I would imagine it is targeted at a similar audience, it just lets you answer a better question.

Given the current impression share for my campaigns, what would incremental spend do for CPA and position with 95% certainty?

What would be the expected CPA in 50% of cases to move from avg position of 1.8 to 1.4? This question can be asked in reverse again with a degree of certainty attached.

The answers to the questions you posted are likely to be averages and possibly medians if the posterior is Gaussian (or close enough). Mixing uncertainty into the equation allows you to provide a floor on probabilistic expectation, it also allows you to ask what the best case is, say the 95th percentile.

I've stuck to 95 and medians here but you can use any percentile you'd feel comfortable with.

I use these techniques for day-to-day estimation in software development, usually for things like project timelines, system requirements, etc.

I often run into developers who think "there is no way to estimate when we will be done". What I think they usually mean is that they cannot estimate a single time in which it will be done, which is completely fair. However, if they are being honest with themselves, I think they can often estimate a range of possible outcomes. Adding a new "Contact Us" form may take a few hours or a few days, but it isn't going to take 1 year.

One of my bigger successes with this kind of model was sizing the resource requirements for a brand new high-performance system that was in it's early stages of development. I created a model that started with what we knew so far from out performance testing, with uncertainty for everything, and projected forward to different confidence levels of sizing. We ended up being pretty having just a little extra, which was perfect considering the multi-month procurement process.

Very cool! What tools are you using for this right now?

For my more routine analysis of LOE/budget, where it is mostly a straightforward summation, I have a template spreadsheet that I just reuse. For more complex cases, I hand write the equations and error-propagation into a custom sheet. A little time intensive, but it gives me an excuse to practice multi-variable calculus.

Glad you like the concept! The post, and Causal, are targeted at anyone who needs to work with numbers —

With those ad questions, there's no getting around the fact that you need to come up with a 'model' for how, e.g. incremental spend impacts CPA/position. Once you have a model you're happy with, there's always going to be uncertainty around aspects of it, and you'll ideally want to account for it. Simulation is a good way to do that.

Causal has data connections that you can use to pull stuff from your CRM. Depending on what you mean by 'optimize', we might be able to do that too — happy to chat in more detail if you're interested: taimur @ causal . app

yeah i suppose i was just wondering how flexible it was and how it fits in the day-to-day of addressing client inquiries. and by optimize in this sense i guess i meant analyze - as in tie that data into forecast projections. i'll play with it and see!

I'm an advertiser, worked agency & in-house, and have used approaches like Causal's in the past.

As the other comments mention, simulations aren't going to let you answer these questions if you can't already answer them, but they can provide you with uncertainty ranges which are valuable in their own right.

Particularly if you're agency-side, being able to go to a client with an uncertainty range for some forecasted KPI is so much better than having to give a single number. Works for them because they can understand the risk, and works for you because you're not going to be held to a single number (which you're never likely to hit in practice).

True - i wasn' really asking about the methodology in question moreso the linked-to SaaS offering.