Let’s take a whirlwind trip to coolest little capital – Wellington. It is a windy place, so hold on to your hats and spreadsheets.
Almost everyone who spends more than 2 days in Wellington would agree that it is a windy place. But how windy is Welly? In this two part series, we will use Power Query, Excel charts and coffee to answer that question.
But, first let’s start with a joke.
What happens when you throw a boomerang in Frank Kitts Park?
You will have to buy another one, coz you are not getting that one back.
Extracting the wind data
In order to understand how windy Wellington is, we need to get average wind speeds by day for last several days. Let’s get the data for last 2+ years (ie from 1 Jan 2016 to 21 Feb 2018).
There are many places where you can collect latest wind data. But when it comes to historical wind data, surprisingly few resources are available. We can use The National Climate database – CliFlo, to gather wind data. But the interface is confusing and I could only locate gust speeds, rather than average wind speeds over time.
We can use wunderground.com to fetch weather data for up to 13 months at a time.
But we need data for almost 26 months.
Very simple, we can query wunderground twice (or thrice), once per each year.
The historical data query URL looks like this:
https://www.wunderground.com/history/airport/NZWN/2016/1/1/CustomHistory.html?dayend=31&monthend=12&yearend=2016&req_city=&req_state=&req_statename=&reqdb.zip=&reqdb.magic=&reqdb.wmo=
All we had to do is, change 2016 to 2017 & 2018 to get respective data.
The actual data set will be a web page. But we can use power query to extract the portion of page that contains weather information.
On to Power Query – Building our Weather Data Extractor
Note: This is a slightly advanced tutorial on PQ. If you are a beginner, start with Introduction to Power Query and work thru examples on PQ tag page before reading any more.
Getting data from the web – building URL in parts
Open Excel and go to Data > New Query > From Other Sources > Web
For Power BI, this would be Edit Queries > New Source > Web
Switch to “Advanced” mode and enter the URL as parts like below. We will switch the 2016 part to parameters soon, so we could get data for any year easily.
In the navigation pane, select “Table 1” which is the weather table.
Set up a parameter for Year
How would we get data for 2017 or 2018? Simple, we use parameters. These are like variables which can be plugged in to any part of your Power Query process.
In Power Query Editor, go to Home > Manager Parameters > New Parameter and call it Year. Enter the default value as 2016.
Now, go back and edit the source settings for the query and replace 2016s with parameter Year.
Cleaning the weather table
Turns out the weather data table is not clean. Although there are 366 days in 2016 (leap year), Wunderground adds headers for each month. So we end up with 378 rows (excluding the header). Each header contains month name and repeat of all the column names. We can extract the month name & combine that with date and year parameter to create the date for each row.
Here is a quick illustration of what we need to do.
But first, rename the very first column
Notice the first column? It is called as 2016. This is ok if we are interested in just 1 year of data. But if we re-run this query with Parameter=2017, our column heading will change. If you have dabbled with Power Query a few times, you will quickly realize that PQ will get in to a nasty fit anytime column headers change and impact downstream steps.
Simple, we shall rename it as FirstCol.
When you apply the new name, PQ will write this M instruction.
#”Renamed Columns”= Table.RenameColumns(Data1,{{“2016”, “First col”}})
This is not a fool proof solution, as when we change parameter to 2017, there won’t be a 2016 column in that new table.
So, instead, we can ask PQ to rename first column of the table.
You can do this by:
- Note: You need “Formula Bar”. Enable “Formula Bar” by clicking View > Formula bar. This way you can actually see all the M code PQ is cranking up whenever you perform some actions on your data.
- Click on fx button on the formula bar to insert a step. Simply type = Table.RenameColumns(Data1,{{Table.ColumnNames(Data1){0}, “First col”}})
- Press Enter
- Bingo, you have renamed the first column of your query to “First col”. This has no reference to 2016 or any year, so it should work on any table you fetch from that weather data page.
Cleaning the weather data – steps
Just follow these steps to clean the weather data.
- Add a custom column called Month and write this formula = if Text.Length([First col]) > 2 then [First col] else null
- Select Month column and Fill Down (Transform > Fill >Down)
- Select First col and change its type to whole number. This will make all month names as Error
- Remove errors from First col (Right click on column header and choose Remove Errors)
- Add a custom column called Date with the formula = Text.From([First col])&”-“&[Month]&”-“&Year
- Change this column to date type.
- Keep only Temp. (°C)2, Wind (km/h), Wind (km/h)2, Wind (km/h)3, Events, Date columns and remove all other
- Rename first four columns to Avg. Temp, Wind Max, Avg. Wind, Wind Gust
At this stage we have one year of wind and temperature data for Wellington. Time to create getWeatherData() function.
Making getWeatherData function in Power Query
Now that we have a parameterized query, just right click on the query and choose “Convert to Function”
PQ will build the function that can take year as input and return a table of weather data for that year (provided Wunderground.com co-operates)
Now, we just need to run this function three times, once each for 2016, 2017 and 2018 to get all the data.
Go back to Excel
Save your queries, but don’t load them yet. If PQ prompts about data load, select “Connection only” and jump to Excel.
- Create a table with 3 rows and type 2016, 2017 and 2018 in that. Call this table Years.
- Load this table to Power Query (Data > From Table)
- Go to Add Column > Invoke Custom Function and invoke getWeatherData function for each year.
- Expand the weather data tables.
- Done!
At this stage, we have data for all 3 years. You can add some data clean up steps if you want. But all the wind & temperature data is here for us to analyze and visualize.
Download Example Workbook
Click here to download the Wellington Wind workbook. As you can see, I have added few more steps in PQ to clean up the data and include a “Is it windy?” conditional column.
Please note that this workbook is designed in Excel 2016. It may not work in older versions of Power Query. You can replicate most of the steps. Try doing it so that you will learn more about Power Query.
In the next part – Wind in Wellington – few visualizations
In the next part of this tutorial, we will build some visualizations to understand how windy Wellington gets and what is the best time to enjoy the beautiful outdoors.
Stay tuned.
How are you using Power Query? Please post about your power query escapades in the comments section. Also tell me how you went about re-creating the steps in this tutorial. I am all ears.
Why there are no undercover cops in Wellington? Their cover was always getting blown. That is why.
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