A lot of startups with some finding inevitably become inundated with the feature monsoon. By that, I mean, the feeling that you know you can hire someone, and add a few features, but you want to do this, that, and the other; you have way too many features you want to add. I think we’re at this stage are cognizant of performing too many half-measures instead of full measures. One idea that’s come up a few times in our internal meetings is the possibility of hiring a data scientist to build a dashboard and crunch our data in a few different ways to simplify our product and enhance our marketing. I know we can hire an engineer with some data science experience, but isn’t an expert. We could probably use this person for a lot more than data science. But are we better served by hiring a data science expert who can really hone in on the numbers and start drawing conclusions?
I agree with Steve, get the basics done and outsource what you can and hire people when you're ready to scale. I try to explain quickly but long enough.
Obviously, I don't know your business so maybe I'm totally wrong in your case but here's what I see. Beside that I'd like to give more general answers (more likely mindset) in this topic.
First, to give a straight answer your question, I think you probably don't need a dedicated data scientist in-house. There are some really impressive startups specialized to this. (You can choose one with European origin, usually less expensive.)
It's necessary to understand the difference between a strategist, a business analyst and a data scientist. Maybe you learn more about these and related terms and you'll figure out what or who you really need.
Data science is for big data and data mining. Big data is another game, if you have big data, you know that and you know who you need. Below that line, we can talk about data/business analysts.
In not all cases but usually data scientists needed at IT, SaaS and large companies where the "everyday analytics" is not enough. Smaller companies have BA/BI, perhaps with data-related skills. Advanced stuff is outsourced to companies who have experts. Marketing or part of it can be outsourced to an agency which also hires external data ninjas when needed. (Real experts are expensive, so it's not a good idea unless you can divide the cost to different projects.)
For example, you may need someone with high data mining and inspection skills if you already familiar with data-driven marketing, marketing automation and you're ready to work from much of data you mine (in a whole new way).
Generally, if you hire someone and break her/him apart, she/he is not gonna be near such productive than a dedicated person. So I won't suggest to hire someone for it and give her/him tasks to fill the work time gap with unrelated tasks from the backlog. You can try to find a part-time worker or freelancer instead and for the other issues another person (one person who's working 12 hours a day is less effective than 2 people who are working 6 hours).
Maybe you simply need a SaaS tool to analyse your data. Service providers often provide support by a professional, advisor services based on the company size and customization, data migration etc.
Maybe you've a more simple problem with the product management and you're missing a great PO (with BA skills) to prioritize and schedule the tasks based on the business interests so the global vision and numbers and also the general market reactions. If you already have a good PO then you can find a freelancer BA to learn more about your business. Maybe you miss a full-time BA. (Still can be a good idea to outsource the product development.)
I'd suggest to avoid unnecessary continuous expenses and keep the HR hours optimized. At the first time you might need someone to set up your tracking, tools, dashboards which needs long hours but the maintenance and reporting can be done by a non full-time worker. (Still easier to find an agency or local firm and to outsource the digital marketing and data analysis to a company.)
In the other hand, you mentioned both the product features and the marketing effectiveness. Therefore here I'd refer back what Steve mentioned about the business model and processes. If you feel deficiency in these basic fields, you may need to improve your business model to be more clear about what to do and to be more productive which is rather more than hire somebody.
Here I should write about I understand your financial borders so difficulties to manage the budget to outsource your tasks and process flows.
How I see you're in the US so I think there's everything already done you might need at the current level so don't reinvent the wheel again. :)
Don't hire anyone until after you have perfected the model - you have repeatable business processes that works and are now ready to scale. Use service companies to help until you get to this point.
I have a whole white paper on this subject - just go to my website to download.