using sum and countifs to get a percentage of 'yes'es across multiple columns by month and team - is there a simpler way? - google-sheets

Question

I've been asked to create a summary for some google form responses, and though I have a working solution, I can't help but feel there must be a more elegant one.
The form collects data related to case checking - every month each team (there's 100+ teams) has to check a certain number of cases based on how many staff are in their team, and enter the results for each case they've checked in the google form. The team that have set this up want me to summarise the data by team, month, and section of the form (preliminary questions, case recording, outcomes, etc). There are 8 sections on the live form, ranging from 1-13 questions, all with Yes/No/NA/blank answers.
(honestly, it's not how I'd have approached setting all this up, but that is out of my hands!)
So they're essentially looking for a live monthly summary with team names down the side, section names along the top, and a %age completed that will keep up with entries as they come in (where we can also use importrange and query to pull the relevant bits into other google sheet summaries, as and when needed).
What I've currently got is this:
=iferror(sum(countifs('Form Responses'!$B:$B,$A3,'Form
Responses'!$F:$F,"Yes",'Form Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1)),countifs('Form
Responses'!$B:$B,$A3,'Form Responses'!$G:$G,"Yes",'Form
Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1)),countifs('Form
Responses'!$B:$B,$A3,'Form Responses'!$H:$H,"Yes",'Form
Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1)),countifs('Form
Responses'!$B:$B,$A3,'Form Responses'!$I:$I,"Yes",'Form
Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1)),countifs('Form
Responses'!$B:$B,$A3,'Form Responses'!$J:$J,"Yes",'Form
Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1)),countifs('Form
Responses'!$B:$B,$A3,'Form Responses'!$K:$K,"Yes",'Form
Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1)))/(countifs('Form
Responses'!$B:$B,$A3,'Form Responses'!$E:$E,">="&$B$1,'Form
Responses'!$E:$E,"<"&edate($B$1,1))*6),0)
It works, but it feels like a bit of a brute-force-and-ignorance solution. I've tried countifs & array, I've looked a pivot but I can't get the section groups, I've had a play with query but I can't figure out how to ask it to count all Yeses in multiple columns at once.
Is there a more elegant solution, or do I have to resign myself to setting up the next financial year's summaries like this?
Edit:

Answer 1

You can use plain array boolean multiplication to achieve the count, as trues are converted to 1s and false are converted to 0s:
=TO_PERCENT(ARRAYFORMULA(
SUM((f!F1:K="Yes")*(f!E1:E>=B1)*(f!E1:E<EDATE(B1,1))*(f!B:B=A3))/
SUM(6*(f!E1:E>=B1)*(f!E1:E<EDATE(B1,1))*(f!B:B=A3))
)
)
Renamed Form Responses to f
Numerator: SUM of
Question filter (f!F:K =Yes) and
Month filter (f!E:E is within month of B1) and
Team filter(B:B = A3)
Denominator: 6 times the SUM of
Month filter (f!E:E is within month of B1) and
Team filter(B:B = A3)

Answer 2

On this sample sheet that you provided you'll notice two new tabs. MK.Retab and MK.Summary.
On MK.Retab is a single formula in A2 that "re-tabulates" all of your survey data into a format that is much easier to analyze going forward. That tab can be "hidden" on your real project. It will continue to build the 6 column dataset forever. It would be a sort of "back end" sheet, only used to supply data to any further downstream analysis.
On MK.Summary is a single formula in cell A1 that Query's that dataset from MK.Retab and shows the percentage of Yes's by month by section by team in a format similar to what you proposed. I coded it to display the most recent month at the left, immediately to the right of the team names, and to push historical data off to the right. Even though people are often used to seeing time go from left to right, I find that the opposite method nice because it keeps you from having to scroll sideways to see the most recent data. It is very simple to change should you want to by getting rid of the "desc" that you find in the "order by" clause of the query string.
I find this kind of two step solution to problems like your useful, because while the summary migth not be exactly what you want, it's always easier to build formulas and analyses off of the data as laid out in the MK.Retab sheet.
As for the formula in MK.Retab, it is based on a method that I came up with a while back that constructs a large vlookup where the [search key] is actually a sequence of decimal numbers that is built by counting the number of rows in your real data set and multiplying by the number of columns of data that need to be repeated for each row. I built a demo some time ago that I'm happy to share with folks if you want to understand better how it works.
You said that your goal was to understand the formulas so that you could modify them going forward as needed. I'm not sure how easy that will be to do, but I can try my best to answer any questions you might have about the method or the solution generally.
What I can tell you is that some of the formulas are more complicated than they need to be because you just used Q1 Q2 Q3 etc instead of the actual questions. if you had a list of the questions asked somewhere (on some other tab, say), and what you wanted to call/name their corresponding "sections", it would make the formula significantly less complicated. As it stands, I had to use the appearance of the word "Comments", in row 1 to distinguish between where one section ended and another section began. The upside to that decision though, is that the formula I wrote is infinitely expandable to the right. That is, if you were to add another 100 columns worth of questions and answers to the sample set here, the formula would be able to handle that and break it out, so long as there was the word "Comments" between each section.
Hope all this helps.