Executives don't get bonuses in MLB for money saved. The league would never allow that as it would interfere too much with payroll spending and the anti-trust exemption. In fact, baseball pays the least of all executives in sports (and very little when compared to the real world)
I looked all over the internet and could find absolutely no evidence to back up this tin foil hat idea that teams don't spend money so it can go to the execs as bonuses, OWNERS pull that crap, but not executives.
Bonuses aren't structured around money saved. It's money made. Which can be the same thing only worded differently.
Virtually every corporation in the Country pays their executives like this. They will have a base salary. For the sake of conversation, let's say McGuirk's is $1M. Then they would have a stretch bonus based on metrics established by upper management/ownership designed to drive profit and growth, usually tiered in some fashion such as: 10% of salary if x metrics are met, 20% if y, 30% if z, 40% if AA, 50% if BB. Usually their will be an upper limit (I have always disagreed with placing a limit because it can stifle growth). With a corporation like Liberty, they won't care AT ALL about wins/losses, attendance, etc. except how they impact the bottom line and as trends of the future and how it affects the value of the franchise (what it could be sold for should they decide to sell). They are not fans. They are owners of a business. "Giving the fans a championship" plays no part in their thinking outside of go to verbage when talking with the media.
You won't find this type of information out there because it isn't released. You MIGHT be able to dig through the financial statements reported by Liberty and find it as a line item report (if you know what to look for) and even then it may be combined with other executives in some way. But, I doubt McGuirk is a big enough fish to even stick his head up out of the water at Liberty.
Liberty almost certainly says:
Here's your comp package - Base Salary, Bonus based on metrics, stock/stock options. Now go run your business as a silo business just like you are the owner. Let's know how much money you make every so often.
They don't care what specific moves are made, just what the bottom line is. If the Braves average making $20M every year, then they will want to see AT LEAST a $20M bottom line next year.