One of the most dreaded courses during my under-graduation is Probability, Statistics & Queuing Theory. We called it PSQT. I struggled to understand the significance and concept of this course as I could barely concentrate in the class. We had a professor, who is probably a genius, but the moment he started the class, I would magically fall in to one of my after-noon naps. When I woke up, we are either in the middle of an elaborate t-test or going thru intricacies of a Markovian queue.
This was all 11 years ago. Later in life, I have embraced the world of probability & statistics. I still fear queues. May be I will get there one day. 😉
A good understanding of statistics & probability theory is necessary if you want to model complex real-life problems using Excel or similar tools. Naturally, Excel has several functions, features & supported add-ins to help you in this area.
Today, I want to share some of this with you. This article is broken down in to 3 parts.
- Learning Statistics & Probability using Excel
- Downloadable Excel Workbooks to understand
- Full blown models & simulations in Excel
#1 – Learning Statistics & Probability Concepts using Excel
Using Excel RAND functions
Excel has several powerful functions (formulas) to generate random numbers, random data. You can combine these functions to generate data that has certain parameters – like a give mean, standard deviation or follows a certain type of distribution.
Go thru Using Excel’s Random Functions for a detailed overview these techniques.
Simulating Dice Throws in Excel
One of the fundamental ways to learn about Probability is to look at dice throws. A dice has 6 faces and on each throw, any of the 6 faces turning up is equally likely. So, we say, each face has 1/6th probability of showing up. If you want to simulate this in Excel, you can use the formula RANDBETWEEN like this, =RANDBETWEEN(1,6). On each run, this formula would throw up a random number between 1 & 6 (including both).
For more, Simulating Dice Throws in Excel
Shuffling a List of Values in Excel
Understanding permutations and combinations is essential when it comes to modeling many real-world problems. Using Excel’s RAND, VLOOKUP and SMALL formulas we can generate a random permutation of a given list of values (in other words – we can shuffle the list).
To learn this read, Shuffling a list of values in Excel
Generate Frequency Distribution from Data
Often, when you are analyzing data, you need to understand how the data is distributed. Again, Excel has just the right function for this sort of thing. FREQUENCY(). In this simple tutorial, learn how to use Excel’s FREQUENCY formula to generate frequency distribution of given data.
Read Frequency Distributions in Excel
Trend Analysis & Forecasting using Excel
One of the most common applications of statistics is trend analysis & forecasting. Again, Excel shines with a lot of powerful formulas, built-in features and charting tools to help you understand the data & predict future based on that.
Since this is a big topic, we have covered it in 3 parts –
Part 1- Introduction to Trend Analysis & Forecasting: In this, we will learn what is trend analysis & forecasting. We will see manual forecasting technique in Excel. We will use Excel charts to depict our analysis and results.
Part 2 – Trend Analysis & Forecasting using Excel Functions
In this second part, we learn about Excel’s functions like LINEST, TREND, FORECAST, SLOPE, INTERCEPT, LOGEST and GROWTH. These powerful formulas can process lots of data and extract the trend information dynamically.
Part 3 – Trend Analysis & Forecasting using Charts & Macros
In the final part, we talk about how to use Excel chart’s trend analysis & forecasting features to estimate the trend & predict future values based on the data.
We also learn how to use Macros (VBA) to augment Excel chart’s trend-lines with useful information.
Visualizing Distribution of data with Box Plots
Box plots are an excellent way to understand the distribution of data. Unfortunately, there is no direct option to make a box plot from given data in Excel. That is where, this tutorial comes handy.
Learn how to create box plots in Excel.
#2 Downloadable Excel Workbooks
Learn Basic Statistics & Gaussian Distribution using this Excel Workbook
Glen, one of our long time readers shared this file with me. It lets you perform statistical analysis, quality control analysis, visualize Gaussian distribution based on the data you enter.
Click here to download the workbook.
Thanks Glen.
More Downloadable Workbooks
Almost all of the links in this page will take you to detailed articles on Chandoo.org, where you can also find downloadable workbook with examples. So just click thru and learn. 🙂
#3 Full blown models & simulations in Excel
A full blown model lets you learn various statistical concepts, Excel features and how to bring them all together to mimic a real-life situation.
Simulating Deal or No Deal game in Excel
In this simulation of Deal or No Deal, a popular television game, we use basic probability, permutations and Excel formulas features. You will learn how to assign random values to the suit-cases, how to use circular references, how to calculate the banker’s offer.
Simulation of Deal or No Deal game in Excel
Generating Housie / Bingo Tickets in Excel
Housie (Bingo) is a popular recreational game where the tickets contain 15 numbers between 1 to 90, arranged in 10 columns (3×10 grid). First column has numbers between 1 to 9, second column has 10 to 19 so on..
Generating a bingo ticket in Excel is a nice exercise in statistics, permutations and Excel formulas.
Learn from Bingo / Housie Tickets in Excel
Data Tables & Monte Carlo Simulations in Excel
Excel has powerful features to let us do complex simulations of real world situations. One such feature is called as data table.
The Data Table allows a set of what if questions to be posed and answered simply, and is useful in sensitivity analysis, variance analysis and even Monte Carlo (Stochastic) analysis of real life model within Excel.
The case of Blue Sky Mining Company
To help you learn about data tables, Monte Carlo simulations, we have put together a fictional mining company – Blue Sky co. and analyzed its performance under various assumptions & simulations.
To learn about this, visit Data Tables & Monte-Carlo Simulations page.
Modeling & Scheduling a FIFO (First In First Out) Queue in Excel
FIFO queues are very common in life. You can see them at Airports, coffee shops, Apple stores; Except at Airports it is FIFOUYC (FIFO Unless You are Crew).
In this article, we model & schedule a FIFO queue using Excel.
More Full Blown Models & Simulations in Excel
For more examples, check out these links.
- One more example of Data Table & Linest
- Simulating 3D dancing pendulums in Excel
- Simulating Monopoly Board Game in Excel
Do you use Statistical Concepts for your work?
As a small business owner, a good portion of my work involves statistical analysis, forecasting and simulation. I run estimates for our website traffic, revenues. I run statistical tests (split tests etc.) to optimize our sales pages, website. I estimate when my kids wake up from their nap (based on past experience) and plan my work accordingly. Thankfully, for the last part, I do not use Excel 😀
What about you? Do you use statistical concepts for your work? What are the things you use and how does Excel help you in that? What are your favorite formulas, features and tips? Please share using comments.
Special thanks to Hui & Glen
Many thanks to Hui, our resident Excel ninja for writing many of the articles on statistics, simulation, forecasting & trend analysis.
Special thanks to Glen for sharing the analyze-this file with us.
Say thanks to them if you enjoyed this.
19 Responses to “How to Distribute Players Between Teams – Evenly”
An excellent solution, especially for large data sets.
Another solution without using solver would be to assign the player with the highest score to Team 1, the 2nd to team 2, 3rd to team 3, 4th to team 3, 5th to team 2, 6th to team 1, 7th to team 1 and it continues. This method would end up with a Std Dev of 0.001247219. This works best with a distribution with lower Std Dev for the dataset.
Full Disclosure: this is not my idea, remember reading something a few years ago. Think it may have been Ozgrid
thinking back I now remember why I read about it. About 10 years back I had to distribute around 300 team members into 25-30 odd teams. Used this method based on their performance scores. I used the method I described to do this and the distribution was pretty fair.
Solver would have saved me a ton of time though 🙂
I think the issue with you first Solver approach was that you took the absolute value of the sum of team deviations (which should always be zero except for rounding) instead of the sum of the absolute values (which is a reasonable measure of how unbalanced the teams are).
Here's another simple algorithm you could use: you start from the top (with players sorted from high to low), and at each step allocate the next player to whichever team has the smallest total so far. You can implement it dynamically with some formulas so it will update automatically when the data changes.
If the scores were more widely distributed (so that this might end up with not all teams the same size), you could add a constraint to only pick among the teams which currently have fewest players at each step, or just stop adding to any team when it hits its quota.
When I tried it on the sample, I got the three teams below, with a STDEV of 0.000942809 (i.e. about half of what Solver got to).
Team 1: John, Hugo, Tom, Josh, Eric, Zane, Charles, Andrew
Team 2: Barry, Michael, Kenny, Joe, Xavier, Patrick, Oliver, William
Team 3: Henry, Steven, Ben, Frank, Kyle, Edward, Cameron, Lachlan
Thanks for sharing!
Hi,
I was looking at all the solutions and this is closest to what I intended to do. I am dividing a bunch of players into 3 soccer teams. Players availability is also a factor while deciding the teams.
So the steps the excel needs to do is as follows:
1) In availability column if "yes" go to next
2) Equally divide 'Goalkeepers', 'Strikers', 'Defenders' basis their quality
So the end result gives each 3 teams a balance of players playing at different positions.
Can this be done on Google spreadsheet with only availability as an input from the user and rest calculates by itself.
Sorry for asking such a pointed question, but I have been struggling to find a solution for it for sometime now!
Hi Ishaan,
I am working on a similar problem at the moment, so I am wondering if you ever found a solution and if you are willing to share what you did.
Hi everyone, this is a variation of the famous Knapsack Problem https://en.wikipedia.org/wiki/Knapsack_problem.
I had to use a VBA implementation recently as part of a problem, where we ar trying to allocate teams of an organization into different locations (we are a large company with many different team). The goal was to optimally allocate teams to individual buildings without putting too many teams into one building and not splitting teams apart.
As we had around 400 teams of different sizes, solver couldn't handle it anymore. Luckily there is a Knapsack algorithm implementation in VBA readily available on the internet :).
I also went with a heuristic approach first!
An interesting mathematical solution but what if Eric and Xavier can't stand each other or Patrick is best friends with Steven - the real life problems that effect "even" teams.
@Joe
You can add more criteria like
If Eric and Xavier can't stand each other
=OR(AND(E15=1,E16=1),AND(F15=1,F16=1),AND(G15=1,G16=1))
It must be False
If Patrick is best friends with Steven
=OR(AND(E5=1,E17=1),AND(F5=1,F17=1),AND(G5=1,G17=1))
It must be True
Note that the 2 formulas above are exactly the same
except for the ranges
One must be True = Friends
One must be False = Not Friends
Nice Post!
Just one question What if number of players are not even or equally divisible.
Nice post Hui!
I download your workbook and just try to change in options the Precision Restriction from 10E-6 to 10-8 and the Convergence from 10E-4 to 10E-10. The process take almost the same time, but the results was great.
The standard deviation I got was 0,000471.
Team 1: John, Tom, Kenny, Frank, Eric, Xavier, Edward, Zane
Team 2: Steven, Hugo, Ben, Joe, Josh, Oliver, Cameron, William
Team 3: Barry, Henry, Michael, Kyle, Patrick, Charles, Andrew, Lachlan
Great application of Solver! Thanks for the link!
Great explanation. Well done... However, I tried with 6 teams of 4 players and solver never did finish.
How about vba code for the same data set.
I have 3 column A B C wherein A has text and B has number Wherein C is blank. And in C1 been the header C2 where I want the name to come evenly distributed the number which is in Column B.
My Lastcolumn is 1000.
Sorry if I'm being slow here, but how is 'Team Score' calculated? I've gone through the explanation several times but it seems to just appear.
@Hrmft
This process uses the Solver Excel addin
Solver is effectively taking the model and trying different solutions until it gets a solution that meets all the criteria
Then solver puts the solution into the cell and moves to the next cell
So yes it appears to "just appear"
Hi ! Thank you so much ! Works great 🙂
I cannot get the fourth Equation to work in my excel spreadsheet
You have =($E$2:$G$25=0)+($E$2:$G$25=1)=1 as a SUMIF solution, I have, =($F$2:$H$13=0)+($F$2:$H$13=1)=1 as my solution but it does not work. The only thing I changed is the ranges. Any suggestions?
Thank you.
Jim
I cannot get the fourth Equation of TURE or FALSE statements to work in my excel spreadsheet You have =($E$2:$G$25=0)+($E$2:$G$25=1)=1 as a SUMIF solution, I have, =($F$2:$H$13=0)+($F$2:$H$13=1)=1 as my solution but it does not work. The only thing I changed is the ranges. Any suggestions?
Sorry I left some of it out in the previous question,
Thank you. Jim