THE BOOK--Playing The Percentages In Baseball

I think the most straight forward way to do what you want to do is:

1. Calculate the value of all players (including Posey)

2. Assign a price to all players being kept (e.g. Posey = 5)

3. Subtract the sum of dollars spent (5 on Posey, X on player B, etc.) from the sum of the budgets of all of the teams (e.g. $260 x 12).  This is Dollars remaining. Call this DolRem.

4. Subtract the value of players kept (25 on Posey, Y on player B, etc.) from the sum of the budgets of all of the teams (e.g. $260 x 12).  This is Value remaining.  Call this ValRem.

5. Every player remaining should have his target price adjusted by multiplying his Value by (DolRem / ValRem).

When I had my fantasy baseball draft, I had a laptop at the draft, and here’s what I did:
I added a column that told what the player was drafted at. Inflation Rate is Remaining Marginal Cap Money / Remaining Marginal Value. For simplicity sake, let’s say Marginal Value is the dollar value initally projected for the player.

In other words…
12 teams, $200 per team, $1 minimum bid, let’s say 23 players per team.
$2400 to draft players, and $2124 marginal (at this point, both marginal cap and marginal value are equal. Inflation adjustment is 1).

Posey is worth $25, but goes for $5. After that point, you’ve got $2120 marginal cap left, but only $2100 marginal value. Inflation at that point is 2120/2100.

Once you have this figure, you can calculate new inflation values for each player as (Value - Minimum Bid) * Inflation + Minimum Bid. You can keep this running the whole time the draft is going, but at the very least, you want to calculate inflation after keepers are figured, because keepers represent the opportunity for huge savings over their projected value.

Not sure if I’m explaining this correctly. Haven’t really thought about auctions in a couple months.

JEH, I see we’re basically saying the same thing. I use marginal dollars and marginal value for my inflation calculation for a couple of reasons. The simplest is that it keeps minimum bid players from being inflated, which is what you want. A $1 player is always a $1 player no matter how crazy inflation gets. Under most circumstances I’m sure it doesn’t really matter.

Persistent reader:  I believe that JEH is discussing how BEFORE the auction one should value players in leagues w/keepers.  I believe Zac is discussing how to decide how much players are worth DURING the auction (as remaining players’ worth will vary depending on whether the players previously taken in the auction were taken for more or less than your perceived worth).  Both are correctly described.  I believe that JEH’s discussion refers directly to your question.  As I read JEH’s explanation, it was a bit confusing to me.  So, I’d say that in your question 1 above, you have absolutely the right idea (take Posey out of the pool and take his $5 out of the $ available).  When you’ve taken all of the Keepers out along with their kept salaries (their “worth” is no longer relevant), you’ll have a pool of players and a pool of $ that you can allocate according to your calculation, and obviously the remaining players w/b worth more than they would be w/o keepers.  One other thing of interest.  Their WILL be a number of players who go for $1 at the end regardless of their “worth”.  If you can figure out about how many there will be, you can arbitrarily give the players at the bottom of your list a $1 value and take them and their $1 salaries out of your pool (obviously for salary calculations only).  You’ll find that this will increase the value of the remaining players and will be more in line with their actual auctioned “prices”.

@3/4

Zac is correct with the marginal dollars.  Because the original post referenced Tango’s method for calculating, which will give a value that is not an integer and because the concept of marginal values adds some confusion (or, at least, necessitates more explanation) I skipped over it.  The impact is minimal to begin with and less so because of the precision (by which I mean decimal places . . . I still don’t think his values are close by necessity, just coincidence ) of the values calculated.

Zac’s method, as described, is fine both before and during the auction (if I understand it correctly).

As far as the number of players going for $1, I don’t know if anyone has offered a heuristic for estimating it (e.g., “about (two times the number of teams) players will go for $1") but the a good guideline to follow is “bid the extra dollar” on a player you want early . . you can likely grab someone you value at $2 or $3 for $1 late.