Last week Joyce asked a question on the Chandoo.org, Comment 24.
I’m wondering if there’s a way to count the number of occurrences of words when they’re all in a cell? Like this:
A1: “Windows NT, Networking, Firewalls, Security, TL, Training”
A2: “Networking, Networking, Training, Security, TL, Training”
A3: “Security, TL, Firewalls, Security, Networking, Windows NT”
Joyce
Hui responded with an Array Formula:
=SUM(LEN(A1:A3)-LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
As the formula is an Array Formula it is entered with Ctrl Shift Enter.
Setup the Problem
Copy the Data Above into Cells A1:A3 or download the example file here: Example File (all Excel versions)
Enter the text string Security into cell C10
And array enter the formula
D10: =SUM(LEN(A1:A3)-LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
Cell D10 should now display the value 4, which is the number of times the Word Security, appears in the Range A1:A3.
Pull The Formula Apart
Lets take a look inside this and see how it works
We will break this formula apart and look at each section independently and then put the answers back together.
=SUM(LEN(A1:A3)-LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
In a cell below the data
D13: =LEN(A1:A3) but don’t press Enter, Press F9
Excel displays ={57,56,57}
This is the number of characters in each cell A1:A3
ie: A1 has 57 characters, A2 has 56 characters, A3 has 57 characters,
You can check this manually by typing =Len(A1) into any spare cell
=SUM(LEN(A1:A3)-LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
In another cell below the data
D15: =LEN(SUBSTITUTE(A1:A3,C10,””)) but don’t press Enter, Press F9
Excel displays ={49,48,41}
What this section does is measure the length of each cell in A1:A3 but only after substituting the word being searched for from C10 with ””, which is a zero length string.
So the second array is shorter than the first Array, by X times the length of the word in C10
=SUM(LEN(A1:A3) – LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
Next we add up the difference between the two arrays
So you can see we have two arrays of numbers
Array 1 = {57,56,57}
Array 2 = {49,48,41}
If we subtract Array 2 from Array 1
= {57-49, 56-48, 57-41}
= {8, 8, 16}
We can do this in Excel to Check
In Cell D17 enter
=LEN(A1:A3)-LEN(SUBSTITUTE(A1:A3,C10,””)) and press F9
Excel displays: = {8, 8, 16}
=SUM(LEN(A1:A3) – LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
The next part is to sum these up
Obviously the sum of 8, 8 & 16 is 32
We can check that
D21: =SUM(LEN(A1:A3)-LEN(SUBSTITUTE(A1:A3,C10,””))) and press F9
Excel displays: 32
=SUM(LEN(A1:A3) – LEN(SUBSTITUTE(A1:A3,C10,””)))/LEN(C10)
The final part of this is to divide the sum (32 in this case) by the length of the text in C10 “Security” = 8 Characters
=32 / 8
= 4
Correct – The number of times Security appears in the cells A1:A3 is 4.
OTHER POSTS IN THIS SERIES:
You can learn more about how to pull Excel Formulas apart in the following posts
Formula Forensic 001 – Tarun’s Problem
WHAT FORMULAS WOULD YOU LIKE EXAMINED ?
If you have any formulas you would like explained please feel free to leave a post here or send me an email:
If the formula is already on Chandoo.org or Chandoo.org/Forums or even forbid another web site, simply send the link to the post and a Comment or ID No. number if appropriate.
If sending emails please attach an Excel file with the formula and data
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