Here's a hypthetical question: You have a first baseman with a WAR of 3.5. Should you trade this player for a SS with a WAR of 2? The simple answer is clearly no. It is quite tempting to argue that since you started at +3.5 and are now at +2, then you have lost 1.5 wins. However, this does not adequately answer the question.
Now here is the same question with more information: Your first baseman still has a WAR of 3.5, but his backup has a WAR of 3. Your pre-trade SS has a WAR of -0.5 What should you do now? Well let's do some simple math. At the shortstop position, you will be gaining 2.5 WAR (2+0.5) while at first base you will lose 0.5 WAR (3.5-3). Your net WAR gain on the trade is 2+0.5 or 2 WAR.
But how could this be? Why would you end up ahead by trading a better player for a worse player? The answer is that WAR is misleading. The "R" in WAR is for a league average replacement, but your replacement is quite possibly not league average. WAR is a measure of a player's value compared a set, uniform baseline, not a measure of his value to your team. If you have two strong players at one position, they are each less valuable to you, even though they remain highly valuable league-wide.
Going back to the example, although the starting first basemen's WAR is 3.5, his actual value to your team is only 0.5 because his backup is almost as good. Similarly, although the replacement shortstop's WAR is only 2, his actual value to your team is 2.5 wins because his replacement is terrible.
So now let's add one final twist. The team you are planning on trading with just read the top half of this article and came to the conclusion that this is a bad trade for them. After all, this trade helps you, so it must hurt them, right? Wrong. Imagine that before the trade, they had two strong shortstops but a very weak first basemen. With this trade, they would lose almost no value at SS (because they can just replace the traded shortstop with his almost equally talented replacement) and they gain a huge amount of value at 1B (by replacing an awful first basemen with a great first basemen).
This illustrates a fundamental economics principle; trades can (and do) make everyone better off. To you, the shortstop is more desirable because he increases your team's overall value, to the team you are trading with, the first basemen is more desirable for the exact same reason.
Finally, this leads to another related principle; you trade what you value less than your trading partner for something that you value more than your trading partner. In this example, you trade the less valuable first basemen for the more valuable SS, while in your trading partner's mind, the value is reversed. You are both right!
So next time sports talking heads argue about who got the bad end of a trade, please remember that a lot of the time, there is no loser (though sometimes your team may just make a terrible, terrible trade).