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:
36 Responses to “Visualizing Financial Metrics – 30 Alternatives”
Although I am one of the contestants, I must wholeheartedly admit that the Dashboard of Chandeep is the best of all. It's design, colors, message-conveying is the greatest. My regards!
I would like to learn how Chandeep highlighted the graph when he made a selection on the slicer.
Any links to previous posts perhaps where this was covered by Chandoo?
Thank You
Ahmad
Dashboard from Abhay simply rocks. To the point and conveys the intended message even for a novice.
Infographic by Pinank - is looking good
I have also contributed to this contest. I am really inspired by various entries in above post. Based on following parameters i would like to rate these:
1. Explanatory - Whether dashboard will be used to explain certain thing or mention a story. This type of dashboard will be static.
2. Exploratory - Here user would like to interact more with the dashboard to extract the relevant story or meaning which is not apparent. Hence, this type dashboard needs to have more interactivity.
3. Scalability - If new or more data can be added to dashboard and still the functionality will work. If user wants to add more companies, years, etc. will it work.
Based on above criteria I would rate following entries as top ones:
1. Explanatory - by Pinank
2. Exploratory - by Chandeep
3. Scalability - In most of the entries additional work would be required to include more data except for mine. new years or companies can be easily added and analysed in chart by me.
These entries are really inspiring i will definitely use it to revise my dashboard.
Abhay's dashboard is good however, if Chandeep can go with the trend analysis Abhay has done (line graphs), then maybe Chandeep's dashboard can excel.
And now I'm angry that I haven't noticed contest announcement earlier and I've sent what I've sent... Building a dashoboard was supposed to be my goal but lack of time forced me to sent sth simplier and now I can see how big mistake it was (when it comes to fighting a competition like this). Nice work guys! It's realy inspiring! Even less advanced works are intresting because of different task approach. So wance again: thanks 🙂
If I had to choose the best ones (IMHO) I would go for William and Edouard as a second place (for both). Despite some weak sides (like label errors or "work place" next to a final chart) they meet my sense of clear data visualisation and contain intresting interactive elements.
The best entry is definitly Chandeep's. Although there was some failing with automatical comenting feature (#arg! in my Excel'10) it's full of advanced dashboarding tricks which makes it easy to read. Furthermore, as one of the few he finished(?) his project - it opens in a "secured mode", with no place to mess anything, no data trash - just choose, point and read/print.
It all deserves to get the Grand Prize!
and BTW: when can we expect another contest? 🙂
Big round of applause to everyone who participated. I'm amazed at the creativity of our community. 🙂
My vote would be for Chandeep, MF Wong, and Miguel.
I have not contributed, but have read this post with a lot of interest. I would like to congratulate all participants for there work & inventiveness.
My #1 spot goes to Gerald for showing all the data in 1 graph & to have still kept it simple & readable.
I would give a prize for innovation to Pinank for the use of icons.
Great to see so much creativity.
I have not contributed also, but have wait his post for a long time (because I have the same kind of issue in my "daily life").
My top 3 is the following :
- Pinank for the effeiciency and for the style
- Arnaud for the calculation behind the chart
- Miguel for the elegant business oriented dashboard
All the entries look very good. However I feel Pinanks entry seems the best as it is very explanatory with good innovative thoughts.
Hi all,
Some brilliant dashboard and interactive entries - really nice stuff and lots of clever tricks.
However, given that the initial question was "Need to quickly visualize 3 variables ( Company, years, Financials) in a single […] chart", unfortunately I don't think any dashboards - as cool as they are - really answer that question. The interactives also assume that this will be opened in Excel rather than seen in a printed hand-out, which essentially means you'd need multiple charts to show all the variables or be limited to a computer screen. Even Chandoo's initial panel chart approach - which is static, and also very simple and clean - is not really a 'single chart'. Furthermore, most of the interactives don't actually show all variables at once but rather slice the data into more manageable chunks, which is not staying true to the original brief.
So, in light of the above, I'd vote for Gerald in first place, Edwin in second and finally my third chart option in third place (yes, I know, voting for yourself is poor form but unfortunately I think the original question disqualifies most of the entries).
Anyway, a fun competition and thanks for following up on this Chandoo.
I am once again in awe of the submittals to a Chandoo contest. The results are so impressive. I have been trying to build nice dashboards for years and take so many courses, but I don't seem to have the eye for design. The color choices, fonts and chart choices are so important and I'm amazed at how some people really have a great talent for making the best selections.
It's nice to have such quality inspiration!
I saw Chandeep's entry on his website and I must say that I was very impressed by it. Simply loved it. Somewhat makes it difficult to keep an open mind towards the other entries.
My ranking:
1. Chandeep for its completeness as dashboard.
2. MF Wong/Miguel for "simple" but smart graphs.
3. Pinank's entry looks like a page from a glossy magazine.
During scrolling I stopped at Chirayu's entry: easy to the eye.
But honestly congrats too all for having the balls to participate and thank you for sharing your creativity!! Hat's off to you.
Miguel, MF Wong, and Pinank.
Thanks to Chandoo and everyone who contributed for the great ideas.
Hi,
I personally liked the dashboard of:
1. Chandeep - His dashboard is clear, crisp and informative, his color combination and design is awesome, also he has shared few details like operating leverage plus he has added few comments. In totality, its a complete packaged dashboard.
2. Miguel - His dashboard is simple and all the information is visible in one shot.
It's very interesting looking through these - you can definitely tell who's done courses in dashboard design and with whom!
I particularly liked Pawels 'sperm chart' 😉 ... squint your eyes - you'll see what I mean). each of the charts or dashboards are put together well - but I agree with Elchin on this one - Chandeeps dashboard set 'tells a story' of the data. Student of Mr Few??
Without a doubt, Chandeep deserves #1. #2 goes to Abhay, and #3 to Pinhank, for the great presentation style if nothing else.
MF Wong
Do not apologize for any delay! Moving from one town to the next only 10 miles away is tough enough - let alone a family moving from one country to another!
THANK YOU for this excellent post!
As one of the participants, I have been looking forward to this post for long. But totally understood the reason of delay, so never mind! Hope all is well in NZ.
Thank you very much to those who like my chart! 🙂
Also thanks Chandoo for suggesting a name for it "Container Chart", which I have never thought about.
Personally I like the infographic by Pinank. Very outstanding design and use of icons. My two-cent worth: Just the lower part of "Yearly Trend" is actually good enough to answer the question, isn't it? 😉
Cheers,
What an outburst of creativity!
Vote for Chandeep and Pinank!
Agreed!
Awesome dashboards
Infographic by Pinank is awesome
Thank you so much for sharing!! i learn so much from these posts
Highly appreciated
Ahmad
South Africa
Fantastic responses from all the contestants. Some really great ideas. I'm inspired and will adapt some of these to my own dashboard work. Thanks for hosting such a great contest!!
Thank you for sharing this valuable resources !!!
I have only a couple of question that wasn't able to solve regarding data-origin.
Nowadays I have the data coming from a "current" situation from a big database containing all kind purchase-orders information of many different projects. I can calculate the current status of each project investments, but I am not able to track automatically the progress of it month to month or week to week by freezing the calculated metrics on each date. This would let me calculate new graphs and the speed of investments execution.
My question would be, if it is possible to calculate something with an excel formula and automatically freeze this values in a new row or new column. I guess that right now, Basic is the only way, but I guess that there could be a function to copy-a-range, insert-range-as-value-only as a new row or a new column or display everything down or left.
This would preserve the excel formulas defined, and add new data, everytime that it is re-calculated.
Any idea?
Great post , loved all chart representation. Congratulations to all participants and winners.
I need updates to this article.
I didn't even realize this got posted. Came across it today. Thanks
Fantastic post but I was wondering if you could write
a litte more on this subject? I'd be very thankful if you could elaborate a
little bit further. Thank you!
Hi Chandoo,
I comeback after a long time on your Blog. So I saw it lately. Its a brilliant idea.
I like all entries and these are amazing efforts from all participants.
Regards
The report presented by Pinanik is excellent and very innovative. Could be an interesting work for portfolio presentation