For centuries, economists (or, actually, thinkers and writers who later historians would come to label economists, since there wasn’t really such a profession 300 years ago) struggled with the notion of value. Like the alchemists that searched in vain for the chemical means to synthesize gold, economists searched for the fundamental way to measure value – the object or thing against which all other things’ values could be measured. They were looking for a good – a bundle of wheat, an hour of work, something – whose value never changed.
One problem was that these thinkers couldn’t agree on what kind of value they were talking about. For example, there is Adam Smith’s famous diamond and water conundrum. On the one hand, water is essential for life and is therefore highly valuable for use. On the other, a diamond can be traded for lots of other things whereas a bottle of water cannot – Smith said that a diamond had a high value of exchange while water had no value in exchange. Smith and others tied themselves in knots trying to undo this incongruity; if there were two different values for a good then it would be impossible to find one fundamental good that worked for both values.
Believe it or not, the same sort of discussion can be found in fantasy baseball. For example, in Victor Wang’s nice article on trading, he wrote (to paraphrase): “Three $10 players may not have the same value as one $30 player.” I interpret this as: “Each of the $10 players gives a certain amount of value in use that when put together, in a sense, equals the value in use of a $30 player, but you may be able to get more or only get less in a trade.” That is, players or groups of players may have different values in use and values in exchange.
Economists eventually figured out that there really was only one kind of value which was value in exchange and that there was no one fundamental good. Each good (say Corn) could be valued against any other good (say Beer) for each person. The value of corn to a person in terms of beer would be the amount of beer he would give up to get one additional piece of corn. If beer and corn could be traded amongst people in a marketplace, then each person would trade with each other until all of them agreed on the relative value of corn and beer. Relative supply and demand mattered: if diamonds or beer was relatively rare, then they would only be traded for lots of water or corn in market.
What about those $10 players? Let’s take a pre-auction thought process. If you wouldn’t rather buy three players that you valued at $10 each than one player that you valued at $30, then that means at least one of these $10 players is worth more or the $30 player is worth less. And it means you would be better off valuing and spending more on those $10 players and spending less on the “$30” player. Nothing is wrong with your math – 10 + 10 + 10 = 30, something is wrong with your values. The most likely problem is that you’re using the wrong value system. The lesson from beer and corn is that value is always dependent on situation – there are no fundamentals. The value of a bottle of beer to you changes depending on how much beer and corn you already possess. Values change with the situation.
This discussion is more than just academic: good value systems should already have taken in to account the fact that players get injured or play rare positions and so on. So, just as you wouldn’t use an expert’s value guide for a 12 team league if you’re in a 10 team league, don’t use old, stale values that you calculated for an auction when you’re valuing a trade after the auction (even if the season hasn’t started yet).