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CDG: Negative $values for players that have to be drafted
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Just FYI, we have a new version of the CDG in place with a fix for the "force positions" valuation error discussed somewhere in this thread.

Originally posted by usualsuspects View PostDo 12 teams really flush an extra $120 on catchers to avoid rostering the worst one, when half the teams will get two positively valued catchers anyhow?
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Originally posted by PD@HQ View PostExcept don't you surrender back your 90point advantage at C when you have to install $1 players at every other position?
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Originally posted by Michael@HQ View Post
OK, so let's worth through an illustration. You are in an auction league with just two fantasy owners and you each must roster a 1B and a C and you each have $5 to spend. You and your opponent share the same projections. There are no adds and drops allowed during the season. The pool looks like this according to your draft software with the forced positions option turned off:
1B  $5
1B  $3
1B  $1
C  $1
C  ($4)
C  ($5)
Your opponent, with the same projections and same software, turns on the forced positions option and his dollar values are reallocated as follows:
1B  $2.71
1B  $1
1B  ($0.71)
C  $5.29
C  $1
C  $0.14
So let's return to the issues as you framed them. Whose dollar values seem nuts? Is it the case that all catchers will simply sell for a buck, maybe two? Is this a game theory problem or a marginal return problem?
If you do, then a game theory solution and a marginal return solution will converge. The rules of the game are important. Setting up massively oversimplified special cases like a two owner league, or leagues with nine catchers that hit like Mike Piazza, 15 that hit like Steve Swisher, and the 1B's are all Lyle Overbay doesn't much help understand the solution for league and player configurations that do occur. If there are six negatively valued catchers that must be bought (typical?) there will be 69 teams that don't have to buy any of them in a "normal" 12 team league. Do 12 teams really flush an extra $120 on catchers to avoid rostering the worst one, when half the teams will get two positively valued catchers anyhow?
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Originally posted by jdwexler;626130Let's say in a 10 team league that the projections put Mauer at 91pts and the 9 other C's at 1pt each. Okay, those 9 C's are worth $1 each and Mauer is worth 90% of the total C dollars. So he's worth a lot by this measure probably $100bucks or maybe more. But, this probably actually [Iunderstates[/I] his value by quite a bit. Suppose the players at other positions were all bunched closer together: 15pts for the top guy then 10, 10, 10, 10, 10, 10, 10, 10, 5. In this case Mauer would be worth your entire $260 budget (and more if you were able to spend it!). You get a 90point advantage at one position that will win the league for you by itself. You can't get that kind of gain anywhere else.
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Originally posted by Michael@HQ View Post... we shouldn't value stinky catcher based on his own production but rather based on the expected production from the roster slot as a whole.
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I think I still see a defect in this valuation method namely that it doesn't allow the system to "see" how the distribution of players at a given position compares to that of other positions.
Let's say in a 10 team league that the projections put Mauer at 91pts and the 9 other C's at 1pt each. Okay, those 9 C's are worth $1 each and Mauer is worth 90% of the total C dollars. So he's worth a lot by this measure probably $100bucks or maybe more.
But, this probably actually understates his value by quite a bit. Suppose the players at other positions were all bunched closer together: 15pts for the top guy then 10, 10, 10, 10, 10, 10, 10, 10, 5.
In this case Mauer would be worth your entire $260 budget (and more if you were able to spend it!). You get a 90point advantage at one position that will win the league for you by itself. You can't get that kind of gain anywhere else.
Is this a correct assessment? Obviously, you will never get something so extreme in real life, but it seems to me that there is something that has to be corrected for on a smaller scale.
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Rob
Here is Tom Tango's formula for assigning $values (much more lucidly expressed than what I could muster):
1. Figure out the points for every player
2. Figure out the last player to be selected at each position, and get his points.
3. Subtract 2 from 1. That’s your player’s QALPAP (quatlus above last player at position).
4. Add up the QALPAP of the 120 nonpitchers and 84 pitchers. That’s the leaguewide total QALPAP.
5. Take the maximum payroll per team x 12 teams. That’s the total league payroll.
6. Take the figure in 6, and subtract out 204$ (that’s the minimum 1$ x 204 players… if your minimum is 500,000$… then use that.) This is your marginal dollars.
7. Take the figure in 6, and divide by the figure in 4. This is the dollar per QALPAP.
8. Take each player’s QALPAP (from step 3) and multiply by step 7, and add the minimum salary ($1 or 500,000$ or whatever it is).
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Originally posted by makelele View PostGood discussion. Let me just add a brief statistical point. Dollar values are on what's called an "interval" scale. One property of interval scales is that the number 0 is arbitrary. A player valued at $0 does not have no value  contrast this with something that is 0 inches tall (ratio scale), reflecting an absence of height. Because of this, when working with dollar values, the numbers are not multiplicative. A $10 player is not necessarily worth twice as much as a $5 player. Or the magnitude of difference between a $5 player and a $10 player is not necessarily the same as the difference between a $30 player and a $35 player. Think of $ values as being similar to degrees Fahrenheit. 0 does not mean a complete absence of temperature, and 100 degrees does not mean there is twice as much heat as 50 degrees.
If you want your dollar values on a ratio scale (like inches), you need to set $0 as the value of a player who contributes 0 R, HR, RBI, SB, and who goes 0forinfinity at the plate so it reflects the true absence of value.
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Originally posted by PD@HQ View PostIn a points league, there can be no negative value
Yes, this was my point: Knowing you will be spending at least $1 provides you an incentive to move up the food chain to avoid the worst negvalue player(s). This does not, in my view, make such player(s) positivevalue players; it makes them positiveprice players. (Although the rules have already required them to be positiveprice because negativeprice bidding is not an option. Which raises an interesting possibility for a rules change  why not allow negativeprice bidding? If I'm willing to take some $5 catcher, why can't I bid $5 dollars? That is, why can't I get $5 added to my remaining total as a reward for taking a negvalue player out of the pool? This would provide a lot of opportunities for owners to arbitrage perceived value differences. To borrow from Michael's example, if we suppose that all 11 other owners are working from the same projections, which say Joe Shlabotnik is a $5 player, and I believe Joe is due for a good year and will be only a $0 player, I could attempt to exploit that difference with a negative bid. Of course, someone else could raise my bid to $4 and it might go on until he veered into positive price  but if he did, it would be a market result, not a rules result.)
Very interesting discussion.
I'm not even sure if you'd disagree with any of this. If that's the case, then fine but then I still can't see the utility of assigning negative $value to these players (ie top 14 at their position players in a 14 team league) for any reason.Last edited by PD@HQ; 03202011, 03:52 PM.
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Originally posted by michaelwe shouldn't value stinky catcher based on his own production but rather based on the expected production from the roster slot as a whole.
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In a points league, there can be no negative value, so I guess the very worst player is your $1 baseline, and everyone scaled up from there. But in Roto, there is a very real negative value, for hitters who deliver shoddy BAs in significant ABs, and no offsetting usefulness in HR/RBI/SB/R. And pitchers, of course, have two ratio categories in which to provide negative value.
I've never played in a traditional roto league. Does it not work this way? I would have thought that if you have to draft a catcher than you are better off spending more than $1 on, say, the #8 catcher in a 12 team league even if he is a drag on your BA or whatever since the #12 catcher will drag it down even more if you get stuck with him
Very interesting discussion.
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Good discussion. Let me just add a brief statistical point. Dollar values are on what's called an "interval" scale. One property of interval scales is that the number 0 is arbitrary. A player valued at $0 does not have no value  contrast this with something that is 0 inches tall (ratio scale), reflecting an absence of height. Because of this, when working with dollar values, the numbers are not multiplicative. A $10 player is not necessarily worth twice as much as a $5 player. Or the magnitude of difference between a $5 player and a $10 player is not necessarily the same as the difference between a $30 player and a $35 player. Think of $ values as being similar to degrees Fahrenheit. 0 does not mean a complete absence of temperature, and 100 degrees does not mean there is twice as much heat as 50 degrees.
If you want your dollar values on a ratio scale (like inches), you need to set $0 as the value of a player who contributes 0 R, HR, RBI, SB, and who goes 0forinfinity at the plate so it reflects the true absence of value.Last edited by makelele; 03202011, 10:13 AM.
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3) In a real life situation, given the presence of middle infield, corner infield, and utility "positions" in most league formats, the talent levels out between positions so that often one has just two positions for the purposes of allocating dollar amounts  catcher and other batters.
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I'm clarifying the above post  sorry if it's rude.
1) In my illustration above, even the forced position dollar values aren't perfect either, although to my eye they are better than the dollar values computed when the forced position option is turned off. The problems are because (i) one bids in dollar increments not in pennies and (ii) no owner can bid more than his remaining dollars minus $1 for each roster spot greater than one. The fact that the pricing model doesn't adjust for those problems would not trouble us nearly as much if we were dealing with a real life situation involving lots of fantasy owners and lots of players to be auctioned. I'll also assert that the magnitude of the forced position problem does not shrink dramatically when we deal with a real life situation involving lots of fantasy owners and lots of players to be auctioned. You may choose to believe my assertions or not but try not to let those other problems distract you from the point I was trying to make with my simplified illustration.
2) Perhaps I should explain how the forced positions method of allocating dollars works because the second set of dollar values was not random given that we had the first set of dollar values. Each player has a single number representing his value. It could be his standing gain points, the sum of his zscores, the number of projected points if one is in a pointsbased league, or his Rotisserie dollar value prior to factoring in forced positions  define that number as "value." The projected dollar value for each player including forced positions is computed as $1 + leaguewide marginal value above replacement player value / leaguewide dollars to be allocated above $1 per player to be rostered, assuming that $1 is the minimum bid and that replacement player value is computed based on the guy's position.
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