Percentage Business Question: Share change for a brand on total country level is lower than any of its constituent channels

[Toomzyada]

Hello!

I'm doing a business analysis for a brand. I calculated the volume share of this brand (brand sales/category sales*100) for two months and their change vs last year. I did this on total country level by their individual channels. Interestingly, The share change for the total country level is lower than any of the channels when normally you expect the total country share change to fall within the range of the values of its individual channels. Is this mathematically possible? How do you explain it? Below is the table for your reference:

Volume share of a Brand
	last month	this month	change
Total Country	7.2%	6.8%	-0.4%
Channel 1	8.9%	8.8%	-0.1%
Channel 2	3.7%	3.8%	0.1%
Channel 3	4.1%	4.0%	-0.1%
Channel 4	1.8%	2.4%	0.6%

 

[stapel]

Hello!

I'm doing a business analysis for a brand. I calculated the volume share of this brand (brand sales/category sales*100) for two months and their change vs last year. I did this on total country level by their individual channels. Interestingly, The share change for the total country level is lower than any of the channels when normally you expect the total country share change to fall within the range of the values of its individual channels. Is this mathematically possible? How do you explain it? Below is the table for your reference:

Volume share of a Brand
	last month	this month	change
Total Country	7.2%	6.8%	-0.4%
Channel 1	8.9%	8.8%	-0.1%
Channel 2	3.7%	3.8%	0.1%
Channel 3	4.1%	4.0%	-0.1%
Channel 4	1.8%	2.4%	0.6%

How are you getting that -0.4 is greater than +0.6?

 

[blamocur]

I don't see any contradiction in your numbers. In fact I came up with a simple numbers for category sales for each channel and month which would match you numbers:
Category sales by channels in last month: 120, 17, 17, 17
Category sales by channels in this month: 102, 20, 20, 20.
BTW, this is not the only possible combination to produce 7.2% and 6.8% for the total using the individual channel percentages.

 

[Toomzyada]

Thanks @blamocur for your response. My point is specifically regarding the last column. Generally when we do these analyses, the share change on total country level (-0.4 in this example), tend to fall within the range of the individual channels (-0.1 to +0.6) and not outside it (Like a weighted average). This was the first time I've seen a value outside it.

 

[Toomzyada]

Hello!

I'm doing a business analysis for a brand. I calculated the volume share of this brand (brand sales/category sales*100) for two months and their change vs last year. I did this on total country level by their individual channels. Interestingly, The share change for the total country level is lower than any of the channels when normally you expect the total country share change to fall within the range of the values of its individual channels. Is this mathematically possible? How do you explain it? Below is the table for your reference:

Volume share of a Brand
	last month	this month	change
Total Country	7.2%	6.8%	-0.4%
Channel 1	8.9%	8.8%	-0.1%
Channel 2	3.7%	3.8%	0.1%
Channel 3	4.1%	4.0%	-0.1%
Channel 4	1.8%	2.4%	0.6%

Change vs previous period*. Column change is the difference of this month and last month.

 

[blamocur]

Thanks @blamocur for your response. My point is specifically regarding the last column. Generally when we do these analyses, the share change on total country level (-0.4 in this example), tend to fall within the range of the individual channels (-0.1 to +0.6) and not outside it (Like a weighted average). This was the first time I've seen a value outside it.

But did you see that the numbers I posted produce exactly the results from your table. I.e., while this seems counter-intuitive it is possible, at least theoretically.