Forecasting with uncertainty
causal.app
causal.app
If you liked this, then I'd definitely recommend reading "The Flaw of Averages" by Sam Savage. It talks about this stuff in a lot more detail, and the style is very entertaining — not at all what you'd expect from a statistics book.
Have you thought to incorporate the "Minimise Maximum Regret" concept? I suppose it is quite an opinionated strategy, but it is a very interesting approach to decisioning, and supposedly leads to robust decisions.
Given current impression share for my campaigns, what would incremental spend do for CPA and position?
What would be the expected CPA to move from avg position of 1.8 to 1.4
Can I tie CRM data to get value of leads/opportunities and optimize for that?
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.
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
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).
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.
it's hard to evaluate the modeling capabilities from a few pages and blog posts. how does it compare to crystal ball on excel, for example?
Compared to Crystal Ball, it can do all the distribution stuff — variables can take on any kind of distribution you define. But we (try to) make it trivial to use these — you can write formulas like "5 to 10", and we map that onto a sensible distribution for you, so you don't need any probability/stats knowledge, whereas CB is a lot more technical. The CB suite also now includes some other tools that can do things like optimisation, which Causal doesn't do yet.
Causal works in most modern browsers, and we're working on handling non-Chrome browsers better :) Not sure what you mean by "coupled to the google ecosystem"!