# What is position scarcity?

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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1. Jeff said...

I agree with Breed.  One reason to take the \$17 2B is that you actually have a chance of the \$5 1B falling to you.  If you take the \$18 1B first, you are guaranteed a \$1 2B.  I would take the chance in a draft of having value drop your way versus taking a slight hit at the top.

2. Donald Trump said...

I dont think position scarcity is that simple.  What if there are 11 Brain McCanns at catcher, and then a bunch of Greg Zauns?  McCann has a lot of value over Zaun, but here he would have a very low value.  You have to take into account the value that every drafted player at a position has to fully evaluate position scarcity.

3. thumble said...

The analysis is flawed, as mentioned in the posts above.

You cannot just look at the 2 scenarios described without also looking at the impact to the other drafters. It takes a few seconds to run this out in your head. Based on top value first strategy and a serpentine draft, the first 2 owners will end up with 1 top flight player each and \$20 of team value while the 3-4-5 owners get 2 middle rated players and team value of \$22-\$24. The 6 owner is left with the dregs after getting the best 3B and a team value of \$16.

And that is how it does typically play out in drafts, you win by getting value everywhere you can…or by denying value to the rest of the field, which is why scarcity works. To the point of the article, you need to understand where the scarcity really is and that means positional depth not absolute value of the top player at that position.

4. Andrew said...

A few articles back there was a discussion of z-scores to evaluate a player’s value holistically.  This is the system I use.

After getting every player’s z-score, I find the average z-score and standard deviation for each position.  This creates a kind of position-wide z-score.  By subtracting this “positional z-score” from the original z-score of each player, I get a “position-neutral z-score.”  For example, the average catcher is almost 0.5 standard deviations worse than the average player.  This means that in my position-neutral z-score I add 0.5 standard deviations to every catcher.  Drafting under this system is incredibly easy: since positional scarcity is already included in the z-score, simply draft the highest score left (at an unfilled position) every time.

My system is similar to yours in that both say that “tiering” players isn’t the way to go, but I find my system a bit more satisfying because I’m able to quantify scarcity.  Take from this what you will.

5. John Dent said...

I really don’t understand your example. Are we assuming that there are six teams and only 3 positions which need to be drafted? And, that I’m drafting first? So, I get the 1st, 12th and 13 picks? So in fact, I could pick either the \$18 1B, or the \$17 2B, plus two \$1 players? If this is the case then, yes, there is an advantage with of drafting the 1B, of a single dollar!

I have no idea where your values come from. Please try to make your examples easier to follow!

6. Jonathan said...

John –
These numbers are for a fictitious league that I use as a simple example.  The point of the article – how to value scarcity, is independent of the actual numbers (that is, it works for most any set of rules).

Andrew and others -
If your system of valuing players directly values scarcity (like the z score does) than of course scarcity will matter in that system. What I ask here is: does it make sense to value scarcity in a value system? And if, how does it makes sense to do it?

7. Ed Schwehm said...

I use a system pretty much exactly like Andrew describes for player valuation, but I also take into account the dropoff between the top player on my list and the next at that position. Using standard deviation and z-score ends up treating the players as a continuum rather than discrete data points.

If you have 2Bs valued at {20, 19, 18, 17, 4, 3, 2, 1}, and the player at the top of your draft board is valued at 18 in the 1B distrubution {24, 22, 20, 18, 16, 14, 12, 10}, then you probably want to reach for the 17-2B.

8. thumble said...

I’ll assume John Dent is responding to my post. If you read the article, the author set up the example with “Take this six-team, three-position table of players as an example” and I extrapolted from there. The values all come from the table in the article.

The point of my response is that where the drop off in value occurs sets the table for the overall team value. The 1st team to pick would get the 1-12-13 picks and get the same \$20 team value as the 2nd team to pick. The 3-4-5 owners after them would get more team value because they were able to get greater value from the middle of the second round.

The real miss here is that the last 1B picked is arbitrarily valued at \$1 because he is readily available, but in reality his production will likely exceed that \$1 because the position is so deep.

I think Andrew has the right approach, make the values context neutral and the strategy will adjust itself as the draft unfolds.

9. William said...

This IS the correct approach.  The only thing that matters is the replacement level.

Players should be valued based on their contribution above replacement level – if not, then your valuation system is flawed.  And replacement level differs by position.

Agree that the example could be a little more clear, but it has the right idea.

10. breed said...

I disagree.  If the distribution of talent was in the case of your example, than you would be correct.  But the fact is that most positions have talent distributions more like 3B than like your 1B of 2B example.

So the option isn’t the \$17 2B combined with \$1 at 3B and/or 1B.  Chances are you will still get a player above replacement level.  The key question… what is the player that you will most likely end up with if you don’t grab that top-tiered player?

When you evaluate it in that manner, the \$17 2B looks much more attractive.

11. eric said...

This is going back to Andrew’s method.

I’ve calculated every player’s z-score, but I don’t think I’m following with the position-wide z-score and the position-neutral z-score.  I’m obviously calculating something wrong.  Can anyone walk me through this method?