contain other errors. It can also highlight cells as an error when they are not (eg P13, in this case click on “Ignore Error”). A very useful starting point nonetheless.
Reviewing the report structure
A crucial step to ensuring that a spreadsheet is error free is to understand its structure, and then to ensure that this structure is correct and consistent.
The simplest way to do this is to identify the different types of cells and their relative positions within the worksheet. For this simple example we are looking to identify:
- Input cells (Numbers)
- Input cells (Text)
- Formula cells
- Formula cells returning an error
To achieve this quickly and simply I have built a basic macro which is within the spreadsheet and can be run from the “RUN” button in the Example tab.
This colors each cell type as follows:
This very quickly identifies some structural issues in the spreadsheet:
So how does this work?
The macro above uses Excel’s Go To Special function which helps you to quickly select cells of different types.
To launch Go To Special, click on Find and Select> Go To Special on the Home tab of the Ribbon:
(Alternatively press F5 or Ctrl + G to launch the Go To dialogue box and then click on Special…)
For example, selecting Constants and leaving just Numbers ticked will highlight all numbers on the current worksheet:
It is worth playing with the options on Go To Special as there are some great functions that I sadly don’t have time to cover here (the precedents, Dependents and Row/Column differences functions are particularly useful).
[Related: More uses of Go To Special in Excel]
And Finally…
As valuable as these initial tests are there are still some issues in the spreadsheet that only a detailed investigation will highlight.
So I’ll leave you to grab a coffee and see if you can find them (they are covered in the Notes and in the Resolved tab).
In the final article of the series we will have a quick look at an example of spreadsheet auditing software.
Also, we are planning to write an article explaining other useful features of Go To Special dialog.
What about you?
Do you use Spreadsheet auditing functions? What is your experience with them? What are your favorite features? Please share using comments.
Thank you Myles
Many thanks to Myles for writing this series. Your experience in this area is invaluable. If you enjoy this series, drop a note of thanks to Myles thru comments. You can also reach him at Excel Audit or his linkedin profile.
20 Responses to “Simulating Dice throws – the correct way to do it in excel”
You have an interesting point, but the bell curve theory is nonsense. Certainly it is not what you would want, even if it were true.
Alpha Bravo - Although not a distribution curve in the strict sense, is does reflect the actual results of throwing two physical dice.
And reflects the following . .
There is 1 way of throwing a total of 2
There are 2 ways of throwing a total of 3
There are 3 ways of throwing a total of 4
There are 4 ways of throwing a total of 5
There are 5 ways of throwing a total of 6
There are 6 ways of throwing a total of 7
There are 5 ways of throwing a total of 8
There are 4 ways of throwing a total of 9
There are 3 ways of throwing a total of 10
There are 2 ways of throwing a total of 11
There is 1 way of throwing a total of 12
@alpha bravo ... welcome... 🙂
either your comment or your dice is loaded 😉
I am afraid the distribution shown in the right graph is what you get when you throw a pair of dice in real world. As Karl already explained, it is not random behavior you see when you try to combine 2 random events (individual dice throws), but more of order due to how things work.
@Karl, thanks 🙂
When simulating a coin toss, the ROUND function you used is appropriate. However, your die simulation formula should use INT instead of ROUND:
=INT(RAND()*6)+1
Otherwise, the rounding causes half of each number's predictions to be applied to the next higher number. Also, you'd get a count for 7, which isn't possible in a die.
To illustrate, I set up 1200 trials of each formula in a worksheet and counted the results. The image here shows the table and a histogram of results:
http://peltiertech.com/WordPress/wp-content/img200808/RandonDieTrials.png
@Jon: thanks for pointing this out. You are absolutely right. INT() is what I should I have used instead of ROUND() as it reduces the possibility of having either 1 or 6 by almost half that of having other numbers.
this is such a good thing to learn, helps me a lot in my future simulations.
Btw, the actual graphs I have shown were plotted based on randbetween() and not from rand()*6, so they still hold good.
Updating the post to include your comments as it helps everyone to know this.
By the way, the distribution is not a Gaussian distribution, as Karl points out. However, when you add the simulations of many dice together (i.e., ten throws), the overall results will approximate a Gaussian distribution. If my feeble memory serves me, this is the Central Limit Theorem.
@Jon, that is right, you have to nearly throw infinite number of dice and add their face counts to get a perfect bell curve or Gaussian distribution, but as the central limit theorem suggests, our curve should roughly look like a bell curve... 🙂
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I'm afraid to say that this is a badly stated and ambiguous post, which is likely to cause errors and misunderstanding.
Aside from the initial use of round() instead of int(),.. (you've since corrected), you made several crucial mistakes by not accurately and unambiguously stating the details.
Firstly, you said:
"this little function generates a random fraction between 0 and 1"
Correctly stated this should be:
"this little function generates a random fraction F where 0 <= F < 1".
Secondly, I guess because you were a little fuzzy about the exact range of values returned by rand(), you have then been just as ambiguous in stating:
"I usually write int(rand()*12)+1 if I need a random number between 0 to 12".
(that implies 13 integers, not 12)
Your formula, does not return 13 integers between 0 to 12.
It returns 12 integers between 1 and 12 (inclusive).
-- As rand() returns a random fraction F where 0 <= F < 1, you can obviously can only get integers between 1 and 12 (inclusive) from your formula as stated above, but clearly not zero.
If you had said either:
"I usually write int(rand()*12) if I need a random number between 0 to 11 (inclusive)",
or:
"I usually write int(rand()*12)+1 if I need a random number between 1 to 12 (inclusive)"
then you would have been correct.
Unfortunately, you FAIL! -- repeat 5th grade please!
Your Fifth Grade Maths Teacher
Idk if I'm on the right forum for this or how soon one can reply, but I'm working on a test using Excel and I have a table set up to get all my answers from BUT I need to generate 10,000 answers from this one table. Every time, I try to do this I get 10,000 duplicate answers. I know there has to be some simple command I have left out or not used at all, any help would be extremely helpful! (And I already have the dice figured out lol)
Roll 4Dice with 20Sides (4D20) if the total < 20 add the sum of a rerolled 2D20. What is the average total over 10,000 turns? (Short and sweet)
Like I said when I try to simulate 10,000turns I just get "67" 10,000times -_- help please! 😀
@Justin
This is a good example to use for basic simulation
have a look at the file I have posted at:
https://rapidshare.com/files/1257689536/4_Dice.xlsx
It uses a variable size dice which you set
Has 4 Dice
Throws them 10,000 times
If Total per roll < 20 uses the sum of 2 extra dice Adds up the scores Averages the results You can read more about how it was constructed by reading this post: http://chandoo.org/wp/2010/05/06/data-tables-monte-carlo-simulations-in-excel-a-comprehensive-guide/
Oh derp, i fell for this trap too, thinking i was makeing a good dice roll simulation.. instead of just got an average of everything 😛
Noteably This dice trow simulate page is kinda important, as most roleplay dice games were hard.. i mean, a crit failure or crit hit (rolling double 1's or double 6's) in a a game for example dungeons and dragons, if you dont do the roll each induvidual dice, then theres a higher chance of scoreing a crit hit or a crit failure on attacking..
I've been working on this for awhile. So here's a few issues I've come across and solved.
#1. round() does work, but you add 0.5 as the constant, not 1.
trunc() and int() give you the same distributions as round() when you use the constant 1, so among the three functions they are all equally fair as long as you remember what you're doing when you use one rather than the other. I've proven it with a rough mathematical proof -- I say rough only because I'm not a proper mathematician.
In short, depending on the function (s is the number of sides, and R stands in for RAND() ):
round(f), where f = sR + 0.5
trunc(f), where f = sR + 1
int(f), where f = sR + 1
will all give you the same distribution, meaning that between the three functions they are fair and none favors something more than the others. However...
#2. None of the above gets you around the uneven distribution of possible outcomes of primes not found in the factorization of the base being used (base-10, since we're using decimal; and the prime factorization of 10 is 2 and 5).
With a 10-sided die, where your equation would be
=ROUND(6*RAND()+0.5)
Your distribution of possible values is even across all ten possibilities.
However, if you use the most basic die, a 6-sided die, the distributions favor some rolls over others. Let's assume your random number can only generate down to the thousandths (0.000 ? R ? 0.999). The distribution of possible outcomes of your function are:
1: 167
2: 167
3: 166
4: 167
5: 167
6: 166
So 4 and 6 are always under-represented in the distribution by 1 less than their compatriots. This is true no matter how many decimals you allow, though the distribution gets closer and closer to equal the further towards infinite decimal places you go.
This carries over to all die whose numbers of sides do not factor down to a prime factorization of some exponential values of 2 and 5.
So, then, how can we fix this one, tiny issue in a practical manner that doesn't make our heads hurt or put unnecessary strain on the computer?
Real quick addendum to the above:
Obviously when I put the equation after the example of the 10-sided die, I meant to put a 10*RAND() instead of a 6*RAND(). Oops!
Also, where I have 0.000 ? R ? 0.999, the ?'s are supposed to be less-than-or-equal-to signs but the comments didn't like that. Oh well.
How do you keep adding up the total? I would like to have a cell which keeps adding up the total sum of the two dices, even after a new number is generated in the cells when you refresh or generate new numbers.
So, how do you simulate rolling 12 dice? Do you write int(rand()*6) 12 times?
Is there a simpler way of simulating n dice in Excel?
I've run this code in VBA
Sub generate()
Application.ScreenUpdating = False
Application.Calculation = False
Dim app, i As Long
Set app = Application.WorksheetFunction
For i = 3 To 10002
Cells(i, 3).Value = i - 2
Cells(i, 4).Value = app.RandBetween(2, 12)
Cells(i, 5).Value = app.RandBetween(1, 6) + app.RandBetween(1, 6)
Next
Application.ScreenUpdating = True
Application.Calculation = True
End Sub
But I get the same distribution for both columns 4 and 5
Why ?
@Mohammed
I would expect to get the same distribution as you have effectively used the same function