CDG: Negative $values for players that have to be drafted

[Michael@HQ]

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 z-scores, the number of projected points if one is in a points-based 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.

[Michael@HQ]

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.

[makelele]

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 0-for-infinity at the plate so it reflects the true absence of value.

[PD@HQ]

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

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 neg-value player(s). This does not, in my view, make such player(s) positive-value players; it makes them positive-price players. (Although the rules have already required them to be positive-price because negative-price bidding is not an option. Which raises an interesting possibility for a rules change -- why not allow negative-price 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 neg-value 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.

[PD@HQ]

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.

I don't understand what this means. We have to assign a value to each player, which we do based on the difference between him and an open slot.

[jdwexler]

In a points league, there can be no negative value

To be clear, a player can have negative points in a points league. A pitcher's negative points from ER, H, & BB can outstrip his positive points from innings and a batter's ABs can total a higher negative value than for which his hits and bbs might compensate. Im sure that in the vast majority of cases players on fantasy teams wind up in the black, but I played in a league last year where useful players had large negative point values. Didn't change the fact that they usually still would have positive $values at the draft table.

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 neg-value player(s). This does not, in my view, make such player(s) positive-value players; it makes them positive-price players. (Although the rules have already required them to be positive-price because negative-price bidding is not an option. Which raises an interesting possibility for a rules change -- why not allow negative-price 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 neg-value 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.

Patrick, I could be misunderstanding your argument, but it seems to me you are making a category error due to semantic confusion over the word "value" (which has been used in a couple different ways here). The whole thrust of this thread has been about the utility of the $values that the CDG gives us to bring to the draft table. This is distinct from the point value (or roto category value). The salient question for me is what $dollar value should we assign to each player so we have an idea how much to bid on him at the draft table. Just because a guy is so bad as to have a negative point projection (or be a drag on your roto categories) doesn't change his value per se. Only his points value relative to your other choices (ie the other players you can draft at his position) affect his $value. If my opponent brings a CDG sheet with negative $values for players in the top 14 at his position (even if those guys are below some leaguewide replacement level they want to set), I am going to crush him in the draft.

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.

[jdwexler]

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 0-for-infinity at the plate so it reflects the true absence of value.

Thanks for this. Sometimes you have an intuitive understanding of something, but it takes a clearly worded expression of it to get a better handle on it.

[jdwexler]

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 league-wide 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).

[jdwexler]

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.

[Michael@HQ]

... 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.

What I mean is that if one is purchasing a stinky catcher in a league with no transactions of any kind, then, yes, the dollar value assigned by one's projection software to the catcher should use his stinky stat line since whoever buys him on drafte day is doomed to live with the catcher the whole season. If instead, one can drop stinky catcher and go with an open catching slot or maybe hope that there is a decent catcher that appears on the waiver wire or the free agent pool who is even better, then one should use the projected stats for the roster slot as a whole, which could be much better than the stinky catcher's own projected stat line.

[PD@HQ]

understates[/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.

Except don't you surrender back your 90-point advantage at C when you have to install $1 players at every other position?

[usualsuspects]

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?

Who plays in a league with only two owners and only two offensive positions?

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 6-9 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?

[jdwexler]

Except don't you surrender back your 90-point advantage at C when you have to install $1 players at every other position?

It depends on the number of other positions. If there are only 8 other positions than Mauer would win the league on his own and be worth your entire budget. You can come up with a scheme for the normal amount of positions too. The point is that there is a scarcity issue here for which valuation systems do not account, and I'd like to know how to mathematically adjust for this. Obviously the adjustments will be much smaller in a normal league, but I think some of the top end talent in my format is being undervalued.

[Michael@HQ]

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?

It is the same principle at work with a full league. Actual behavior will not always be rational, but teams should allocate their dollars based on their projections using the forced positions. A failure to do so means that they are flushing their money chasing first basemen when if one just waits, one can roster the last first baseman for $1 even if everyone agrees he'll produce $3 of value.

[RAY@HQ]

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.