What’s in a value?

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).

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  1. Rob Moore said...

    I had the same reaction to that article – if 3 $10 guys aren’t equal to one $30 guy, then the valuation is clearly off somewhere.

  2. thumble said...

    Relative supply and demand matter…

    There are far more $10 layers in the market than $30 players. I have alternatives available to create $30 worth of value from the available pool. That’s why the market would balk at 3 $10 players for 1 $30 player regardless of intrinsic value. I can readily find other players roughly valued around $10 that may meet my needs more easily.

    There is also the missing point that a $30 player occupies a single slot in the lineup to create that value, the 3 $10 players would limit my future options by occupying 3 slots. It is not 3x$10 for 1x$30, you have to displace 2 additional players and their added value, even if their individual value is $1.

  3. Rotodog said...

    A couple points I feel are important in roto valuation.

    10+10+10 =30. That is true, but what I call a 10 dollar player may be different than what you feel is a 10 dollar player. So…..

    The Value of any player at any time is what his perceived value is..Simple . Value = perception.

    The perfect valuation system at the end of the year should only be used to identify and exploit the hidden value that certain players have.

    The last thing I want to mention is that three 10 dollar players with UPSIDE or perceived upside, can be worth more than a 30 dollar player at any given point, especially if that 30 dollar player has demonstrated his ceiling prior…

    Those are my additions to the above posts.

  4. Sanstodo said...

    The reason three $10 players are not worth one $30 player is the opportunity cost of filling three roster spots instead of one minus the increased risk of losing the entire investment due to injury.  Even if their contextless value is equal (10 +10+10=30), as long as there are finite roster spots and a different number of $10 and $30 players, their value in context will differ.

  5. Sanstodo said...

    I’ll agree that, upon re-reading, he is taking the roster spot valuation into account.  But I’m not sure about the injury risk valuation.  Even if the risk of injury to all the players equals out so that we have a true valuation of 10+10+10=30, there is still the risk of losing the entire investment due to a single freak injury (or in other words, the chance of lightning striking once is significantly more than it striking three times).  Do you automatically factor in the additional chance of catastrophic, unforeseeable loss?  I would argue that most people do not.  Then again, it could mean that we’re valuing individual players incorrectly in context by ignoring the chance that they could lose a season due to a tragic deer meat carrying accident, in which case his point stands.

  6. Moe said...

    The logic with the roster spot (and injury) seems appealing at first, but is not: The “value” of only needing one roster spot is part of the $30 price.
    If you only add up the production, the $30 player may only produce like 2.5 $10 players but because he only uses one slot his value is the same as 3 $10 players.

    Hence Jonathan is right, if it doesn’t add up for you, something’s wrong.

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