Recently, we discussed about the case of unwieldy data and how we lookup what we want using formulas like SUMIFS. Today, let us learn few more ways to solve the same problem.
First, a re-cap of the problem:
Here is a data-set:
The problem – build a lookup formula
And the problem. Oh, simple. Write a lookup formula to find how many customer walk-ins we have on any given day.
In the previous article, we discussed how to use SUMIFS to solve this problem. There were several amazing & awesome solutions shared by our readers in the comments section too.
Suitable structure spawns simple solutions
Poorly structured is the 2nd biggest problem of analysts. The first one is not enough coffee. That is why there is a dictum in the data analytics world.
Structure is everything
So, we can easily solve our lookup problem, if our data were to magically re-arranged in 2 column fashion – Data & Value.
This transformation can be done in 2 ways:
Option #1: Transforming Data – Using Formulas
We can use data fetching formulas like OFFSET or INDEX to re-arrange data in 2 columns.
Assuming,
- Our 2D data is in a named range data,
- There are running numbers starting with 0 in the cell J5
We can use below formula to fetch first column:
=IFERROR(INDEX(data,2*(INT(J5/7))+1,MOD(J5,7)+1),"")
for the second column, below formula works:
=IFERROR(INDEX(data,2*(INT(J5/7)+1),MOD(J5,7)+1),"")
How does this formula work?
I will explain the formula for first column. Deciphering 2nd column formula is your homework.
Here is the formula again: =IFERROR(INDEX(data,2*(INT(J5/7))+1,MOD(J5,7)+1),"")
Before understanding the formula, let’s take a minute to examine the structure of our raw data.
- Odd rows contain dates
- Even rows contain values
- There are 7 columns in total
- So to get the first date, we need to go to row 1 (first odd number), column 1
- To get the first value, we need to go to row 2 (first even number), column 1
- But to get 8th date, we need to go to row 3(2nd odd number), column 1
- So on
Let’s go from inside out.
2*(INT(J5/7))+1portion: This gives row number (ie odd number). J5 refers to running number and its value is 0. So we get 2*(INT(0/7))+1 = 1- This will be 3 when J5 becomes J12 (ie 8th date)
MOD(J5,7)+1portion: This gives column number. It will result in values 1 thru 7 in a cyclical fashion. Thanks to MOD.INDEX(data, ..., ...)portion: Now that we have both row & column numbers, INDEX formula kicks in and gets the corresponding date.IFERROR(INDEX(...),"")portion: This is to help in case we ran out of all dates & values in our INDEX formula. Read about IFERROR here.
Once you have the formulas for first date & value, simply drag them to get rest of the values.
Option #2: Transforming data – Using VBA
VBA Macros are perfect for scenarios like this. Usually transformation is something you need to do every-time you import data from external systems. So simply write a macro that can do this automatically.
Assuming our data is in the range data and the first cell of our extraction range is startHere, you can use below macro:
Sub rearrangeData()
'takes the values in DATA named range and rearranges them
'from the named cell startHere
Dim cell As Range, i As Long, j As Long, evenRow As Boolean, firstRow As Long
i = 0
j = 0
firstRow = Range("data").Cells(1).Row
For Each cell In Range("data")
evenRow = (cell.Row - firstRow + 1) Mod 2 = 0
If evenRow Then
Range("startHere").Offset(j, 1).Value = cell.Value
j = j + 1
Else
Range("startHere").Offset(i, 0).Value = cell.Value
i = i + 1
End If
Next cell
End Sub
How does this macro work?
Before jumping in to the lines of code and demystifying the logic, Let’s understand what we need to do:
- For each cell of data,
- If it is in odd row, put the cell data in Date column at end
- Else, put the cell data in Value column at end
- Repeat
This is what our code is trying to do.
Let’s examine the For Each loop, as this is the most critical part of our macro.
- For each cell in the range data
- We check if we are in evenRow using simple arithmetic on row numbers
- If we are in evenRow then
- We put the cell value in row j (number of values so far), column 2
- We increment j
- Else
- We put the cell value in row i (number of dates so far), column 1
- We increment i
- Close the IF condition
- We check for next cell in the data range
Advantages of Transformation over SUMIFS approach
Both options for transforming data have few advantages:
- They work with any type of data (unlike SUMIFS, which works only for numeric lookups and has few other issues)
- Once data is restructured, you can do other types of analysis like creating pivot tables, adding extra calculated columns etc. easily.
Download Example Workbook
Click here to download example workbook that shows original SUMIFS solution, both options for transforming data & few other formulas. Play with it to learn more. Check out the code by pressing ALT+F11.
How would you transform data?
My favorite techniques for transforming data are – VBA, formulas, Power Query, pivot tables & SQL. Depending on the situation, time availability, where my data is, I choose one of these options to scrub my data.
What about you? How do you clean up / scrub data like this? Please share you thoughts & tips with us in comments.
Instructions for washing your dirty data
If your work involves scrubbing dirty data, check out below tutorials too:
- Extract numbers from text using VBA and formulas
- Filling blank cells with above values in tables
- Cleaning up in-correctly formatted dates
- Fixing in-correctly formatted phone numbers
- Reverse a list using INDEX formula
- Transpose a table using formulas
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... 🙂
[...] posts on games & excel that you may enjoy: Simulating Dice throws in Excel Generate and Print Bingo / Housie tickets using this excel Understanding Monopoly Board [...]
[...] Correct way to simulate dice throws in excel [...]
[...] Simulate dice throws in excel [...]
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