Bregman only making 20 million over 4 years of arbitration is wildly optimistic. Springer is heading into Arb 3 having already made 16 million and should make 12ish again this year. I think 30 million is the bottom estimation for what Bregman should expect over his arb years with more than 40 a possibility depending on if he can repeat what he did last year a couple more times. If he gives up free agency years by signing a long term contract now I would think he's expecting 20 mil+ as a AAV so like 7 years for 150 is more realistic if he wants another dip into free agency at 31.
The thing the Astros have going for them in negotiations (if there are any right now) is that he's a college player that will hit FA for the first time at 29 years old and the market has been much tighter on guys turning 30 and paying them long term. So there is an incentive for Bregman to give up a couple years of FA (maybe more) if he feels the deal is fair. Even broken/injured Josh Donaldson just got 20+ so Bregman has to be thinking his market value is at least more than what Donaldson can get.
The thing the Astros have going for them in negotiations (if there are any right now) is that he's a college player that will hit FA for the first time at 29 years old and the market has been much tighter on guys turning 30 and paying them long term. So there is an incentive for Bregman to give up a couple years of FA (maybe more) if he feels the deal is fair. Even broken/injured Josh Donaldson just got 20+ so Bregman has to be thinking his market value is at least more than what Donaldson can get.