How do you decide an app launch UA budget?

+ 1 on Eric's answer, especially re launch budgets being a function of cashflow - and how scenario plans can be very effective(elements of which I've used in launches as well). To address a couple of other aspects of your question:

1. One metric other than what you've mentioned that can be critical is k-factor - either from referrals or organic lift from paid installs(or both). Getting a clearer idea of how much 'free' traffic you can expect can be valuable in modeling out your growth.

2. Rather than a 'trampoline' launch, I've been a part of launches where a staggered incremental rollout has been effective. What this means is to spend an initial launch budget(suggest starting anywhere from $10k to $100k/month based on your cashflow), assess actual revenue and LTV based on your launch. And if your actual LTV(or ROAS) is close to what your predicted LTV/ROAS is, then you scale up within your SANs - and/or to additional channels.

Good question. I think you need to establish a few other things before you set a "launch budget":

• In a "massive success" scenario, how much cash do we have available to spend on this?
• What kind of payback do we need in order for this to be economically viable at various levels of expenditure?

I've made the point in a number of articles on Mobile Dev Memo that an advertiser can go broke buying LTV > CAC profitable traffic. So what's more important to think about in setting a budget is what kind of payback you need against various levels of spend to produce a healthy level of cash flow.

That said, a trampoline launch is not a good idea in the year 2020: there's simply no reason to "go big" at some arbitrary launch date with the impact of platform featuring having diminished to the extent it has. You can adjust budgets in real-time based on early-funnel metrics during your launch week; you don't need to commit to some level of spend before you set your app live in the App Store and Google Play.

That said, what I recommend (and what I did with the launch of Angry Birds 2) is:

• Create a set of scenarios that lead to various payback windows, oriented around early-stage metrics;
• Decide what total daily budgets should look like in each of those scenarios eg. let's say you break profitable unit economics into three scenarios: "Best Case," "Medium Case," "Worst Case" based on payback windows. How much would you spend each day in those various scenarios? How would that budget be allocated (eg. if you're spending $50k a day, what share does Facebook get? And what about at $20k? $5k?). Answer all of these questions before you go into launch;
• During the launch, at various spend levels, be ready to increase / decrease spend as your validate these Day 0, Day 1, etc. ROAS metrics (and even earlier-funnel metrics like cost per first purchase, etc.).

You often see some bigger companies spend a ton of money on new launches, and I wonder how much of that is due to company politics / having a big marketing team ("When all you have is a hammer...") as well as an inability internally of building a financial model that incorporates things like ROAS curves and cohort evolutions. Part of the reason I released Theseus as an open source library was to give advertisers the tools to do these kinds of scenario analyses.