Wrong but useful. Working @Twitter, tweeting about data science and people management.
"Wait, it's all her views?" 
"Always has been"
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It's partly about being on their side, even when you think some ideas are dumb. Answer some seemingly pointless questions, help run experiments you think won't work. Don't go overboard, but be supportive. It builds trust, and it's damn hard to influence people who don't trust you
And as you're building that trust, always ask WHY they care about the things they're asking. Curiosity helps build trust as well, and more importantly, it helps you get ahead of the curve.
I've also heard that being a thought partner means being involved in project ideation, but IMO, the ideation stage is already too late. Ideation is often about the what and the how of building product, but data is uniquely good at figuring out what should be next.
By asking WHY a PM cares about certain data requests, you get a sense over time of their underlying concerns and motives, and THAT is what you need to drill into. Deeply understand those issues, how they connect to the rest of the product, their past and present trajectory...
Then develop a narrative about those things, and let it be a little overly simplistic. If you want someone to act on your recommendations, make them easy to understand. Tell them how they're supposed to interpret your data, even if it doesn't come naturally to you.
And most critically, find a way to directly connect your point about what's next to what they're doing now. It demonstrates you aren't off in la-la-land, that you care about building things WITH them. It builds a bridge so it's easy for them to seek out your perspective.
True partnership (thought partnership or otherwise) takes time, effort, humility and curiosity. Time is the hardest to achieve in the tech world, where everything moves so fast, but the other three are possible on shorter time scales.
Of all of them, humility matters most. Yes, young data scientist, you are smart and people should listen to you. But the people you work with are also smart, and you should listen to them too! Maybe they're wrong, but with an open mind, you may just learn something.
And either way, it's ammo for later. You need to know where people are now if you have any hope of convincing them of where to go next.
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