Using Arrays To Update Table Columns
We are creating a lot of reports everyday and these reports contain a lot of data which is presented in various styles as per the requirements. The data that allows us to create the reports is usually referred as raw data and in most of the cases is stored in hidden sheets.
I am sure you all are aware of a feature called as Excel Tables OR Structured References in Excel. Excel Tables is (in my opinion) the best way to store your raw data and put Formulas in the columns where necessary, this way you eliminate the need of a Cell Based Reference formula (example =SUM(B4:B50) and replace them with =sum(YourTable[YourTableColumnName]).
Another good feature of the Excel Tables is you just need to put the formula in 1 cell and it is replicated for that column by Excel.
Sometimes these formulas take a lot of time to calculate when we have really huge data points. In this scenarios it is better to have hard-coded values instead of the formulas to gain on speed.
In this post we will learn about how we can make use of Array’s to quickly populate the excel columns with the desired results before publishing our reports and other documents.
Here is a demo of what I mean:
Below is the code that allows us to add a new column to our data table and then taking input from the Date Time column provides us with the Week Of column.
Sub UpdateWeek()
Dim myarray As Variant
Dim theRange As Range, startCellRow As Long
Dim tempStr As String
Dim myNewCol As ListColumn
‘If our column already exists then delete it
On Error Resume Next
Worksheets(“Data”).ListObjects(“cs”).ListColumns(“WeekOf”).Delete
‘adding our new column
Set myNewCol = Worksheets(“Data”).ListObjects(“cs”).ListColumns.Add
myNewCol.Name = “WeekOf”
‘Selecting the first cell of the column that contains our dates
Worksheets(“Data”).ListObjects(“cs”).ListColumns(“Date Time”).Range.Cells(2).Select
‘building a temporary Range address, this will be used to upload the entire range into the array
tempStr = ActiveCell.Address
startCellRow = ActiveCell.Row
tempStr = tempStr & “:$” & Mid(Sheets(“Data”).ListObjects(“cs”).ListColumns(“Date Time”).Range.Cells(2).Address, 2, 1) & “$”
tempStr = tempStr & LastRowInOneColumn(Mid(Sheets(“Data”).ListObjects(“cs”).ListColumns(“Date Time”).Range.Cells(2).Address, 2, 1))
‘loading the range into the array
myarray = Range(tempStr).Value
‘Looping through the array and converting each element to the relevant Week format
For i = LBound(myarray) To UBound(myarray)
myarray(i, 1) = Format(myarray(i, 1) – Weekday(myarray(i, 1), vbMonday) + 1, “ddd dd-mmm”)
Next
‘Setting the range address for our output column
Set theRange = Range(Cells(startCellRow, Worksheets(“Data”).ListObjects(“cs”).ListColumns(“WeekOf”).Range.Column), Cells(UBound(myarray) + (startCellRow – 1), Worksheets(“Data”).ListObjects(“cs”).ListColumns(“WeekOf”).Range.Column))
‘storing the values from our array to the WeekOf Column
theRange.Value = myarray
End Sub
Let’s Understand the code
We first delete the column if it is already existing to make sure we always get the new values as output. This is done by the below line of code.
Worksheets("Data").ListObjects("cs").ListColumns("WeekOf").Delete
Once we have deleted the column, we add it again as a blank column and change the name to “Week Of”.
Set myNewCol = Worksheets("Data").ListObjects("cs").ListColumns.Add
myNewCol.Name = "WeekOf"
After this we need to select the first cell of the column that contains the Date Time.
Worksheets("Data").ListObjects("cs").ListColumns("Date Time").Range.Cells(2).Select
Once we have selected the first cell of you Date Time column we then make use of the LastRowInOneColumn function to get the last row and create a range address. We use this range address to assign all the values contained in the Date Time column to an array.
tempStr = ActiveCell.Address
startCellRow = ActiveCell.Row
tempStr = tempStr & ":$" & Mid(Sheets("Data").ListObjects("cs").ListColumns("Date Time").Range.Cells(2).Address, 2, 1) & "$"
tempStr = tempStr & LastRowInOneColumn(Mid(Sheets(“Data”).ListObjects(“cs”).ListColumns(“Date Time”).Range.Cells(2).Address, 2, 1))
‘loading the range into the array
myarray = Range(tempStr).Value
Once we have loaded all the Date Time values into an array, we do a simple For loop to change the value in the array to the relevant Week Of
For i = LBound(myarray) To UBound(myarray)
myarray(i, 1) = Format(myarray(i, 1) - Weekday(myarray(i, 1), vbMonday) + 1, "ddd dd-mmm")
Next
We perform this operation on the same element and store the modified value in itself.
Once we have all these done, we need to define the Output range, that is where we need to the Week Of values to be stored. This is done by using the Range and Cell functions.
Set theRange = Range(Cells(startCellRow, Worksheets("Data").ListObjects("cs").ListColumns("WeekOf").Range.Column), Cells(UBound(myarray) + (startCellRow - 1), Worksheets("Data").ListObjects("cs").ListColumns("WeekOf").Range.Column))
'storing the values from our array to the WeekOf Column
theRange.Value = myarray
And lastly we assign all the values stored in the array to the new range address we have create above.
Download Demo File
Click here to download the demo file & use it to understand this technique.
What about you? Do you use them often? Please share your experiences, techniques & ideas using comments.
If you are new to VBA, Excel macros, go thru these links to learn more.
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About Vijay
Vijay (many of you know him from VBA Classes), joined chandoo.org full-time this February. He will be writing more often on using VBA, data analysis on our blog. Also, Vijay will be helping us with consulting & training programs. You can email Vijay at sharma.vijay1 @ gmail.com. If you like this post, say thanks to Vijay.
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