Today is February 29th, and that means, this year we have one more day to be awesome. So lets celebrate it in Excel style!
Lets learn 14 different ways to tell if an year is leap year, using Excel Formulas.
Why 14? because, we are awesome like that.
Why 14 methods to just find the year in cell D4 is leap year or not? Because, we all know that by learning different ways to solve a problem, we become smarter, more awesome and have more fun. So lets roll.
Before we start..,
Since all the 14 methods rely on certain calculations, I have created some names. See below:
All the names are self-explanatory, except the febDays. So lets take a look at it.
febDays formula
For one of the methods, we need to have all the dates in February in a list. If we want the first of Feb as a date, we can use =DATE(year,2,1). But we want all dates in February. That means, we need to use a list (array) in third parameter of DATE like this:
=DATE(year,2,{1,2,3,4,….,28,29})
Instead of typing all the 28/29 numbers, we can use ROW formula to generate these, like:
=ROW($A$1:$A$29) would give me a numbers from 1 thru 29.
But the problem is in many years Feb has only 28 days, and for rest, it has 29 days. So we modify the second part of row formula and use the last DAY of the Feb, like this:
=ROW($A$1: INDEX($A$1:$A$29,DAY(EOMONTH(feb1st,0))))
To get the last day of a month, we use = DAY(EOMONTH(1st date, 0))
I think you can put the rest of pieces together to solve this puzzle.
Moving on,
#1 – The year has 366 days
This is the obvious one. We use =DATE(year+1,1,1)-jan1st=366 to check if there are 366 days between January 1st of next year and this year.
#2 – February 29th is not March 1st
Because in Excel all dates are numbers, when we use a formula like =DATE(2011,2,29), Excel gives us the date of March 1st, even though we wanted 29th Day of February in 2011. So a simple leap year check is to see if February 29 is March 1st or not!
=DATE(year,2,29)<>mar1st
#3 – February has 29 days
This is another obvious test. In a leap year, February has 29 days. So=DAY(EOMONTH(feb1st,0))=29 will be true for leap years.
#4 – February 1st and March 1st are not on same day of week
In non leap years, Feb has 28 days (a multiple of 7), so both Feb and March start on same day of week. So, =WEEKDAY(feb1st)<>WEEKDAY(mar1st) will be TRUE for leap years.
#5 – Adding 365 to January 1st does not change year
Well, that is obvious too. =YEAR(jan1st)=YEAR(jan1st+365) is TRUE for leap years.
#6 – 30th Day of February is March 1st
If an year is leap year, 30th day of February [DATE(year,2,30)] is same as March 1st. So, =DATE(year,2,30)=mar1st is TRUE for leap years.
#7 – 0th Day of March is Feb 29th
In real world there is no zeroth day for any month. But in Excel, since all dates are numbers, 0th day refers to last day of previous month. So, =DAY(DATE(year,3,0))=29 will be TRUE in leap years.
#8 – April 1st and January 1st are on same day of week
In leap years, there are 91 days between January 1st and April 1st. And since 91 is a multiple of 7, both April 1st and January 1st start on same day of week. Hence, =WEEKDAY(jan1st)=WEEKDAY(apr1st) will be true for leap years.
#9 – Only 2 more months start on same day of week as January
In leap years, both April and July start on same day of week as January. (Where as in non-leap years, Only October starts on same day of week as Jan).
To test this, we will of course use the SUMPRODUCT. like this:
=SUMPRODUCT(–(WEEKDAY(DATE(year,ROW($A$2:$A$12),1))=WEEKDAY(jan1st)))=2
The portion WEEKDAY(DATE(year,ROW($A$2:$A$12),1)) gives all the first day of weeks from February to December. And then we just check how many of these are same as January 1st’s week day.
#10 – Next year’s February 1st and this year’s February 2nd are NOT on same day of week
In non-leap years, there are 364 days between February 2nd and next year’s February 1st. Since 364 is a multiple of 7, both of these days are on same day of week. Which is not the case in leap years (as the difference becomes 365). So, =WEEKDAY(feb1st+1)<>WEEKDAY(EDATE(feb1st,12)) will be TRUE for leap years.
#11 – February 1st’s day of week occurs 5 times in that month
This a bit tricky to test, but then again we have SUMPRODUCT. So, =SUMPRODUCT(–(WEEKDAY(febDays)=WEEKDAY(feb1st)))=5 will be TRUE for leap years. The name febDays has all dates in February. I think the rest is easy to understand.
#12 – February starts and ends on same day of week
29 days means both 1st and 29 are on same weekday. So, =WEEKDAY(feb1st)=WEEKDAY(EOMONTH(feb1st,0)) will be true for leap years.
#13 – Spreadsheet day (October 17) and February 1st are on same day of week
Debra, who is a well known Excel blogger & author started the whole spreadsheet day thing. She says, we should celebrate October 17 as spreadsheet day. I love that idea, mainly because, it is just 3 days before my birthday and I like celebrations. And I also like Excel 🙂 So blame her if you do not like this way of testing for leap years.
In leap years, there are 259 days between February 1st and October 17. And since 259 is a multiple of 7 (and 37), we know that they are both on same day of week. So, =WEEKDAY(feb1st)=WEEKDAY(DATE(year,10,17)) is true for leap years.
#14 – Finally, the year is divisible by 4 and if it is divisible by 100, then also by 400
Finally, we are going to test the whole “an year is leap year if it is divisible by 4 and if it is divisible by 100, then it is also divisible by 400” thing. This is a slightly tricky one to test. The formula, =((MOD(year,4)=0)*((MOD(year,100)<>0)+(MOD(year,400)=0))=1) will be TRUE for leap years and false for non-leap years.
Download Leap Year Test Workbook
Click here to download the workbook with all these 14 examples. Play with the formulas, named ranges to understand these techniques.
How do you check it is a leap year?
If you are working and you get paid on first day of a month, then one clear way of knowing leap year is that you get your salary one day later. Other than this, what method would you use to find if an year is leap year. Go ahead and be creative. Share your ideas and formulas using comments. Next leap day is 4 years away. Go
Want to learn how to Dates & Times in Excel – Read these:
If you deal with data that has a lot of date / time stuff, then understanding various Excel features in this area is a must. Read below pages to learn more.
- 10 tips on working with dates & times in Excel
- Calculate difference between 2 dates
- Find thanksgiving day for any year
- Check if 2 ranges of dates overlap
- Rolling months in Excel
- How to convert text to dates
- Even more on Excel dates & times
Want to master Date & Other Excel Formulas?
If you want to learn how various formulas in this post work and know more about everyday Excel formulas, please consider joining my Excel Formula crash course. It has detailed video tutorials on more than 40 everyday Excel formulas and teaches you all the powerful techniques to become a formula ninja.
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