Here are some alternative ways to say "educated guess," depending on the context and nuance you want to convey:

More formal:

* Informed conjecture

* Reasoned hypothesis

* Intelligent speculation

* Well-founded assumption

* Calculated estimate

* Logical deduction

* Informed opinion

More informal:

* Best guess

* Smart guess

* Informed hunch

* Gut feeling (but with some basis)

* Thinking out loud

* Taking a shot in the dark (but with a good aim)

More specific:

* Statistical estimate (if based on data)

* Historical analysis (if based on past events)

* Professional judgment (if based on expertise)

* Intuitive understanding (if based on experience and insight)

The best choice depends on the specific context and the desired tone.