I'll somewhat arbitrarily define a "competitive" team as one that projects to win at least 80 games. Teams that project to win less might look competitive for a month or two, but can't really hang in there once luck (including injury luck) evens out. This is what we had this year.
So lets do the math. We start out with 48 wins, which is what a team of replacement level players gets you. To get to 80 we need 32 WAR. How do we get there.
1) Our stars Freeman and Simmons need to be healthy and approach their normal production. I'll be slightly optimistic and say 8 WAR from those two.
2) Continuing along a slightly optimistic path, I'll project 2 WAR each from Peterson, Olivera, Markakis and Maybin. 8 WAR from this group bringing us up to 16. As I said this is slightly optimistic given none of them are going to achieve 2 WAR this season.
3) 6 WAR from Miller and Teheran. This brings our total up to 22.
4) 4 WAR from the pen and bench (including players who might start the year in the minors), bringing the total up to 26.
I am assuming replacement level performances from left, catcher and three rotation spots.
So we are about 6 short of 32 with what we currently have on the team.
We have 25-30M to spend on player acquisitions. At the going rate of about 7M per WAR on the FA market, we can realistically get 4 more WAR. This brings us up to 30.
That is a very awkward number to be at. For that kind of team, you need a significant amount of luck (from injuries, hitting with runners in scoring position, strand rate, as well as players outpeforming projections) to make the playoffs. At the same time it is not a terrible no-hope team. We could improve a little further by making some trades that in effect borrow from the future for the present or by backloading contracts. Not sure we want to do that in 2016.