Analytics specialist
Sets up what gets counted and makes sure the numbers are true. Sounds like a minor role and is the reason every other number on this site means something or nothing.
When your project needs this person
Mandatory on a shop. On a site with forms it can be part of the build, but it must be explicit.
What happens when they are missing
Every report afterwards is guesswork. The most common version is a shop whose analytics shows half the real orders, with three different agencies making decisions on a wrong number.
How this appears in an offer
Appears as "tracking setup" or "conversions". If it appears nowhere, assume it was not done.
What they do NOT do
Does not interpret the numbers for you and does not do the marketing.