Might depend on what "win" is supposed to mean in this context. If it's intended to mean "languages with type inference are more productive", then sure, evidence would be nice. If it's intended to mean "type inference helps cut down on the need for explicit type annotations", I don't think evidence is really necessary.

Not sure if this qualifies as evidence, but a quick search shows there are papers exploring the topic of whether type inference is a "big win" or not.

Benefits of Type Inference for an Object-Oriented Real-Time Language

https://www.researchgate.net/publication/220391749_Benefits_...

EDIT: Granted, this particular paper may be more claims without solid evidence.

I think the claims might be the evidence you're looking for.