Friday, March 27, 2009
What is position scarcity?Posted by Jonathan Halket at 1:01am
Position scarcity—the relative supply of "good" players at each position—plays a large role in fantasy draft and auction strategy. Good strategy demands a good measure of position scarcity. Is second base a "deep" position this year? I've heard some experts bemoan the paucity of good outfielders this year. Conceivably, measuring position scarcity might mean taking into account the expected values of every player in baseball, or at least every potential starter. In this article, I will argue that measuring scarcity is much easier: All you need to do is look at the expected performance of exactly one player at each position, the replacement level player at that position, and compare these players to each other. This should save you lots of time and potential mistakes.
Take the last pick in your draft. The player that would be picked there is a replacement level player. Actually, there is a replacement player for each position. This is the last player picked at each position.
Now take a valuation system. It can be whatever system you want as long as it obeys the following: It only compares pairs of players, and when it compares them it doesn't know or care what position they play. As you will see, pairwise comparisons are all you need to build up a proper value system. So, to reiterate, this system takes in things like expected home runs, RBIs and other stats (scoring or otherwise) but not things like position or "position scarcity."
Take each position replacement level player (PRLP) and value him at $1.
Now, for each position, compare every player eligible at that position (assume for now that there is no multi-eligibility) to the replacement player at that position. After you're done you will have dollar values for every relevant player in your league. Take this six-team, three-position table of players as an example.
1b 2b 3b Highest $18 $17 $10 $17 $1 $8 $16 $1 $6 $15 $1 $4 $5 $1 $2 PRLP $1 $1 $1
For these fictitious players: There is one really good player at second base and then a bunch of players that are not better than the PRLP at second base; at first base, the top five players are all much better than the PRLP there.
In a simple league with no bench or multi-position eligibility, the PRLP players will go in the last round of the draft: There's no reason to waste a higher round pick on them (unless there are more positions than players, of course). That's why they are valued at $1.
Now, convince yourself that the best thing the team with the first pick can do is to draft the player with the highest value, regardless of the distribution of values by position (as long as your opponents don't draft according to some crazy strategy scheme like "Always draft the best second baseman with my first pick"). That All-Star second base looks mighty tempting, doesn't it? After all, if you don't get him, you're left with the dregs at for second base. But you should not draft him first. The difference between him and his position's PRLP isn't wide enough (and note that you got that by only comparing him to the PRLP, without accounting for any kind of scarcity). Go ahead and and try it—drafting the second baseman first will yield a total team value of $26 (the $17 second baseman, the $8 third baseman and the $1 first baseman), while drafting the $18 first baseman first will yield a total team value of $27 (with the $8 third baseman and the $1 second baseman).
So, now to define position scarcity. A position (say, second base) is scarce if you can take a player from another position (say first base) and he would have a higher value if you compared him with the PRLP at second base than you got by initially comparing him to his PRLP at first base. A necessary and sufficient condition for a position (say, second base) to be scarce is that the PRLP at second base is worse (using your pairwise system) than the PLRP at another position, say first base (note: you can't see this from the dollar values in the table above, since these values were for intra-position only).
As a corollary: Scarcity has nothing to do with the distribution of talent above replacement level within the position.
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