The following comes from my latest article for The Hardball Times.
Every year, big names fall on the waiver wire. Be it a prospect call-up, a frustrated owner prematurely cutting ties (e.g., what I did with Madison Bumgarner this year), a move of desperation in light of shallow benches and deep injuries (e.g., the "perfect storm" league where I own Hanley Ramirez, Joe Mauer, David Wright, Pablo Sandoval, Jason Heyward, Ike Davis, Brandon Beachy, Josh Johnson and former DL pains Brian Matusz and Geovany Soto, or some other occurrence, an economic game of how much to spend on whom and when inevitably results.
So how much do you spend on Eric Hosmer, an early elite prospect call-up? Or Jerry Sands, a supposed impact player of a less-elite level? Or what do you do if Anthony Rizzo and Mike Moustakas are both sitting on waivers after their call-ups last week (some leagues play where you cannot own or bid on a player until they have one game under their belt)? Do you wait for Brett Lawrie and Dustin Ackley?
The answer is never a clear one, and I cannot give you a simple answer. FAAB bid recommendations are a lot like snowflakes. Value is infinitely complex and unique, and it depends on the size of the league (12 teams? Five outfielders?), the format of the league (mixed? AL-only?), the depth of benches and DL spots, and your team's current standing in your league.
What I can tell you, however, is that the timing of the FAAB bid makes a major impact on the expected return of the player, and that timing is rarely considered a factor.
One of the more distinct concepts I can still recall from my days as an undergrad studying economics is the discount factor. Put simply, a discount factor, often an interest rate, accounts for the difference between present and future value. A dollar now is never (okay, maybe almost never, as deflation/stagflation does exist sometimes) worth a dollar in the future.
Let's say, for example, the bank pays five percent interest on your CD account, and that you can open a CD account with any balance. If you begin in year N with X amount of money, and you put that money in the beginning of year N into that CD account, it will grow in value to X*1.05 dollars. In other words, the future value of X is 1.05X.
Conversely, we can evaluate the value of future money now by looking at the same interest rate. Instead, suppose that you will have Y dollar in the future, say because of an impending lawsuit settlement. You cannot have the money from the source now, but will have to wait one year.
If you want to figure out either how much money you would need now to attain Y in one year by putting said money into the CD account noted above (or alternatively how much you should sell the rights to collect on your settlement for), you just need to do the math from above in reverse. If present value (P) times interest rate (R, here five percent) equals future value (again, Y), then Y = 1.05P, or the present value is Y/1.05.
As you will notice, with the denominator being larger than one, present value is lower than the future value. That may seem simple enough, but it is a powerful thing to note that is often ignored in trading and FAAB budgets.
It is to say, alternatively, that a transaction worth Z today is more valuable than a transaction worth Z in the future; that trading for Prince Fielder today is more valuable than doing so in two weeks, and that bidding on Hosmer now is better than bidding the same amount on Anthony Rizzo in the future, even if you think both players are equally valued.
So what does this all mean? It means that shelling out FAAB money on Hosmer in the beginning of May is more valuable than shelling out a similar sum on Rizzo in the beginning of June. The season is only 162 games long, and every day you wait, your opportunity cost is approximately 0.6 percent of potential value.
This 0.6 percent figure could and should be thought of as a discount rate applied to a player's expected production in evaluating FAAB money. It means that a worse player today could be worth more than, or equal value to, a better player who will not be on waivers until some period in the future.
Let's use Rizzo and Hosmer as an example in comparative bidding, and begin by assuming that the two are roughly equal in rate value (production per game). Both are highly-touted, power-hitting prospects that play in offense-suppressing parks with comparable-enough 2010-2011 minor league numbers.
Hosmer was called up about 35 days earlier than Rizzo. If each player, over a comparable sample of plate appearances, is roughly equal to X dollars of production, Rizzo's late call-up induces a penalty value of -15.4 percent. In other words, if you think Rizzo is worth a FAAB bid of X, then your bid on Hosmer should be approximately 15 percent larger than what you would bid on Rizzo.
As the expected waiver pool thins, there is also a scarcity premium that should be considered. Imagine that by the All-Star Break, all of Domonic Brown, Hosmer, Rizzo, Moustakas, Ackley, and Desmond Jennings have been called up.
That could leave Lawrie as the lone "impact" hitting prospect of great consideration that you can count on to be on the big league roster getting a healthy series of playing time. If Lawrie is worth X to you at his call up time, then you better bet more than X, particularly if it is a hard-to-fill position like second, shortstop or third.
This might all seem simple in form, but timing truly is an overlooked value concept in fantasy baseball, where we preach patience.
On one hand, we say "ride out his slump" and caution blowing all your FAAB budget on the first day of the season to acquire a huge prospect like Heyward or Michael Pineda. On the other hand, as noted above, every day you wait is another day the impact of the move you seek to make loses some gravity of impact.
A lot of owners bid conservatively on Hosmer in my leagues, whom I won on every FAAB bet I could place for under $70, because, as they relayed to me, why overbid now when there are comparably valuable players looming out there, some who play premium positions, such as Rizzo, Moustakas, Lawrie, and Ackley (who, in my eyes, is just Kelly Johnson with less power and a bit more batting average). "Why throw away $70 on Hosmer when I know I can probably win Rizzo for less?" one owner relayed to me.
The answer is all of the things I have said above. With Hosmer off the board, there is one less prospective impact player on the waiver wire. You also get Hosmer, even if inferior to Rizzo, a whole month earlier. Particularly if you were employing Luke Scott or Ike Davis at first entering May, having Hosmer today over Rizzo in the future could mean the difference between a league title and another disappointing finish.
Showing posts with label Auction. Show all posts
Showing posts with label Auction. Show all posts
DME's Expert Draft Team
Here is my roster from a 12-team experts draft with deep, weekly rosters (5 OF, CI, MI, 2 C, etc.) post-trade I just made (I traded Carlos Santana ($25) + Carlos Carrasco ($1) for Shin-Soo Choo ($23) + Kyle Drabek ($3)). My team should be really good in June...
C-Joe Mauer ($30)
C-Brian McCann ($24)
1B-Freddie Freeman ($1)
2B-Chase Utley ($31)
SS-Hanley Ramirez ($49)
3B-Adrian Beltre ($24)
MI-Mike Aviles ($4)
CI-Chipper Jones ($1)
OF1-Shin-Soo Choo ($23)
OF2-Carlos Beltran ($4)
OF3-Franklin Gutierrez ($1)
OF4-Johnny Damon ($1)
OF5-Dustin Ackley ($1)
UT-Mike Moustakas ($3)
SP-Ubaldo Jimenez ($17)
SP-Mat Latos ($19)
RP-Jonathan Broxton ($9)
RP-Brandon Lyon ($3)
P-Luke Gregerson ($2)
P-Rafael Soriano ($2)
P-Jonny Venters ($1)
P-Brandon Webb ($1)
P-Mike Minor ($1)
BN-Kyle Drabek ($3)
BN-Joba Chamberlain ($2)
BN-Michael Pineda ($1)
BN-Dallas Braden ($1)
BN-Juan Francisco ($1)
As you can probably tell, I'm not exactly proud of this roster. Certain major buys of mine (Beltre for $24, Latos for $19, Broxton for $9) felt really stupid in hindsight when guys like Ian Kennedy went late for $2, only three other closers went for $9 or more, and Michael Young went for a measly $8. My "get elite catchers, shortstops and closers" strategy also went limp...this is a poor stars and scrubs team, but it projects for elite batting average, which will give me waiver wire flexibility as I try to Frankenstein together a team.
C-Joe Mauer ($30)
C-Brian McCann ($24)
1B-Freddie Freeman ($1)
2B-Chase Utley ($31)
SS-Hanley Ramirez ($49)
3B-Adrian Beltre ($24)
MI-Mike Aviles ($4)
CI-Chipper Jones ($1)
OF1-Shin-Soo Choo ($23)
OF2-Carlos Beltran ($4)
OF3-Franklin Gutierrez ($1)
OF4-Johnny Damon ($1)
OF5-Dustin Ackley ($1)
UT-Mike Moustakas ($3)
SP-Ubaldo Jimenez ($17)
SP-Mat Latos ($19)
RP-Jonathan Broxton ($9)
RP-Brandon Lyon ($3)
P-Luke Gregerson ($2)
P-Rafael Soriano ($2)
P-Jonny Venters ($1)
P-Brandon Webb ($1)
P-Mike Minor ($1)
BN-Kyle Drabek ($3)
BN-Joba Chamberlain ($2)
BN-Michael Pineda ($1)
BN-Dallas Braden ($1)
BN-Juan Francisco ($1)
As you can probably tell, I'm not exactly proud of this roster. Certain major buys of mine (Beltre for $24, Latos for $19, Broxton for $9) felt really stupid in hindsight when guys like Ian Kennedy went late for $2, only three other closers went for $9 or more, and Michael Young went for a measly $8. My "get elite catchers, shortstops and closers" strategy also went limp...this is a poor stars and scrubs team, but it projects for elite batting average, which will give me waiver wire flexibility as I try to Frankenstein together a team.
Valuing Players With Your E.Y.E.S.
The following is taken from my latest article for The Hardball Times:
I have come to love the auction draft fantasy format. Tired of watching my targeted sleepers and studs go a few picks before my turn, sick of being entirely helpless and at the mercy of my fantasy provider's value rankings, I opted to work the free market in recent seasons.
The glory of auction is that every owner has a chance at every player. The auction format and bidding market equalize the stress of not having a top five pick in your league's snake draft, precluding you from one of the upper echelon elite players. Auction is not without its own stresses, however. The free market operates efficiently only when its participants are informed. Like the seller of an album of baseball cards who does not understand the value of a 1963 Topps Pete Rose card, an uninformed bidder is substantially less likely to profit on the open market.
Being informed requires more than knowing raw stats and having a player projection. Believing that Jay Bruce will hit .280 next season with 30 home runs, five to 10 stolen bases, and 85 runs and RBI is nice, but unless you know the league average player output, Bruce's projection is meaningless. Player valuation requires some appreciation of relative category weights and scarcity. To deal with this issue and weight player values, I have a methodology, which I explain below. I have also included a pricing guide applying this methodology to Oliver's 2011 preseason player projections as of Feb. 1.
First, three points that will inevitably arise:
My methodology, like any pricing guide, has an inherent limitation: the quality of the projection system. My methodology weights relative stat production, but if the projections are weak, then the pricing guide will inevitably be weak. For the purpose of this article, I used Brian Cartwright's Oliver projection system from The Hardball Times to create a pricing guide. Oliver has proven to be a very reliable system, on par with ZiPS (not released in full yet) and CHONE (now defunct). You can access Oliver's statistical projections (and more) by subscribing to THT Forecasts.
Second, for the purposes of simplification, I analyze all hitters as utility players. Some people like to adjust their numbers to account for position, but I'd rather just index the top 20 players by position after I have my Z-Score totals and know how much actual value, unbiased by position, each player is going to provide.
Third, there are better and more accurate methodologies out there. One is readily available via THT Forecasts. Another system is one created by Tom Tango a few years back. I know that Zach Sanders (of Fangraphs) and some others are working on something very similar as well. What I present to you today is merely what I do on my own, which I hardly proclaim to be unique. I am certain that someone out there probably uses, and invented before me, this same methodology to value players.
In honor of Steve Phillips, who values baseball players with his eyes and heart, I have dubbed this system of dollar valuation the Expected Year's Evaluation Statistic, or E.Y.E.S. for short.
Determining the size of your expected active player pool (those players who will be on some player's team as either a starter or bench player) is essential because only a limited set of major league talent gets used in fantasy. This is true even of AL- and NL- only formats. Because not every player gets drafted, valuing players is a two-tiered process. First, you separate potential active roster talent from "the rest." Then, you evaluate the players in the pool. This will be explained in further detail below.
Before we can determine a potential player pool, we must determine an approximate depth for the pool. Let the number of teams in your league equal X. Let the total number of drafted hitters per team equal Y, and the total number of drafted pitchers per team equal Z. For the purposes of this analysis, I am going to use a 12-team league with one of each active infield position player (C, 1B, 2B, SS, 3B), one corner infielder (CI), one middle infielder (MI), five outfielders (OF), and one utility player (UTIL), for a total of 13 hitters per team. I am also going to use nine generic pitching slots. There is also the matter of the bench. I usually play in leagues with five bench spots, which will be spit three to two between hitters and pitchers. This gives us a grand total of 192 batters and 132 pitchers, for a total of 324 players.
Of course, the player pool is quite subjective and often much deeper than a consensus 324 players. In step 2, I deal with this problem, but 192 hitters and 132 pitchers will be our starting point.
A Z-Score sounds much more complex than it really is. Okay, maybe not, but Excel (or Open Office) makes Z-Score calculations easy. Simply put, a Z-Score measures how many standard deviations from the mean (either positively or negatively) a given statistic is. For our purposes, players with high Z-Scores will help you in a given statistical category. Players with a Z-Score of 0 will have a neutral effect. Players with Z-Scores below 0 will hurt you in a category. The greater (or lower) a Z-Score, the more of an impact, for better or worse, a given player will have for your fantasy team in a calculated category.
To fill out a player pool, I first calculate the Z-Scores for every player for each of the hitting and pitching categories. For hitters, I use only a pool of players expected to accrue a minimum of 400 plate appearances. I am sure there are a few fantasy-valuable players out there who will come to the plate fewer than 400 times this season, but they are few, so I have ignored them for this demonstration. Per Oliver's 2011 projections, the pool of hitters who are expected to have 400-plus plate appearances is 436 players deep. Among these 436, the mean batting average is .265, the mean home run total is 14.0, the mean stolen base total is 8.1, the mean runs total is 62.6 and the mean RBI total is 61.0. The standard deviations for these respective categories are .019, 7.9, 7.8, 11.6 and 17.1.
To calculate any given category's Z-Score for a player, you simply take the difference of that player's stat against the mean for that stat and divide it by the standard deviation. For instance, Albert Pujols is projected by Oliver to hit 43 home runs. To calculate Pujols' home run Z-Score (labeled Z-HR in my charts), we take the home run mean(14) and standard deviation (7.9) and use the following formula: (43-14)/7.9. If you plug that into your calculator, you will find that Pujols' Z-HR is 3.67.
Now do this for every player for every statistic, and when you are done, sum up each player's cumulative Z-Score. Then repeat this process for pitchers, using wins, saves, ERA, WHIP and strikeouts. I also like to use K/9 for the purposes of evaluating pitchers.
By now, you have probably wondered how I plan to value rate stats. A .300 hitter is not nearly as valuable as a .290 hitter if the .300 hitter is getting two-thirds the playing time of the .290 hitter. To deal with this problem, I determined the average at-bat total for all players expected to accrue 400 or more plate appearances (468.8) and I multiplied the batting average Z-Score by the player's actual at-bats total divided by the league average at-bats total. This adjusts the Z-Scores for batting average to reflect playing time. I do something similar with innings pitched for pitchers.
Once we have a series of player Z-Score sums for batters and pitchers, we need to select the "cream of the crop" to represent the potential player pool. If you recall above, we determined that, at least for our example, our league would use 324 active players (192 batters and 132 pitchers). Accordingly, I begin by selecting the 192 batters and 132 pitchers with the highest Z-Score sums. These players should represent our best "all-around players" for drafting.
This is not the end of step 3, however. Fantasy teams are dynamically comprised and owners often draft one or two category guys to fill holes and to stream. To account for this, I then rank the residual player pool by categorical Z-Score. I then pull out any player with a Z-Score of 1.0 or higher in any fantasy category. I also add any remaining players who I think are "interesting" to my player pool, even if their categorical Z-Score is less than 1.0, as $1 buys to keep an eye out for. Not even the best projection systems gets every player right, and this element of player selection requires personal judgment. For instance, Oliver is incredibly bearish on Aaron Hill, who I like for 2011. His Z-Score sum is not within the top 192 and he does not have a Z-Score of 1.0 or greater in any single category. Nonetheless, I added him to my player pool.
Doing this, I ended up with 235 hitters and 166 pitchers, for a grand total of 401 players. This seems reasonable.
Now that we have our pool of 401 players, we need to recalculate our Z-Scores to reflect the draft pool talent. If you want remotely reliable numbers for draft day, it is pointless to value player X against undrafted players. These 401 player represent the best of the fantasy crop, and accordingly, the means and standard deviations in each category between them will change. Among the 235 hitters in our example sample, for instance, the mean batting average jumps up to .272 (from .265), the mean home run total jumps to 17.2 (from 14.0), the mean stolen base total jumps to 10.6 (from 8.1), the mean runs total changes to 70.4 (from 62.6), and the RBI total bumps up to 69.1 (from 61.0). The standard deviations also change to 0.018, 8.8, 9.3, and 18.0, respectively. The average expected at-bat total also rises from 468.8 to 497.2.
Re-calculating and re-summing each player's Z-Score, we are left with the expected relative value weights of each player.
Once we have relatively weighted Z-Score sums for each player, we now need to determine each player's dollar value.
To calculate dollar values, we must determine the total amount of money in our fictional economy. Simply put, we need to determine how much money exists to be split among the players with positive Z-Scores (all players who are ultimately assigned Z-Scores below $1 will have their dollar values rounded up to $1). Using the standard $260/team budget, applied to our 12-team fictional league, we find an economy with $3,120 in it. In real life, you could barely buy a pimped-out MacBook pro with that money, but here you can buy CC Sabathia!. Alas, I digress.
Take this $3,120 total and divide it by the total Z-Score sum across all hitters and pitchers. The Z-Score sum from which to divide the economy value by should not include any players with negative Z-Scores; ignore these players for the sake of Z-Score valuation. Doing this will give you a rough dollar value estimate per Z-Score. Take this dollar value and then apply it to each player's Z-Score to get your estimated dollar value for that player.
Keep in mind that the minimum bid for any player is $1. Certain players in our draft pool, particularly the "one category" players (hitters or pitchers with a Z-Score of 1.0 or greater in only a single category), have Z-Scores below 1.0. Other players probably have Z-Scores that, when multiplied by our Z-Score dollar value, have Z-Scores under $1. Because these players will actually cost you at least $1, all players with dollar values under $1 are rounded to $1.
And there you have it. That is how you can calculate dollar values (EYES) for auction on your own. Use your EYES (not your heart) on draft day! Empower yourself with information. Of course, you could also do none of this analysis, save yourself some time, and purchase a subscription to the substantially more accurate THT Forecasts, which has its own built-in pricing guide for Oliver. I guarantee you those numbers are much better than mine.
I have come to love the auction draft fantasy format. Tired of watching my targeted sleepers and studs go a few picks before my turn, sick of being entirely helpless and at the mercy of my fantasy provider's value rankings, I opted to work the free market in recent seasons.
The glory of auction is that every owner has a chance at every player. The auction format and bidding market equalize the stress of not having a top five pick in your league's snake draft, precluding you from one of the upper echelon elite players. Auction is not without its own stresses, however. The free market operates efficiently only when its participants are informed. Like the seller of an album of baseball cards who does not understand the value of a 1963 Topps Pete Rose card, an uninformed bidder is substantially less likely to profit on the open market.
Being informed requires more than knowing raw stats and having a player projection. Believing that Jay Bruce will hit .280 next season with 30 home runs, five to 10 stolen bases, and 85 runs and RBI is nice, but unless you know the league average player output, Bruce's projection is meaningless. Player valuation requires some appreciation of relative category weights and scarcity. To deal with this issue and weight player values, I have a methodology, which I explain below. I have also included a pricing guide applying this methodology to Oliver's 2011 preseason player projections as of Feb. 1.
First, three points that will inevitably arise:
My methodology, like any pricing guide, has an inherent limitation: the quality of the projection system. My methodology weights relative stat production, but if the projections are weak, then the pricing guide will inevitably be weak. For the purpose of this article, I used Brian Cartwright's Oliver projection system from The Hardball Times to create a pricing guide. Oliver has proven to be a very reliable system, on par with ZiPS (not released in full yet) and CHONE (now defunct). You can access Oliver's statistical projections (and more) by subscribing to THT Forecasts.
Second, for the purposes of simplification, I analyze all hitters as utility players. Some people like to adjust their numbers to account for position, but I'd rather just index the top 20 players by position after I have my Z-Score totals and know how much actual value, unbiased by position, each player is going to provide.
Third, there are better and more accurate methodologies out there. One is readily available via THT Forecasts. Another system is one created by Tom Tango a few years back. I know that Zach Sanders (of Fangraphs) and some others are working on something very similar as well. What I present to you today is merely what I do on my own, which I hardly proclaim to be unique. I am certain that someone out there probably uses, and invented before me, this same methodology to value players.
In honor of Steve Phillips, who values baseball players with his eyes and heart, I have dubbed this system of dollar valuation the Expected Year's Evaluation Statistic, or E.Y.E.S. for short.
Step 1: Determining the size of the player pool
Determining the size of your expected active player pool (those players who will be on some player's team as either a starter or bench player) is essential because only a limited set of major league talent gets used in fantasy. This is true even of AL- and NL- only formats. Because not every player gets drafted, valuing players is a two-tiered process. First, you separate potential active roster talent from "the rest." Then, you evaluate the players in the pool. This will be explained in further detail below.
Before we can determine a potential player pool, we must determine an approximate depth for the pool. Let the number of teams in your league equal X. Let the total number of drafted hitters per team equal Y, and the total number of drafted pitchers per team equal Z. For the purposes of this analysis, I am going to use a 12-team league with one of each active infield position player (C, 1B, 2B, SS, 3B), one corner infielder (CI), one middle infielder (MI), five outfielders (OF), and one utility player (UTIL), for a total of 13 hitters per team. I am also going to use nine generic pitching slots. There is also the matter of the bench. I usually play in leagues with five bench spots, which will be spit three to two between hitters and pitchers. This gives us a grand total of 192 batters and 132 pitchers, for a total of 324 players.
Of course, the player pool is quite subjective and often much deeper than a consensus 324 players. In step 2, I deal with this problem, but 192 hitters and 132 pitchers will be our starting point.
Step 2: Calculating preliminary Z-Scores
A Z-Score sounds much more complex than it really is. Okay, maybe not, but Excel (or Open Office) makes Z-Score calculations easy. Simply put, a Z-Score measures how many standard deviations from the mean (either positively or negatively) a given statistic is. For our purposes, players with high Z-Scores will help you in a given statistical category. Players with a Z-Score of 0 will have a neutral effect. Players with Z-Scores below 0 will hurt you in a category. The greater (or lower) a Z-Score, the more of an impact, for better or worse, a given player will have for your fantasy team in a calculated category.
To fill out a player pool, I first calculate the Z-Scores for every player for each of the hitting and pitching categories. For hitters, I use only a pool of players expected to accrue a minimum of 400 plate appearances. I am sure there are a few fantasy-valuable players out there who will come to the plate fewer than 400 times this season, but they are few, so I have ignored them for this demonstration. Per Oliver's 2011 projections, the pool of hitters who are expected to have 400-plus plate appearances is 436 players deep. Among these 436, the mean batting average is .265, the mean home run total is 14.0, the mean stolen base total is 8.1, the mean runs total is 62.6 and the mean RBI total is 61.0. The standard deviations for these respective categories are .019, 7.9, 7.8, 11.6 and 17.1.
To calculate any given category's Z-Score for a player, you simply take the difference of that player's stat against the mean for that stat and divide it by the standard deviation. For instance, Albert Pujols is projected by Oliver to hit 43 home runs. To calculate Pujols' home run Z-Score (labeled Z-HR in my charts), we take the home run mean(14) and standard deviation (7.9) and use the following formula: (43-14)/7.9. If you plug that into your calculator, you will find that Pujols' Z-HR is 3.67.
Now do this for every player for every statistic, and when you are done, sum up each player's cumulative Z-Score. Then repeat this process for pitchers, using wins, saves, ERA, WHIP and strikeouts. I also like to use K/9 for the purposes of evaluating pitchers.
By now, you have probably wondered how I plan to value rate stats. A .300 hitter is not nearly as valuable as a .290 hitter if the .300 hitter is getting two-thirds the playing time of the .290 hitter. To deal with this problem, I determined the average at-bat total for all players expected to accrue 400 or more plate appearances (468.8) and I multiplied the batting average Z-Score by the player's actual at-bats total divided by the league average at-bats total. This adjusts the Z-Scores for batting average to reflect playing time. I do something similar with innings pitched for pitchers.
Step 3: Distillation
Once we have a series of player Z-Score sums for batters and pitchers, we need to select the "cream of the crop" to represent the potential player pool. If you recall above, we determined that, at least for our example, our league would use 324 active players (192 batters and 132 pitchers). Accordingly, I begin by selecting the 192 batters and 132 pitchers with the highest Z-Score sums. These players should represent our best "all-around players" for drafting.
This is not the end of step 3, however. Fantasy teams are dynamically comprised and owners often draft one or two category guys to fill holes and to stream. To account for this, I then rank the residual player pool by categorical Z-Score. I then pull out any player with a Z-Score of 1.0 or higher in any fantasy category. I also add any remaining players who I think are "interesting" to my player pool, even if their categorical Z-Score is less than 1.0, as $1 buys to keep an eye out for. Not even the best projection systems gets every player right, and this element of player selection requires personal judgment. For instance, Oliver is incredibly bearish on Aaron Hill, who I like for 2011. His Z-Score sum is not within the top 192 and he does not have a Z-Score of 1.0 or greater in any single category. Nonetheless, I added him to my player pool.
Doing this, I ended up with 235 hitters and 166 pitchers, for a grand total of 401 players. This seems reasonable.
Step 4: Calculating primary Z-Scores
Now that we have our pool of 401 players, we need to recalculate our Z-Scores to reflect the draft pool talent. If you want remotely reliable numbers for draft day, it is pointless to value player X against undrafted players. These 401 player represent the best of the fantasy crop, and accordingly, the means and standard deviations in each category between them will change. Among the 235 hitters in our example sample, for instance, the mean batting average jumps up to .272 (from .265), the mean home run total jumps to 17.2 (from 14.0), the mean stolen base total jumps to 10.6 (from 8.1), the mean runs total changes to 70.4 (from 62.6), and the RBI total bumps up to 69.1 (from 61.0). The standard deviations also change to 0.018, 8.8, 9.3, and 18.0, respectively. The average expected at-bat total also rises from 468.8 to 497.2.
Re-calculating and re-summing each player's Z-Score, we are left with the expected relative value weights of each player.
Step 5: Calculating dollar values
Once we have relatively weighted Z-Score sums for each player, we now need to determine each player's dollar value.
To calculate dollar values, we must determine the total amount of money in our fictional economy. Simply put, we need to determine how much money exists to be split among the players with positive Z-Scores (all players who are ultimately assigned Z-Scores below $1 will have their dollar values rounded up to $1). Using the standard $260/team budget, applied to our 12-team fictional league, we find an economy with $3,120 in it. In real life, you could barely buy a pimped-out MacBook pro with that money, but here you can buy CC Sabathia!. Alas, I digress.
Take this $3,120 total and divide it by the total Z-Score sum across all hitters and pitchers. The Z-Score sum from which to divide the economy value by should not include any players with negative Z-Scores; ignore these players for the sake of Z-Score valuation. Doing this will give you a rough dollar value estimate per Z-Score. Take this dollar value and then apply it to each player's Z-Score to get your estimated dollar value for that player.
Keep in mind that the minimum bid for any player is $1. Certain players in our draft pool, particularly the "one category" players (hitters or pitchers with a Z-Score of 1.0 or greater in only a single category), have Z-Scores below 1.0. Other players probably have Z-Scores that, when multiplied by our Z-Score dollar value, have Z-Scores under $1. Because these players will actually cost you at least $1, all players with dollar values under $1 are rounded to $1.
And there you have it. That is how you can calculate dollar values (EYES) for auction on your own. Use your EYES (not your heart) on draft day! Empower yourself with information. Of course, you could also do none of this analysis, save yourself some time, and purchase a subscription to the substantially more accurate THT Forecasts, which has its own built-in pricing guide for Oliver. I guarantee you those numbers are much better than mine.
