Who does the BI team report to? Business or IT?

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First off, here is my answer: both to business and IT. But the thing is, I don't think there is just one BI team. There many teams, working in collaboration. Let me dive in to explain my take.
DEFINITION
Of course we first need to define things a little. Traditionally, we think of "the BI team" as the group in IT that does everything, from taking care of hardware to development and support. They staff projects with delivery folks and generally assist the business in exploiting the data assets they make available. But over the years, we have also seen pockets of IT-trained people sitting in the business, doing almost the same thing! Some organizations even have a central business group that "leads" BI governance and sometimes manages the portfolio of BI business-driven projects (led by a Chief Data Officer, for instance). Some organizations (airlines come to mind) have all three, born of a mix of specific, urgent needs, budgets and politics surrounding the various lines of business. So I have a hard time getting my head around "one BI team".
Let's break it down then.
LEADERSHIP AND THE DATA STRATEGY
When I go back and think of all the organizations I have come across, the most critical success factor has always been leadership. Now leadership can come from anywhere. But in an ideal, non-dysfunctional world, the executive team is convinced that data & analytics are critical to support their strategic goals. The CIO teams up with the CDO and/or the CAO (or really any of the key executives leading a strategic part of the organization, in the absence of these two roles) and are directly mandated and co-responsible to create a cohesive Data Strategy and execute on it.
Some of the strategy clearly belongs with IT (ex. architecture, platform, development methodology) and some of it belongs with the business (ex. data governance). Weakness or incomplete coverage by either means that the Data Strategy, assuming it is defined properly - a big assumption at this point - will not be executed successfully. Nature deals with voids efficiently by filling them, and this will be no different; IT will compensate by taking on business roles it doesn't have the skills for (and creating a change management problem in the process), or business will go ahead and have its shadow IT and solutions (that will create yet another silo and support problems).
A FOUNDATION
Let's then assume the Data Strategy is a product of perfect business-IT collaboration. There is an important part that is technology here. Many organizations dictate that any IT asset must be developed and funded via business projects. This doesn't work. There are key capabilities, like a data/analytics platform, which we cannot ask the first business project that needs it to justify the cost of building it. The impacts are that otherwise good business projects will be delayed or rejected (cost being artificially too high) OR the IT portion of it will be reduced to some quick-and-dirty minimally viable (if even) construct that creates yet a new data silo.
The platform needs to be designed to help the whole organization, should be justified on its own and architected to be built incrementally. The CIO must have the trust of the rest of the executive team and the courage to defend the need for the platform to be developed or modernized as a foundation, an investment by the company, no by a particular LOB. This foundation can be funded and justified by a portfolio of ROI-driven analytics, business-driven projects, put into a comprehensive roadmap, and the sum of the present value of economic benefits for these projects can be added together to justify the foundation that just one project never would be able to.
FEDERATED MODEL
Living the data-driven dream works best (or only perhaps?) via a federated model where technology work is the responsibility of IT (to make sure the platform and the tools work, to provide development services, all the expertise of IT) and the analytics/data program is lead by the business (prioritize the projects and govern the data assets, arguably critical and yet often puzzlingly not done) - both being active roles, not an advisory one. The PMO is fully engaged to provide healthy management that favours agile for larger projects. Since everything is not necessarily a project, IT applies DataOps to deal with small requests and bug fixes. The platform is designed with collaboration, agility and scalability in mind because each LOB has its squad of data scientists and "data spanners" who know the business well and which data can be brought to bear to solve specific business questions. A modern data architecture dream supporting people working together to create real value.
SO, LEADERSHIP (AGAIN)
And there are no turf wars tolerated - this starts with the CEO all the way down. The culture is one of collaboration and the belief that everyone has a part to play for data to create real value - we need each other. IT needs to be more nimble and open (the business certainly is) and the business needs to respect that IT has expertise that they do not have and should not distract themselves with (business leaders should not work around IT, they should instead relentlessly insist that it delivers on its basic mission).
CONCLUSION
Anything different than this would surely be a compromise, right? It's a question of leadership. Circling back to the original question - where does the BI team report into, my answer is both IT and the business. Leadership comes from and must exist on both sides. The roles are different but both indispensable. IT manages the cost of ownership and operation of the technology foundation, the business governs the data asset and the business analytics priorities, and both collaborate and staff to deliver projects, to federate the data that everyone needs, to make this data usable and reusable and maximize its value and contribution to the business goals.