It is election time in USA, and that means there is a whole lot of drama, discussions and of course data analysis. There are tons of cool visualizations published on all the data. Previously, we talked about “How Trump happened” chart.
Today let’s take a look at the beautiful decision tree chart by NY Times explaining what would happen if each of the 10 swing states vote for Democrats or Republicans. Go ahead and look at that chart. And when you are done playing with it, come back.
My first thought after looking at the chart is: Wow, that is cool. I wonder how we can recreate that experience in Excel?
But as you can guess, making a dynamic tree visualization in Excel is pretty hard. You can create a bubble chart mixed with XY chart to show all the nodes of the decision tree, but as this tree has 2^10 nodes at the bottom level (and 2^11-1 total nodes) our chart would look very clumsy and busy.
So, instead of replicating NY Times chart, why not make our own version that explains the data? You can reuse this idea when visualizing outcomes of several what-if scenarios.
Demo of interactive decision tree chart in Excel
First, take a look at our Trump vs Hillary chart.
How to create a decision tree visualization in Excel – Tutorial
1. Arrange decision and outcome data
In a table (or range) list various decision and outcome combinations. For our case of Trump vs. Hillary in 10 swing states, there will be 2^10 outcomes (1024). Arrange this data in a format like below.
2. Calculate the outcome
Based on each of the decision combinations, calculate the outcome and add it as a column to your table. Alternatively, you can also type or import the outcome data (along with decision combinations)
3. Create a pivot table from your data
Since we are going to use slicers for user interaction, we need to create a pivot table from all this data.
Add all the decision variables and outcome to row labels area. Rearrange the pivot in tabular layout. Disable sub-totals and grand totals.
4. Add slicers
Go to Insert > slicer and select all the decision parameters. In our case, we will pick all the 10 state names.
Once all the slicers are inserted, format them.
- Set up slicer labels in multiple columns
- Adjust their size
- Apply a custom style if you prefer.
- Keep the headers on the slicers for now. We will remove them at a later stage.
Related: Comprehensive guide to slicers – what, how, where, when and why
5. Calculate % of outcomes for each candidate
Now that we have slicers, whenever you make a selection, the pivot table will be filtered. Calculate number of outcomes favoring each candidate and use that to make a stacked bar chart.
6. Add bells & whistles
You can add a few bells and whistles to this pretty slicer controlled stacked bar chart even prettier.
- Add messages that display %s (or confidence levels etc.) for each outcome.
- Display the outcome once it is certain (a la head shot of Hillary or Trump)
Related: Display shapes & images in Excel charts
So there you go. Your interactive decision tree visualization is ready.
Oh, last but not least – resetting all slicers
This is the only place we need to open the hood of Excel and mess with internal wiring. Just add a simple macro to reset all slicers in the workbook. Then assign this macro to a text box with the text “Reset all” on it.
Sub resetSlicers()
'Reset all slicers
Dim sC As SlicerCache
For Each sC In ActiveWorkbook.SlicerCaches
sC.ClearManualFilter
Next sC
End Sub
Download decision tree visualization workbook
Click here to download decision tree visualization example workbook. Play with the slicers to find outcome of 2016 US election. Copy the ideas to your model / dashboard to showcase outcomes based on user inputs.
Note: this workbook has VBA. Enable macros to enjoy the reset button.
How do you visualize decision trees
As I said earlier, making decision trees in Excel is tricky if not hard. If you have Power BI, you can use R scripts to make a decision tree. But if you are stuck with Excel, creating a dynamic tree like structure is tricky. That is why, I went with the stacked bar chart approach.
What about you? How would you visualize various scenarios and outcomes in Excel? Please share your thoughts and implementations in the comments section.
Want more? Check out these awesome Excel charts
Here are few more inspiring Excel charts for you.
- Mapping spread of obesity in USA
- Earth vs. Venus cosmic dance (pictured aside)
- Mapping up & down trends in a time series
- Narrating story of change
- Network chart to map relationships between people
- More advanced charts
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