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Not sure you can do any better than a min/max range on this without knowing at least something about the crossover in accounts at the least. e.g. the 12m Facebook users could be completely distinct from the 6m LinkedIn or one group could be a subset of the others.
Worst case scenario is that all your reached people are the same i.e. the 3m LI and 2.4m Twitter are just subsets of the 6m FB and all unreached users are distinct: you've reached 6/(12+1+3.6) = 38.9%. Best case scenario: the reverse, all your reached people are distinct and the overlap in accounts is 100%, i.e. (6+3+2.4)/12 = 95%.
Other than that you have to make assumptions - in your calculation it looks like you've assumed all LinkedIn users have a Facebook account and your probability of reaching them on one platform is independent of whether you reached them on the other.
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Worst case is easy. Find the largest single population % * effectiveness and assume that dominates all the others
best case is similarly easy. Assume no overlap and just keep summing the population*effectiveness until you reach the total population.
For the tough bit I made a guess, and just messing about in Excel (attached) quickly...
I've assumed that the users are randomly spread (which is unlikely).
Starting out
universe population: 30,000,000
effectiveness of no advertising: 0%so you have 100% of the population untouched
next step
facebook: population 12m (40%)
effectiveness: 50%
so you'd expect someone at random to have a 20% chance of being hit by facebook
so given you have the entire population left, your chance of them being hit by nothing or facebook is 0% + 20%next, Linkedin
pop: 4m (13.33%)
effectiveness: 75%
random hit by linkedin: 10%
pop hit by linkedin after being missed by the prev lot. (100-20%) * 10% = 8%
total hit population 28%Twitter
pop: 6m (20%)
effectiveness: 40%
random hit by twitter: 8%
pop hit by linkedin after being missed by the prev lot. (100-28%) * 8% = 5.76%
total hit population 33.76%
etc.
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frankenbike
duncs
@Soul
Wondering if anyone here might have some thoughts on how to look at a problem I have...
I'm trying to understand how I can deduplicate reach across channels. For example, I'm targeting an audience in the UK.
On FB, there are 12m of them and I've reached 50% (or 6m people)
On LinkedIn, there are 4m of them and I've reach 75% (or 3m people)
On Twitter, there are 6m of them and I've reached 40% (or 2.4m people)
Is there a way of calculating the probability of the maximum reach I can achieve when deduplicating the data sets, ie, not knowing the crossover in data between them, how many total people I may have reached? It won't be cumulative (6+3+2.4) and it won't be 100% duplication (6m people) but somewhere in the middle.
I think, for two channels, I can calculate as follows:
P(FB)=6/12
P(LinkedIn)=3/12 - Using largest audience size as a base...
P(FB)xP(LinkedIn) = 6/12x3/12 = 0.125
Total possible reach is therefore 6+3=9
With de-duped reach being 9/12-0.125 = 62.5% or 12x62.5% or 7.5m people
Problem is, I have no idea how to scale this to multiple channels.
@Sam_w - I guess you probably deal with this a lot...