I promise we're leading to something more interesting here!
Prerequisites for understanding: None.
Prerequisites for derivation: N/A.Finances
As much as we'd all love our teams to have infinite access to wealth, even the richest franchises have a budget. Teams allocate a certain portion of their financial resources to fill out each spot on the roster, and spending more in one place necessitates spending less elsewhere. If a team is inefficient with money, sinking significant amounts into players who aren't worth what they're paid, they're punting one of their major resources. This is bad from both the team and fan perspective: they're setting wins on fire alongside those dollars. Don't buy into the notion that since it's not your money it doesn't matter, because it's your happiness at stake as well.
Of course, efficiency (i.e. wins earned per dollar spent) should never be the only factor by which we judge a team's financial acumen. A team could quite easily get rid of everyone making over the MLB minimum salary ($400,000 per year at time of writing), which would give them the cheapest roster ever, relative to the rest of the league. And they would probably be terrible. Efficiency for its own sake is not a goal any sensible organisation aspires to. We want our teams to spend as much money as they have, but to spend it wisely. Winning the same amount of games as another organisation that spent ten million dollars more might be nice for the owner's bottom line, but in pure baseballing terms means absolutely nothing.
While there are 25 places on a roster (except in September), only a small majority of the players occupying these spots actually start in games. In the National League you have eight starting position players and the rotation, and the AL adds a designated hitter. This means that there's only so much talent one can actually add to the team before one starts experiencing vastly diminishing returns on investment. There's not a whole lot of point in having so many excellent players as some of them are forced to sit on the bench, especially since the substitutes will still be being paid top dollar despite not contributing much on the field. Still, a team does have to put a full 25-man roster out, and they're relying on the bench to provide depth, which implies that there must be some value in bench players. The key for teams is in balancing the rules of the roster with their finances.
The minimum total salary for a baseball team is $10 million per year (25 roster spots that must be fielded times $400,000 minimum per player). Despite MLB's attempts to restrict runaway spending, there is no maximum salary. A minimum salary implies a minimum talent level, which in turn implies some sort of soft 'win floor', below which teams will be hard pressed to find themselves in. It's instructive to think of baseball talent as a pyramid, with the best of the best at the pinnacle, and more players in lower tiers. By the time you're getting to the type of player who'd be happy to sign for $400,000 per year, you have an essentially unlimited number of players to chose from (remember that we only have 750 roster spots to fill in at the MLB level) - but the average talent level of that group is going to be pretty low. The idea of a minimum talent level and corresponding winning percentage then leads us towards some curious (and important) concepts...