If you look at Bogaerts situation - ARB years 2017, 2018, 2019 then into the blue yonder ... a Free Agent entering his Age 27 season. So let's price his 2020 and 2021 seasons at 35M and 38M, which for a guy his age with the revenue jumps you'd project seems like a pretty reasonable guess. So now the arb years ... since almost nobody actually goes to arbitration anymore, the comps analysis for arbs are pretty useless. That said, clearly the Red Sox have leverage here. So let's plug in $10M, $12M, $16M ... if you use a 7% discount rate, this comes to an AAV of $17.4M ($86.7M/5 years). So, a long term deal should be able to give more money up front, while maintaining the AAV (so you pay a fair price to buy a couple years of FA).
So something like 5 years at $21.1M per year would get you an equivalent total value ... and be a fair price for the extension. For the Sox, it buys two years of his free agency - for Bogaerts it gets him $20M more up front and still gets him into the FA pool before his 29th birthday.