Building a roster is very similar to creating an investment portfolio. I wouldn't take my life savings and bet it on oil futures, much like I wouldn't take my entire front office payroll and invest it all on one free agent. This simple concept is asset diversification, one that can be evidenced in mutual funds that are so common in today's financial market. The benefits of said diversification are illustrated here:
"Diversification involves the mixing of investments within a portfolio and is used to manage risk. For example, by choosing to buy stocks in the retail sector and offsetting them with stocks in the industrial sector, you can reduce the impact of the performance of any one security on your entire portfolio."
This concept can be applied to roster construction. If I spread my assets across an entire roster, the bust of one single player will not jeopardize the whole of my team. In this way the concept of a "top-heavy" roster is a completely legitimate concern--if the Angels were to lose Mike Trout for a whole season, they would likely lose their place as a contender (a legitimate one, at least) overnight. But if I had five players that summed up to the same value as Mike Trout, then the loss or bust of one would only result in a 20% loss. Granted, dealing with a larger number of assets can create a larger variance--there's definitely less volatility in Mike Trout's performance--but you get the idea. Brian Cashman understands this and understands it well.
There were certainly big ticket options on the trading block this July--Jon Lester, David Price, Jeff Samardzija, and even John Lackey to an extent. All of these would obviously be a boon to any team, but would also carry a considerable amount of risk for just one asset. The approximate value added for a Jon Lester, for example, would have the following framework:
Value_Added = (RoS_WAR - Replaced_Pitcher_WAR) * (1 - Prob(DL_stint))
For the sake of this exercise, let's assume that a DL stint will last one 15-day DL stint, or approximately 3 starts. We can also assume that the replaced pitcher is replacement level. If we find the probability of a DL stint using Jeff Zimmerman's formula, then we would find it to be 10.48% over a 12 start rest of season. If Jon Lester's Rest of Season projection was 1.3 fWAR and the probability of a three-start DL stint is 10.48%, then his actual value is about 1.16. That's not extreme, but about 10% is a large degradation of such a short-term and expensive asset.
What does this have to do with the Yankees' situation? Well, they didn't make that bet. In acquiring Brandon McCarthy, Martin Prado, Chase Headley, and Stephen Drew, one does not need to hope that that 10% chance does not come to fruition. Because each individual upgrade is relatively small, the discount rate of injury or bust rate affects a smaller portion of the investment.
These acquisitions added about two wins of value, according to Eno Sarris of Sports on Earth. What makes this investment even smarter is not just the gain, but that the probability at which this investment could be lost is much lower than a team like the Athletics where a freak injury or bust would essentially sink the whole asset. Because Brian Cashman treated trade deadline acquisitions much like one would treat a mutual fund, the odds that the whole of his deals are a bust are incredibly low.