Average of ratios ("on the fly") in excel table - excel

Question

I have this excel table used as a DB named "csv" :
Ticket agent_wait client_wait
1 200 105
2 10 50
3 172 324
I'd like to calculate the average of the ratios of the agent wait. ration_agent being calculated as agent_wait / (agent_wait + client_wait).
If the table were like this:
Ticket agent_wait client_wait ratio_agent
1 200 105 0.65
2 10 50 0.16
3 172 324 0.24
I'd just do the average of the ratio_agent column with =AVERAGE(csv[ratio_agent]).
The problem is that this last column does not exist and I don't want to create an additional column just for this calculation.
Is there a way to do this with only a formula ?
I already tried
=AVERAGE(csv[agent_wait]/(csv[agent_wait]+csv[client_wait])) but it gives me the answer for only one line.

Answer 1

You can use the formula you have used, but you need to enter it as an array formula. What this means is, after entering the formula, do not press Enter, but hold Ctrl+Shift and then press Enter. The resulting formula will turn into this after you do that:
{=AVERAGE(csv[agent_wait]/(csv[agent_wait]+csv[client_wait]))}
And give your the value you are looking for. Use the correct columns (first csv[agent_want] to csv[client_wait]) if you are looking for the average client_wait instead.
It has come to me that your question might be an XY problem. Please take a read on this answer. It might help you decide on what you are actually looking for.
In brief if you want a measure of how much time:
agents spend waiting, out of all the waiting between agents and clients, calculate the totals first and get the average of these totals. Outliers e.g. a special case where an agent spent lots more time on a client than the client themselves will heavily affect this measure. Use this measure if you want to know how much time agents spend waiting when opposed to how much clients wait.
=SUM(csv(agent_wait)/sum(csv[agent_wait]+csv[client_wait]))
agents each spend waiting on any particular call, calculate the ratios first then the average of these. Outliers will not affect this measure by much and give an expected ratio of time an agent might spend on any interaction with a client. Use this measure if you want to have a guideline as to how much an agent should spend waiting for each unit of time a client spends waiting.
=AVERAGE(csv[agent_wait]/(csv[agent_wait]+csv[client_wait]))

Answer 2

It also wouldn't be correct to do the =AVERAGE(csv[ration_agent]) calculation. An average of the average isn't the overall average. You need to sum the parts and then compute the overall average using those parts.
Ticket | agent_wait | client_wait | ratio_agent
------ | ---------- | ----------- | -----------
1 | 200 | 105 | 0.656
2 | 10 | 50 | 0.167
3 | 172 | 324 | 0.347
Total | 382 | 479 | ?????
The question is what goes in for the ?????.
If you take the average of the ratio_agent column (i.e. =AVERAGE(Table1[ratio_agent])) then you get 0.390.
But if you compute the ratio again, but with the column totals, like =csv[[#Totals],[agent_wait]]/(csv[[#Totals],[agent_wait]]+csv[[#Totals],[client_wait]]), then you get the true answer: 0.444.
To see how this is true try this set of data:
Ticket | agent_wait | client_wait | ratio_agent
------ | ---------- | ----------- | -----------
1 | 2000 | 2000 | 0.500
2 | 10 | 1 | 0.909
Total | 2010 | 2001 |
The average of the two ratios is 0.705, but it should be clear that if the total agent wait was 2010 and the total client wait was 2001 then the true average ratio must be closer to 0.500.
Computing it using the correct calculation you get 0.501.