Over on Twitter, I came across this beautiful chart, aptly titled – Joyplot. It is the kind of chart that makes you all curious and awed. So I did what any Excel nerd would do. Recreated it in Excel of course. This post takes you thru the process.
Peak time for sports and leisure #dataviz. About time for a joyplot; might do a write-up on them. #rstats code at https://t.co/Q2AgW068Wa pic.twitter.com/SVT6pkB2hB
— Henrik Lindberg (@hnrklndbrg) July 8, 2017
First let me share the final outcome.
Joyplot in Excel – Peak time of the day for sports and leisure
Here is the final overlapped area chart with a bit of formatting thrown in. It is a pretty close imitation of Henrik’s original chart. Click on it to enlarge.
Creating Joyplot in Excel – Tutorial
As you can guess, the chart is a just an overlapped area chart (ie each area sits behind another, unlike stacked area chart where they are umm, well, stacked!)
Let’s start with a look at data. Henrik’s original data has 10,656 rows, each row containing activity name, time and p value – how much survey respondents enjoyed [@activity] at that time.
Here is a snapshot of first few rows.
Scrubbing and re-arranging the data
As you can see, while this format is excellent for storing, it is very tedious if we want to make one chart with all series. So let’s scrub.
- We need to figure out if an activity should be included or not. I am using the same criteria as Henrik’s. Exclude activities with p value less than 0.003 or activity title “Playing sports n.e.c. *” (not elsewhere classified)
- To do this, we first pivot the data on activity and max(p). Then filter this pivot two ways – max(p) >=0.003 and label not equal Playing sports n.e.c. *
Tip: You may need to enable multiple filters per field in the field settings of row labels. - We will end up with 28 activities.
- Then add a helper column to original table that looks up the pivot and tells if an activity should be included or not
- To do this, we first pivot the data on activity and max(p). Then filter this pivot two ways – max(p) >=0.003 and label not equal Playing sports n.e.c. *
- Add two more columns to original table to tell peak time and modified time. This will help us in rearranging and sorting the data. Modified time just moves time by 3 hours (Henrik’s chart is plotted from 3AM to 3AM). At this stage our data looks like this:
- Now, pivot the data once again. This time,
- exclude activities by using report filter on include? column.
- Set up peak and activity in row labels area, modified time in column labels area and p in values area.
- Arrange the report in tabular format, turn off sub-totals.
- We get this:
- Calculate normalized values by dividing each p value with maximum p value for that activity. We can use another range of 28×288 cells to do this. We get this:
- The next 2 steps may seem confusing. It will become clear once you look at the charts.
- Define an offset value. Start with 0.5. You can change this later. In a separate 28×288 cell range, calculate gaps by multiplying offset with position of an activity. Something like this:
- Now, finally calculate activity + gap values by adding up respective cells in each of the 28×288 ranges. We get this:
At this stage, our data is a shape ready for visualizing.
Creating and formatting overlapped area chart
The chart creation process has 5 steps.
- Select the 28×288 range of cells created in step 7 and insert an overlapped area chart.
- Now, copy the gaps range (created in step 6 above) and paste them on to area chart as new series (just ctrl+c your data and select the chart, press ctrl+v)
- Adjust the order of series so that each activity is sandwiched by appropriately named gap series
- Tip: adjusting 56 series is painful with the chart select data > move series up/down buttons. Instead, just select the series, look at formula bar. The SERIES formula has last parameter as order. Change this number. It is easy to figure out the number once you try a few.
- Change all gap series fill color to white. This instantly creates the floating area chart effect.
- Change the colors of activity series. Apply white / off-white border to these series. Your joyplot is ready.
Quick overview of the chart creation process:
Let’s examine the result of each those 5 steps with a smaller dataset so you can see how everything fits together. Here is the data for this example:
- Create an overlapped area chart with activity+gaps data. We get this:
- Add gaps as new series to chart. You get this:
- Move the gap series so that they sandwich activity series. Use Chart Data > Move series up/down buttons or SERIES formula
- Apply white color fill formatting for gap series. This creates floating area chart effect as below:
- Finally, format the chart by apply some colors and border formatting etc.
So there you go. The final outcome does look joyful.
Alternatives to Joyplot
While joyplot is awesome, it is not easy to make. Fortunately, there are a few simpler alternatives that we can whip up in Excel as soon as you have either the pivot or normalized values. Below I have shown two such examples. Read about sparklines or conditional formatting heatmaps for more.
Joyplot alternative – using sparklines:
Tip: to get axis on your sparkline, just type the times separated by a single space. Then go to format cell (ctrl+1) and set horizontal alignment to distributed. Viola, Excel will fill the cell by adjusting spaces.
Joyplot alternative – Conditional Formatting Heatmap
Download Joyplot Workbook
Click here to download Joyplot Excel workbook. Examine the data scrubbing formulas, pivot and chart settings to learn how this is created.
If you are familiar with R, then go thru Henrik’s R code. It is much shorter than the Excel gymnastics we did with circular pivot table referencing. That said, some of the data re-arrangement could be done with same ease in Power Query too.
Your thoughts on Joyplot?
The only step we missed in Excel implementation is moving average smoothing of the area charts. It can be easily added as a step between 3 and 4 in data stage.
How do you like Joyplot? Would you create something like this for your business / personal data? Share your stories and thoughts in the comments section.
More joy for you…
If you love this, you are going to enjoy these charts too.
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