In April 2017, Shenricus, posed a question in the Chandoo.org Forums:
“I have 24 people who each have their own score. I’ve been trying to figure out how I can divide these names into 3 even teams – or as close as possible.”
I answered with a Solver Based solution, and Bosco Yip also added to my solution with a slightly different approach.
This caused me to reconsider my first attempt and finally I posted a Final Solution, which was also a Solver based solution, but was a much more robust solution than my original solution or Bosco Yip’s solution.
This post will examine the thought process used to derive the solution and then implement that using solver.
As always a Sample file is provided so you can follow along: Download Sample File here.
Approach
Shenricus gave us a list of 24 players and a score for each player.
The players are Ranked from Best to Worst.
We have no other information as to the Sport or Score.
The question posed by Shenricus is to distribute the players into teams so that each team is “As even as possible”.
Considering that we have 24 players and need to put them into 3 teams, we will assume each team has the same number of players and hence requires 8 players.
My initial though was to setup a Delta or Difference between each Players Score and the Mean (Average of all scores).
First calculate the Average of All the Scores
Then calculate the Differences between the each players Score and the Average
Next we need to distribute each player into one of 3 teams.
Solver will put a value of 1 when a Player is in a Team, and a 0 when the player is not in a Team.
Next add a Formula to Calculate the Sum of the Variations from Mean for each Team
and Finally Sum these up
We should be able to get Solver to Minimise this value.
So lets look at how Solver is setup.
How Do Use Solver?
Solver is found in the Data, Analyze Tab.
Your screen may look different to mine depending on which version of Excel you are using and if you have your Excel window at a maximum size or not.
If you cannot see it, you may not have Solver Loaded.
How Do We Install Solver?
Right Click on any part of the Ribbon
Select Customize the Ribbon
Select Add-ins on the Left menu and
Manage Excel Add-ins in the Manage Dialog and press Go…
Finally Select Solver and Ok
Solver will now be visible in the Data, Analyze Tab
How Do We Setup Solver?
Click anywhere in the model
Goto the Data, Analyze Tab
Select Solver
The Solver Dialog is show as:
Lets look at each of the highlighted sections first and I will discuss this first as a plain English and then I will discuss how it is implemented in Solver
Solver is asking us to Set our Objective, to a Minimum, Maximum or Value, by changing some cells, Subject to some constraints.
Set Objective
Solver is asking what our objective is?
In our Even Teams example we want to minimise the variance in the average Team Scores
By Changing variable Cells
We want to achieve our objective by setting Each Player to be a Member of 1 team
That is Each player must have a 1 in a Column of Team 1, Team 2 or Team 3
Subject to the Constraints
We have a Number of Constraints that our model will be subject to
Each player must have a 1 in a Column of Team 1, Team 2 or Team 3
Each Team must have 8 players
All 24 Players must be used only once each
Each player can only be in a Team, he can’t be shared between teams
Solver operates using a number of techniques to Solve the above problem.
Simplistically it iterates values into the Variable Cells, subject to meeting the constraints.
It measures the output and re-iterates until a better solution is reached.
In Solver Speak
Lets look at how our model is setup in Solver
Objective
The Objective is to Minimise the Sum of the Team Scores
That is to Minimize Cell E27
Variable Cells
We will be changing the allocation of players into each team.
This is the Variable Cells $E$2:$G$25
Subject to the Constraints
The variable cells will be changed by Solver subject to meeting our 4 criteria defined above
a. That each team has 8 players, each cell in $E$29:$G$29 is 8
b. That each player only plays in 1 team, that is cells $E$2:$G$25 can only be 0 or 1 (binary)
c. That all 24 players are used, ie: $H$26 = 24
d. That all 24 players are used only once, each cell in $H$2:$H$25 = 1
We haven’t yet setup Conditions C or D above in our model yet
So add a Column H
H2: =Sum(E2:G2) and copy that down to Row 25
This will add the Total of each Team per Player and should be 1
And add up the total of these in H26, This is the Total of all allocated Players and should be 24
H26: =Sum(H2:H25)
In solver setup each of these sections then click Solve
After a Minute or so, Solver will return to tell you that it has found a Solution
Select Keep Solver Solution
Lets check things
Firstly we can see that
1. The sum of the Team Scores, E27, is a very small number, as we requested
2. Each player was only used once Column H, True
3. All 24 Players were used H26, True
4. Each Team has 8 players, E29:G29, True
5. Each player is not split between teams, E2:G25, True
So all our Criteria are met, however if we start to look at the solution in more detail we can see that Team 3 has been assigned the Best 8 players, where as Team 1 has mostly the worst players, Team 2 is in the middle.
Solver has solved our problem, but our problem obviously hasn’t been correctly specified.
Solver has setup 2 teams with Low Negative Scores to Offset Team3 with a High Positive score, with the overall result being a low average Team Score
If we look at the Total Scores for each Team, E31:G31
We can see that the Total Team Scores vary between 7.705 and 7.891
A spread of 0.186
What we actually need to specify is that the Variation in these Total Team Scores is Minimised. That is the spread between the 3 scores is minimised.
There are Statistical Measurements called Variance and Standard Deviation
Without going into too much detail, each is a measure of how far a set of numbers are spread out from their average value.
Refer Wikipedia Wikipedia Variance, Wikipedia Standard Deviation
Luckily we can easily calculate these using Excel
In cell E33 =STDEV.P(E31:G31)
Excel displays 0.078969
So the Standard Deviation of these 3 Team Scores is 0.0789
However we need to re-run the Solver Model with a new Objective
Firstly, reset all the players to 0, ie Players are not assigned to any Team
Select E2:G25 and type 0 Ctrl Enter
Click anywhere in the model,
Goto the Data, Analyze Tab
Select Solver
Set the Objective to $E$33
The Variable Cells and Constraints remain unchanged
Now Click Solve
After a minute or so, Solver will announce it has a New Solution
Accept that as before
Lets check things
Firstly we can see that
1. The sum of the Team Scores is a very small number, as we requested, Ok
2. Each player was only used once Column H, Ok
3. All 24 Players were used H26, Ok
4. Each Team has 8 players, E29:G29, Ok
5. Each player is not split between teams, E2:G25, Ok
If we look at the solution in more detail we can see that
The three Teams now have a spread of both good and not so good players
But the important thing to notice is that the Standard Deviation of the 3 Team Scores is now 0.001699, or 2.1% of the previous Standard Deviation.
This shows the teams are much more “Evenly” matched
Solver has solved our problem.
Bosco’s Solution
During the thread Bosco proposed an alternative, algebraic solution.
It involved distributing players according to simple rules
The team who got the Best player also took the worst player,
The next team who got the Second best player also took the second worst player
The next team who got the Third best player also took the third worst player, etc
This is shown:
We can see that it also meets all of the constraints of the model, but has a Standard Deviation 0.00368, that isn’t as low as the Solver solution 0.001699.
What are these Other Solving Methods?
When you were setting up Solver you may have noticed a dialog asking, Select a Solving Method:
The best discussion I have found on these alternative Solver Techniques is shown on the link below
http://www.engineerexcel.com/excel-solver-solving-method-choose/
Closing
We can see how Solver has been used to distribute players according to player ratings and even out teams.
Unfortunately, Shenicus never came back to the forums and so we don’t know how his teams went ?
How have you distributed players or anything else ensuring things are even ?
Let us know in the comments below:
67 Responses
Sure it’s a nice new command. It would be useful if everyone had access to it. But if there is any chance you will be sharing the file with someone who has a onetime payment Office license, or an older version of Office you can’t use it.
That is my biggest gripe with many new features MS is launching. With such vast userbase and existing spreadsheet “systems”, all of these formulas are going to create more trouble than imagined. That said, we should learn new things, especially if you move to a new job chances are you will be using a different version of Excel there.
I love to learn new things, like this new command. But I can’t afford, literally don’t have the money, to keep paying for 365.
This is the thing that especially offends me about the Office 365 pricing scam/scheme. Sure, if they want to milk more money from users using the rental scam, fine I know I don’t have to fall for it. But restricting new “features”, like new commands to 365 is offensive. It makes one-time payment users “second class” customers, especially anyone who has paid for Office 2019. At least in the past new features/commands came only came out every few years, with new versions so there was some logic to the separation. But now the new features are coming every few months and there is no real separation between 2019 and 365, but still they limit the new features to 365. Even 2016 is close enough. MS “accidentally” pushes a few new features to 2016, when they feel like it or when they are too lazy to do the extra work to prevent them from going to 2016.
I agree with Ron I have MS Office 2019 which I used for Charity work but a pensioner I find the cost of the MS365 unaffordable. Perhaps there is some way for a Ms Guru to perhaps create 3rd party update for the stand alone versions.
I will however continues with Ms 365 this year as I have just renewed the subscription
thanks very much for keeping us abreast of latest developments and also the excel community for their useful feed back
regards Brian 18/03/2024
Good point. I suggest using the free MS Office online (you just need onedrive account) to maintain old files and work on them. The only limitation is that it is browser based, so you won’t be able to do many advanced things. But it is better than the alternative of shelling out $100+ every year.
Yes, of course this is the latest and excellent update from Microsoft but this feature will take years to come in the market because most of the people or offices are still using Office 2007 or 2013.
Dear Chandoo Sir
Thank you for updating latest idea this idea is centralized lookup formula all about.
this idea is realy impressive and samart
I couldn’t observe any benefit, over MATCH+INDEX.
Hmm, the base scenario is similar to index+match, but XLOOKUP makes life simple with single formula and default “exact match” setup. Plus I find the “lookup from last” and “less than” “greater than” options very useful and less cryptic than MATCH options.
Thanks for sharing, it added some excitement to my Friday morning! I don’t have 365 but am still excited to be aware of the existence of these features! I know that vlookup on larger sets of data can really take up some resources–it makes sense, it’s performing a lot of operations for us while we sit and sip on coffee. 😉 However, I’m wondering if you’ve you noticed a difference in performance with xlookup? Is it slower, faster, or pretty much the same in terms of calculation speed?
I haven’t tested it against VLOOKUP or INDEX+MATCH. If anything, I would guess that the performance should be similar as they could all use same logic internally. I will try this and share some outcomes later.
I would love to know the results. We’re crunching a ton of data and I love the simplicity of XLOOKUP, but we can’t handle the sluggishness of VLOOKUP. I hope XL is faster!!!
I believe XLOOKUP has been written to deliver exact matches at the same speed as a binary (vlookup’s approximate) search.
Here is a nice overview of differences in performance of different lookup formulas. Unexpected, but XLOOKUP is not always fastest.
https://professor-excel.com/performance-of-xlookup-how-fast-is-the-new-xlookup-vs-vlookup/?amp#What_is_the_8220binary_search_mode8221_of_XLOOKUP
You can use an if logic to wrap around a vlookup with a TRUE argument to speed up lookups.
A nice addition to the function list. Very usefull and easier to use then INDEX + MATCH.
Since XLOOKUP is in beta testing, it would be great if Microsoft development team added a 5th. argument: if_na. That is: if XLOOKUP returns #N/A, an alternate value could be returned instead. Therefore, it wouldn’t be necessary to do =IFNA(XLOOKUP(…), value_if_na).
Good idea. But I feel this can be a dangerous precedent as no other formula in Excel has fail-safe option (other than IFERROR and IFNA ofcourse). So may be leave it to return error.
Don’t overlook the new FILTER function. That has a final [if_empty] setting.
Although I don’t have and expecting to be around soon in EXCEL 2019, my question is there a way to work around the new function “xlookup” but not the old ones.
However it is appreciated tip,thanks
Chandoo
You can also use XLookup like
=Sum(xlookup():Xlookup())
Refer the example 4 at:
https://support.office.com/en-us/article/xlookup-function-b7fd680e-6d10-43e6-84f9-88eae8bf5929?ui=en-US&rs=en-US&ad=US
This makes it hugely powerful as it is returning an address like Index can do
Great point Hui. I am yet to find a practical use case for summing between lookups, but I am pretty sure others will find this useful.
Here is an idea.
If you wish to analyse data for a given month, the relevant portion of the Sales table (sorted by date) is given by
= XLOOKUP( EOMONTH(month,0), EOMONTH(+sales[Date],0), sales,0,1 ) :
XLOOKUP( EOMONTH(month,0), EOMONTH(+sales[Date],0), sales,0,-1 )
which can be referred to as a named formula ‘selected’. Being a reference to the original table, range intersection with columns works. Hence
= XLOOKUP( MAX(selected sales[Net Sales]),
selected sales[Net Sales], selected sales[Sales Person] )
provides an answer to
Who had most sales for February?
Caution: The formula requires 7 separate searches of the data but they are very fast.
I use VLOOKUP a lot with named ranges, are you able to reference those in XLOOKUP?
@Hamish… you should be able to use any reference styles that work with other formulas in XLOOKUP. So yes for names, structural, cell and references to other sheets / workbooks.
Hamish, Yes it all works perfectly. That includes cases in which the data table does not comprise raw data but rather is made up of dynamic arrays. Naming the anchor cell of each dynamic array allows expressions such as
= XLOOKUP( MAX(selectedNetSales#), selectedNetSales#, selectedSalesPerson# )
Conversely, if the returned field is comprised of anchor cells for separate dynamic lists (e.g. employment data for the specified salesman) then the list can be returned by adding ‘#’
=XLOOKUP(0,sales[Net Sales],EmployeeInfo,1)#
Since the documentation says it returns a reference array, could you write formulas that could answer questions that need to perform a function upon a result set that contains multiple rows such as:
1. What is the total Profit/Loss for SalesPersons named [Jamie]?
2. What is the MAX/MIN Net Sales for SalesPersons named [Jamie]?
3. What was the Average Net Sales for everyone that had exactly [8] Customers?
I think the answer to your question is ‘no’ unless you are willing to sort the table so that the records you wish to aggregate form a continuous range. That is, the formula
= SUM(
XLOOKUP(salesPerson,sales[Sales Person],sales[Profit / Loss],,,1):
XLOOKUP(salesPerson,sales[Sales Person],sales[Profit / Loss],,,-1))
only works if the data is sorted by Sales Person.
Otherwise it looks like SUMIFS (and similar) offers the best solutions with FILTER a close second.
= SUMIFS( sales[Profit / Loss], sales[Sales Person], salesPerson )
= SUM( FILTER(sales[Profit / Loss], sales[Sales Person]=salesPerson ) )
XLOOKUP allows us to look for a variable in a column and return a value from a row: combining VLOOKUP ad HLOOKUP in essence.
I watched a video last night in which the presenter showed an example that returned an error. The solution that the presented was using is this: =XLOOKUP(A4,B7:B9,C6:E6)
To see the problem in action, put a b c in the range B7:B9 and 1 2 3 in the range C6:E6 and in A4 enter a or b or c
I solved this problem in this way:
=XLOOKUP(A12,B15:B17,TRANSPOSE(C14:E14))
I have also set up a financial analysis example in which I wanted to find, for every line item in an income statement, which month was exactly equal to the mean of that row or which was immediately below the mean or immediately above it. Or Median, or Standard Deviation …
I used XLOOKUP() and IFS() together with Data Validation (although that is optional) and while the formula is a little unwieldy, again I am effectively combining vertical and horizontal lookups.
Excellent find and tip Duncan 🙂
Hi,
Can you please tell me if there is any way to return multiple values with a single match.
Thanks in Advance
when will be in excel 2019
Thanks
Never.
“New features” like the XLookUp() command are only added to Office 365. They will never be added to Office 2019. They may show up in Office V-Next, when ever it comes out, in the near future. MS has not yet announced a new version. If they follow the pattern in the last few versions that would be fall 2021. But that is only a guess.
I have it now in office 2021
I downloaded your sample spreadsheet and three of your first seven examples are incorrect. Then I stopped.
Which version of Excel are you running? XLOOKUP doesn’t work in any version except Office 365.
Hi, Chandoo.
Great tips, thanks!
In example #11, “What is the ‘net sales’ for Johnson? = 1540” the formula only takes into account the first match for Johnson (D10)?
In row 21 Johnson appears again so the correct answer should be 4192 (D10 + D21).
Imagine a DB with hundreds of records!
How can we deal with duplicates using XLOOKUP?
Thanks.
Is there an easy way to handle if the cell is blank in the data table to prove the result of a blank? With VLOOKUP, previously to get this result, I had to do:
=IF(VLOOKUP($B2,data,6,FALSE)=””,””,VLOOKUP($B2,data,6,FALSE))
I am hoping that I don’t have to resort to the same lengthy format. I did try the “Value Not Found” example you provided (love it). However that is when the search value is not listed, not when the search value is found and the result value is a blank cell.
Thanks for everything you do!!!!
Hi Sherry,
Are you using the IF formula to show “” instead of 0 ?
If so, you can use this structure
=XLOOKUP($B$2, data[col1], data[col6]) & “”
This will force 0 to convert to empty space. It won’t impact other results though, (assuming column 6 is text)
column 6 is a date.
A bit longer, but to force the ‘value not found’ you could remove the entry from the lookup array
= XLOOKUP(lookupValue,
IF(data[col6]””, data[col1]),
data[col6], “Missing data”)
Hi Chandoo,
I’ve been waiting for this function for months so that I could replace all my INDEX / MATCH / MATCH statements. However, I have hit a snag with using nested XLOOKUPs as replacements. If the inner XLOOKUP can’t find a value, then whatever value I specify as the [if not found] value causes the outer XLOOKUP to fail and return #VALUE. So the [if not found] functionality works if a single XLOOKUP can’t find the search value, but it causes nested XLOOKUPs to fail. Can you see any way around that?
Thanks
Hey Stuart… Can you share an example of what result you are expecting in nested case? One option is to use a single IFERROR outside all the nested functions.
@Stuart
Do not limit yourself to thinking of [if_not_found] as being a text string, e.g. “Oops”; it can be a formula in its own right, returning a default row from the original table or even a lookup from an alternative table.
What it must return is an array in order to form a valid parameter for the outer XLOOKUP.
Hi Peter,
You’ve got it! As you suggest, by setting the inner XLOOKUP to return an array full of zeroes (or whatever) solves the problem. The outer XLOOKUP can of course just have 0, or whatever, stated its if_not_found value.
I am surprised that I haven’t come across this issue or solution anywhere else. There are lots of blogs / videos which mention using nested XLOOKUPs as a replacement for INDEX / MATCH / MATCH. I can’t say I’ve read or watched them all, but the ones I have don’t mention this issue. I suspect there are / will be a lot of people getting #N/As or, worse, #VALUES depending on what they specify as the inner function’s if_not_found.
Thanks for your help!
I am trying to lookup a date and name and return the number of hours from another worksheet? If I’m mixing text and dates, will this still work?
Great article. But,…two questions:
1) I do have Office 365. Yet, the XLookup is not recognized by Excel. Your sample file displays a #NAME? Why?
2) In your samplefile you have a leading ‘_xlfn.’ in front of the formula. Why is that?
Hi Michael…
Can you confirm what is your current version of Excel is? Also see if you can update to newer version. You can do both from File > Account.
Great Job..
My values that I want to join are not exact, i.e.
000025868 and 0000258 68 Total
Is there a way to join the data?
Interesting. Assuming the space is in the lookup column, try this:
=xlookup(“000025868″, substitute(lookup_col, ” “,””), result_col)
Getting a #N/A as the results.
Is there a way to convert “0000258 68 Total” to 000025868 (or visa versa) before I run the =XLOOKUP?
If you just want to remove the word “total” at the end, use SUBSTITUTE for that. If there can be other words, you are better off first running the data thru Power Query so you can clean it.
One thing that is possible is to take a numeric lookup value and convert it to text before searching a text lookup array. For example
= XLOOKUP(TEXT( value, “0000000\?00\*” ), array, return, , 2 )
will perform a search with wildcards that allow “Total” to be appended or any character to be inserted two digits before the end of the number.
That would pick up
“0000258 68 Total”
but you would need an alternative test to match the number 25868, itself.
Check the reference, while selecting data the xlookup function automatically starts from new line. Try changing it to the first row and it would work.
YOU ARE THE EXCEL KING!
Thank you
Hi Chandoo,
I have 2 sheets with 5 columns. data in columns A:C is similar except that changes are made in columns A and C. I want to lookup in column C in Sheet2 and update Sheet1 columns A:C.
for example
Sheet1
ColA ColB ColC
123 AB12 One
234 BC23
323 CB22 Six
Sheet2
ColA ColB ColC
123 AB12 One
234 BB22 Two
323 CB22 Six
I don’t think we can claim that XLOOKUP “replaces” INDEX+MATCH. Yes, it provides a suitably powerful alternative, and is absolutely a full replacement for VLOOKUP and HLOOKUP, but it can’t easily play some of the “math” games that are possible with INDEX+MATCH and sometimes even necessary when the data isn’t in a convenient layout.
What if you needed the row above or below the match or if the data was laid out in repeating sections where you first needed to know the location of the section header and then the location of a given item within each section? Both of those problems can be solved with plus/minus shifting of the number returned from the MATCH.
So I would argue that INDEX+XMATCH are the true replacement for INDEX+MATCH, thus taking full advantage of the X — defaulting to exact matches, virtual sorting, and so on — while preserving the ability to “shift” the match as needed.
I’m looking for a price in a multiple column price list. With Vlookup, I specified the entire table and for the column, looked at the user selected model/column. In Xlookup, how to specify the column number and the range up and down or can I just specify the column number only?
One advantage that VLOOKUP retains over XLOOKUP is the ability to supply a lookup column number dynamically, as a purely numerical result of a calculation. To replicate this functionality using XLOOKUP, you would need seperate logic to calculate the column reference (i.e. the column’s number, range name or range address) and pass it to the XLOOKUP formula. You could do this inside the XLOOKUP function by setting up the 3rd param of XLOOKUP to be based on your “user selected model/column”.
Using Xlookup with “match mode” = -1 and “if not found” = “ABC”
Now if the lookup value is not found in the lookup_array excel gives the the highest value from the return_array.
This is not what I expect from xlookup.
It should return “ABC”
Can you explain why?
Chandoo,
I am having trouble with XLookUp. How do I get it to return multiple values such as employees with salary greater than $45,000 or to sum all the sales in the East region? Are these more pivot table inquires?
Is XLOOKUP more useful for finding one record than multiple records?
Thank you,
Jennifer Jeffords
Hi Chandoo,
Is it possible to use XLOOKUP to return a status such as “Checked” and “NoCheck”(something similar to IF stmt)
Thank you.
I used the index and match to look up the hourly rate for a job classification as a part of a drop down. Now, I want to calculate the hourly rate multiplied by hours worked and the cell will not calculate. What might be the problem? The results cell of the look-up is formatted to be currency?
You show return array can be more than 1 column but what about Look up array? What if I want to find a value than can be in 1 of 3 columns and then return one value from another column.
You can use XLOOKUP for such things too.
For example, if you have three columns: home phone, cell phone and email address
and a column with customer name
and you want to lookup the name of the customer when you specify any value from one of those 3 columns,
you can use the below XLOOKUP.
=XLOOKUP(TRUE,BYROW(C3:E22=I2,LAMBDA(a, OR(a))), B3:B22, “No record found!”)
Here I2 contains the search criteria (either home phone, cell phone or email)
B3:B22 have names
C3:E22 have the home / cell / email values
Hi my name is Musawir Rasool i am from India in a state of jammu and Kashmir I love watching your videos and lot from your videos
Thanks
And one more can u teach me full power bi?
Hi Chandoo,
I was referring to your xlookup-examples file, and in that I saw your formula for Sl. 8 – Who has least sales? You wrote formula =XLOOKUP(0,sales[Net Sales],sales[Sales Person],,1) but I think a more better way would be to write =XLOOKUP(MIN(sales[Net Sales]),sales[Net Sales],sales[Sales Person],,1). This is because your formula would not reliable unless you’re specifically looking for a salesperson who has exactly 0 in sales, which is not the same as the least sales — unless 0 happens to be the lowest. Also, the 1 as the last argument means “approximate match in ascending order,” which could return wrong results if 0 isn’t found.