As part of Speedy Spreadsheet Week, I have emailed a few renowned Excel experts and asked them to share their tips & ideas to speedup Excel. Today, I am glad to present a collection of the tips shared by them.
Excel Speeding up & Optimization Tips by Hui
About Hui:
Hui (Ian Huitson) has been writing & contributing to Chandoo.org for more than 2 years. Many of you know him from Formula Forensics & Data table related articles on Chandoo.org. See about Hui page for more about him.
In no particular order:
- Minimize the use of Volatile Functions
- Organize your workbook layout and data methodically
- Where possible use fixed values or Named formulas instead of lookups even if the values only change rarely, flag those for manual checking
- Don’t Start equations with a + that actually adds 0.4% calculation time
- Minimize use of the Data Table command to running summaries only at the end of a project
- Review the logic of the model and all if’s or lookup choices for necessity or alternatives
- Use negatives instead of multiple positives where appropriate in conjunction with If’s and Lookups
- Learn about Conjunctive Truth Tables, they Rock for reporting
- Array formulas can do the work of dozens of normal cells, but use cautiously
- Use Named Formulas and UDF’s instead of multiple Helper Cells/Rows or Columns
- Minimize of us Conditional Formatting
- Minimize use of linked workbooks especially if over network drives
- Take an advanced Excel course like the ExcelHero Academy
- Minimize the use of Excel 2007
Links:
Excel Speeding up & Optimization Tips by George
About George:
George runs Excel Unusual, where you can learn about using Excel for engineering, simulations & games. In his work, he builds complex spreadsheet models all the time. So I asked him to share a few tactics with us. He wrote 2 articles in response to my request.
Links:
Excel Speeding up & Optimization Tips by Gregory
About George:
Gregory runs Excel Semipro, where he shares Excel tips & ideas. I asked him to contribute to the Speedy Spreadsheet Week. This is what he says,
Tips by George:
To speed up my worksheet files, I have one primary rule: do not use the OFFSET function, which is volatile and can slow things down considerably. In newer spreadsheets I use Tables and The imposing INDEX function to keep ranges automatically updated. In Excel 2003 I use an event-based approach, with named ranges, the worksheet deactivate module, and VBA to keep lists and ranges updated.
Links:
Excel Speeding up & Optimization Tips by Luke
About Luke:
Luke is one of the Excel Ninjas at Chandoo.org where he contributed more than 1000 posts. I asked Luke to share some optimization tips based on his vast experience of using Excel & helping others. This is what he suggests:
- In VB, whenever I see a line like Selection.something that’s usually an indicator that I’m using extra lines. Either I need to apply the method directly to the object instead of selecting it, or I need to use a With statement.
- With Event macros, don’t forget the all-important lines of Application.EnableEvents = False and Application.EnableEvents = True so that you don’t cause multiple events to be triggered.
- See a section of code that you’re repeating? Probably need to make this a separate Sub or Function that you can then reference from the main code.
- When building your formula page, think top-down. Cells near the top of worksheet should be referenced in formulas that are below, not vice-versa. XL likes to calculate left to right, top to bottom. Scattering cell references around makes it work harder.
- When using large amounts of data that you want to be charted, sometimes I’ll build a formula sheet within the workbook with data, and then just build another workbook that uses a data query (referencing the formula results) to generate the charts.
- This might be more along the lines of auditing a worksheet, but sometimes it’s hard to see how I’ve laid out my constants and formulas, and using a worksheet map helps bring things into focus (related: create a worksheet map)
Want to become better in Excel? Join Chandoo.org courses
Excel SchoolLearn Excel from basics to advanced level. Create awesome reports, dashboards & workbooks. |
VBA ClassesLearn VBA & Macros step-by-step. Build complex workbooks, automate boring tasks and do awesome stuff. |
Excel Speeding up & Optimization Tips by Narayan
About Narayan:
Narayan is one of the Excel Ninjas at Chandoo.org where he contributed more than 1000 posts. I asked Narayan to share some optimization tips based on his vast experience of using Excel & helping others. This is what he suggests:
Period-to-Date and Cumulative SUMs
There are two methods of doing period-to-date or cumulative SUMs. Suppose the numbers that you want to cumulatively SUM are in column A, and you want column B to contain the cumulative sum; you can do either of the following:
You can create a formula in column B such as =SUM($A$1:$A2) and drag it down as far as you need. The beginning cell of the SUM is anchored in A1, but because the finishing cell has a relative row reference, it automatically increases for each row.
You can create a formula such as =$A1 in cell B1 and =$B1+$A2 in B2 and drag it down as far as you need. This calculates the cumulative cell by adding this row’s number to the previous cumulative SUM.
For 1,000 rows, the first method makes Excel do about 500,000 calculations, but the second method makes Excel do only about 2,000 calculations.
Subtotals
Use the SUBTOTAL function to SUM filtered lists. The SUBTOTAL function is useful because, unlike SUM, it ignores the following:
Hidden rows that result from filtering a list. Starting in Excel 2003, you can also make SUBTOTAL ignore all hidden rows, not just filtered rows.
Other SUBTOTAL functions.
Using SUMPRODUCT to Multiply and Add Ranges and Arrays.
In cases like weighted average calculations, where you need to multiply a range of numbers by another range of numbers and sum the results, using the comma syntax for SUMPRODUCT can be 20 to 25 percent faster than an array-entered SUM.
{=SUM($D$2:$D$10301*$E$2:$E$10301)}
=SUMPRODUCT($D$2:$D$10301*$E$2:$E$10301)
=SUMPRODUCT($D$2:$D$10301,$E$2:$E$10301)
These three formulas all produce the same result, but the third formula, which uses the comma syntax for SUMPRODUCT, takes only about 77 percent of the time to calculate that the other two formulas need.
Dynamic Ranges
These are most often created using the OFFSET and COUNTA functions , as in the following :
=OFFSET(Sheet1!$A$1,0,0,COUNTA(Sheet1!$A:$A)-1,1)
Sometimes , when data is stored in the form of records , so that all columns have data to the same extent , there may be several dynamic ranges ; say we have ORDER_ID in column A , CUSTOMER_ID in column B , and the AMOUNT in column C. Thus there may be several dynamic ranges as follows :
=OFFSET(Sheet1!$A$1,0,0,COUNTA(Sheet1!$A:$A)-1,1)
=OFFSET(Sheet1!$B$1,0,0,COUNTA(Sheet1!$B:$B)-1,1)
=OFFSET(Sheet1!$C$1,0,0,COUNTA(Sheet1!$C:$C)-1,1)
These can be simplified to :
=OFFSET(Sheet1!$A$1,0,0,COUNTA(Sheet1!$A:$A)-1,1)
=OFFSET(Sheet1!$B$1,0,0,COUNTA(Sheet1!$A:$A)-1,1)
=OFFSET(Sheet1!$C$1,0,0,COUNTA(Sheet1!$A:$A)-1,1)
These can then be optimized by storing the COUNTA value in a cell , and using the cell reference within the OFFSET formula :
=OFFSET(Sheet1!$A$1,0,0,Sheet1!$F$1,1)
=OFFSET(Sheet1!$B$1,0,0, Sheet1!$F$1,1)
=OFFSET(Sheet1!$C$1,0,0, Sheet1!$F$1,1)
Where Sheet1!$F$1 contains the formula : =COUNTA(Sheet1!$A:$A)-1
For more, refer to MSDN.
Resetting the USED RANGE
Pressing CTRL END will take the cursor and place it on the cell which Excel thinks is the last used cell in the worksheet.
Suppose you do this , and the cursor lands on D27 ; now navigate to any cell which is as far away as you can imagine , say AA3456 ; enter any character , even a space will do ; then clear the cell contents by pressing the DEL key.
Pressing CTRL END will now take the cursor to AA3456.
To reset the USED RANGE , go to the Immediate Window of the VBA Project , and enter the following statement :
Application.ActiveSheet.UsedRange
Your used range should now be reset to its earlier value of D27 ; pressing CTRL END will now take the cursor to D27.
Refer to this Stackoverflow discussion for more.
Excel Speeding up & Optimization Tips by Jordan
About Jordan:
Jordan runs Option Explicit, an Excel VBA blog. He shared these tips with us,
- When reading and writing to ranges, use .value2 (this is noticeable for large, iterative calculations)
- Ensure that ALL spreadsheet errors are handled. The most common errors I see ignored are #Ref errors and #Div (for dividing by zero). Use Go To Special… to find these errors and either delete them or use IFERROR to handle them. In my opinion, Excel errors are one of the biggest contributing factors to slow spreadsheets.
- When using INDEX, include the row or column number even if you don’t need it. For example, if I’m pulling data from only one column, I need only write =INDEX(A1:A10, 1) to pull the first item. However, =INDEX(A1:A10, 1, 1) appears to be a hair faster. Try it.
- Cut down on Lookup functions. In many instances, the lookup table has already encoded information in the correct order. Instead of looking up, say, Stage 2, just use INDEX on the desired column and pull from row 2.
Thanks to Hui, George, Gregory, Luke, Narayan & Jordan
Many thanks to all of you for sharing these ideas & tips so that we can speed up Excel. If you found these tips useful, say thanks to the contributors.
More on Excel Optimization & Speeding up:
Read these articles too,
- Optimization & Speeding-up Tips for Excel Formulas
- Charting & Formatting Tips to Optimize & Speed up Excel
- Optimization Tips & Techniques for Excel VBA & Macros
- Excel Optimization tips submitted by our readers
Want to become better in Excel? Join Chandoo.org courses
Excel SchoolLearn Excel from basics to advanced level. Create awesome reports, dashboards & workbooks. |
VBA ClassesLearn VBA & Macros step-by-step. Build complex workbooks, automate boring tasks and do awesome stuff. |
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