"We Can't Afford to Sign Good Players"

That's the lament of many small market sports teams. It's also nonsense, or at best misleading. Suppose signing a good player means the team would win more games; and suppose that winning more games would, in turn, mean the team would earn more revenue this year and in the future from ticket sales, broadcast contracts, and stadium advertising and concessions. These suppositions are eminently reasonable.

The only question of relevance for the team, then, is whether the expected additional revenue generated by a player is enough to cover the expected additional costs of signing the player. In eco-speak, is the expected marginal revenue product greater than or equal to the marginal factor cost? If so, then the team should try to sign the player, even if it has to borrow the money (so long as the borrowing costs and all other opportunity costs are included in the calculations). Whether they can afford to pay the player from their current income is not relevant; whether the player will add to their profits is what is relevant. Or more precisely, to take account of the time dimension, what is important is whether signing the player will add to the net worth of the team.

The Arizona Diamondbacks appear to understand this concept (even if some analysts might question whether they are applying it wisely). They have explicitly decided to borrow in order to make some free-agent signings that they expect will pay off over time. See here (thanks to Adam G for the link). Also, see here for Phil Miller's usual high quality analysis.