This week in the Chandoo.org Forums, Greg asked the question, “I would like to conditionally format the data labels position to be above the plot line in a scatter plot if a certain cell contains ‘True’ and below the plot line if that cell contains ‘False’.”
Greg also wanted a Non-VBA Solution.
This post will describe how this is achieved as well as extend the idea into the fourth dimension.
All the charts in this post are available in the sample file: Download Sample File.
The Concept
The concept applied here to achieve the final result that Greg wants is that charts can use multiple data series.
These data series do not have to be visible but they can, at the same time, have Data Labels or other formatting applied.
The Application
First setup a set of data,
I have used values A to P as X Axis Labels and used a formula =Randbetween(10,20) in column C for the Y Values for the chart
Now add a Data Validation to a cell G3
Goto the Data, Data Validation Tab and select Data Validation
next add 2 columns
D3: =IF($G$3,C3,NA())
E3: =IF($G$3,NA(),C3)
Copy these down to Row 18
Select the Range B3:E18, note it includes the X Axis Labels and Headers
Now goto the Insert, Chart tab and select the chart type you want to use. I have chosen a Line Chart
Excel will draw a Chart with 3 series of lines
Now is a simple job of applying labels and formatting as applicable
The first thing to notice is that the chart has 3 series, Random Value, True and False
We can only see the True series, as it is in front of the Random Value series, The False series is hidden for now.
Select the True Series by Clicking on it
Then Right Click on it and Add Data Label
Excel adds the Data Labels to the True Series
Right click on any of the Data Labels and select Format Data Label
For the True values we will plot them above the Data Point
Change the values as shown above
Right click on the Data Series Line (the orange line) and select Format Data Series
Change the Line Type to No Line
The Orange line is gone and there is now a Blue Line, this is the Random Values series
Note we can still see the Data Labels for the True Series, even though the True Series Line is not visible
You can set or disable markers whilst you are here as well
Next select the False Series, by changing the Data Validation cell to FALSE
We can now see the False Data Series and the Random Values Series which is behind the Grey Line as before.
Right click the False Data Series, Add Data Labels
Then Right Click the New Data Labels and Change there settings to be below
Finally set the False Data Series Line Line Type to No Line
Now we can see the Rand Value series (Blue line) with the Data Labels showing for the False Series below the line
Change the Data validation from True to False and vice-versa and observe that Excel is only showing the series Labels for the Data Series which has values and doesn’t have #N/A errors in Columns D & E
So we are seeing 3 Series and 2 sets of Data Labels, it is just that we have set Two of the Line Types to No Line and Excel doesn’t display Series Values where the Value is the error value #N/A.
Now set the data Validation to True and select the Data Labels Font Color to Blue
Repeat the Process for the False Data Labels and set them to Red
Finally clean up the legend
Select the Chart, then click on the legend
Then click on TRUE and press the Delete Key
Repeat for the FALSE Legend
Our Final Chart
Change the Data Validation cell to True/False to verify that the system is working.
The techniques described above can be applied to most chart types.
Care must be taken with Column and Bar and other cumulative chart types.
Extensions
Having seen how Excel treats the #N/A error we can use that to create a number of variations for our Data Labels
Conditionally Format Data Labels above and below a set value
This is achieved by using a formula that applies to individual data points in each series
so that when a Data Point in a series (>15) is less than 15 it will return a #N/A error and not be displayed and also when a Data Point in a series (<=15) is greater than 15 it will return a #N/A error and not be displayed
Add a Third or more Set of Conditional Data Labels
This is achieved by simply adding a Fourth Data Series to the chart and adjusting the formulas as appropriate
Add Conditional Formatted Text Data Labels to Highlight Points
These are achieved by using the above techniques but instead of Displaying Values for the Data Label Series, we use the Value From Cells option
Add Conditionally Formatted Markers to Highlight Points
This is achieved by using the above techniques but alter the markers for the two helper Columns as well as the Data Labels
Explore
You can explore how these are constructed using the sample file.
All the above charts are shown in the sample file: Download Sample File.
Selecting Chart Series
One of the annoying aspects of dealing with charts and formatting individual series is the ability to select hidden or covered series
Fortunately there are a number of ways to get around this.
Use the arrows Keys
In older versions of Excel, you can select a Chart, then use the Up/Down arrow keys to cycle through all the chart objects.
Once you had the object you wanted Press Ctrl+F1 to bring up it’s format Properties
Unfortunately Microsoft in its wisdom has removed this functionality in recent versions of Excel, so try it, If it works, Enjoy, If it doesn’t keep reading
Use the Tab Menu
If you select a Chart you will see two extra menu items on the Tab Menu
These are the Chart Design and Chart format Tabs
Select the Chart Format Tab
Then Goto the Drop down on the Far Left of the Tab
It contains a list of all the available Chart Objects,
Select the Chart Object you want, then press Ctrl+1 to bring up the format options
Use the Chart Format Menu
If you select a Chart and select any part of the chart press Ctrl+1 and the Format Menu for that object is shown
Now use the small drop down just under the Format Title and select the Object you wish to change
Warning
Despite being able to use the Excel =NA() function to force an #N/A error, which is ignored by Excel, future versions of Excel maybe about to change this behavior.
Some people using the Excel 365 Insider Fast Edition are noticing a new Dialog option.
So keep in mind if all of a sudden this behavior changes, you may have upgraded Excel and introduced this new menu
You can read more about how to use this new functionality here:
http://www.exceluser.com/excel_dashboards/two-business-uses-for-excels-new-chart-feature.html
Comments
If you have any other ideas about how to use this functionality let us all know in the comments below
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