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A New Way to Think About "Buying Low" and "Selling High&#3 (1 Viewer)

Aabye

Footballguy
My thoughts are pretty lengthy, so apologies for the sheer volume here. I'm interested in feedback/criticism.

A New Way to Think About “Buying Low” and “Selling High” in Dynasty

The Old Way

Before I get started in earnest, I want to get specific about the old notion of what it means to buy a player “low” or sell a player “high.” First, every NFL player has a specific dynasty value, expressible in remaining career VBD points. VBD points is the cental footballguys concept that a player's value is found by computing his fantasy output relative to a baseline of players at his position. Career VBD is just the sum total of a player's yearly VBD totals. For example, after the 2002 season, Priest Holmes had a remaining value of 272 VBD points. After the 2003 season, Holmes had a remaining value of 41 points. We can call this number a player’s “TRUE VALUE.” Of course, we don’t know any active player’s true value at any time, since we can't determine with certainty what the future holds. Since true value is not ascertainable, we have to make due with a players “PERCEIVED VALUE,” which is each person’s best attempt to estimate a player’s true value. Finally, I’m going to call the method by which one assigns a player's perceived value (in terms of remaining VBD points) a MODEL.

Now I’m going to idealize the situation a bit and assume that an owner is able to simply trade VBD points for a given player. Instead of trading players for players, we treat players like stock and use a medium of exchange (here VBD points) to buy and sell.

With these terms defined and stipulations given, we can define what it means to “buy low” or “sell high”:

You “BUY LOW” when the VBD points you pay for a player are lower than his true value.

You “SELL HIGH” when the VBD points you get for a player are higher than his true value.

Fairly simple idea. It’s good to note here that “buy low” and “sell high” do not mean that we sell a player at his peak value or buy a player at his lowest value point.

 
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A Better Way

Let’s add another pair of concepts: a PERFECT MODEL is one that sets a player’s value at some number of career VBD points (x) such that you cannot profitably bet that the player’s value will be either higher or lower than x. This definition also gives us another definition: an IMPERFECT MODEL is one that set’s a player’s value at some number (x) such that you can profitably bet that the player’s value will be either higher or lower than x.

Since people do value players differently, it follows that some people are using imperfect models. And that means that those models can be exploited.

Let’s say that A’s model deviates 10% from the perfect model and that B’s model deviates 20% from the perfect model. In real numbers, this means that for some player, A assigns a value = the value assigned by the perfect model ± 10%. And, of course, B assigns a value = the value assigned by the perfect model ± 20%. So if the perfect model would set a player’s value at 100, A will value that player at either 90 or 110 and B will value that player at either 80 or 120. There are now 4 possible situations:

A = 90 and B = 80: A buys for 90 or less

A = 110 and B = 80: A buys for 110 or less

A = 90 and B = 120: B buys for 120 or less

A = 110 and B = 120: B buys for 120 or less

If we sensibly assume that A and B meet halfway, we get this configuration:

A = 90 and B = 80: A buys for 85

A = 110 and B = 80: A buys for 95

A = 90 and B = 120: B buys for 105

A = 110 and B = 120: B buys for 115

A is always underpaying for the player and B is always overpaying, relative to the perfect model. It doesn’t matter whether both overvalue or undervalue the player or if one of them overvalues and one of them undervalues. A always wins.

Now it may be objected that while A always underpays with respect to the perfect model, this does not mean that A is paying less for a player than that player is actually worth. Likewise, B may overpay with respect to the perfect model but that doesn’t mean he’s paying more than the player’s true value. This is correct. But regardless of the strength of the model, there is no way to determine a player’s true value, and so there is nothing we can do to improve our situation. Your model should attempt to match the PERFECT MODEL, not a player’s TRUE VALUE.

Consider the following game of betting on the value of the roll of a die: You may roll a fair, six-sided die once and you will receive $1 · the # shown on the die. How much should you be willing to pay to play? We can figure this out by taking each possible outcome multiplied by its probability, then adding them all up to get our expectation.

$1·(1/6) + $2·(1/6) + $3·(1/6) + $4·(1/6) + $5·(1/6) + $6·(1/6) = $3.50

Our expectation for any particular roll of the die is $3.50, so we should be willing to pay any amount that is lower than that. At $3.50 it becomes a fair game and for any amount >$3.50, we’re getting ripped off. The above equation gives us a perfect model for the game. But notice that if you agree to pay $3.25 to roll the die, you’re still going to lose half the time. Perfect models aren’t crystal balls. They just allow you to maximize expectation.

Now lets imagine instead that you thought about the game in terms of paying less than the true value of any particular roll. In this case you’ll try as hard as you can to guess the value of the roll, then pony up some amount of money that is lower than they value you predict will be rolled. This is a terrible way to proceed. You’ll end up rejecting good deals and accepting bad ones and you’ll evaluate the wisdom of each particular bet based on the results that you get.

If you chase the old concept of buying low, this is exactly what you are doing. You try to guess the true value for some player and then try to pay less than that value. “Well, I think Frank Gore has 3 more good seasons left in him, which works out to (x) number of VBD points, so I’ll acquire him if I can pay less than (x) for him.”

 
The Bad News

It’s easy to conceptualize all of the possibilities for a six-sided die. But how can you weigh all of the possibilities for an NFL player? In 2006, Brandon Marshall came into the league as a 3rd round draft choice of the Denver Broncos. He did nothing his rookie year. Then he broke out and posted more than 1,300 yards in his second season. Then there was a coaching change in Denver. Then he was traded to Miami. Then his wife stabbed him. How can you figure out what to expect out of this player in the future?

Let’s start with a fairly comprehensive list of factors that would probably go into modeling a player’s dynasty value:

Age

Draft Stock

Talent

Surrounding Talent

Job Security / Opportunity

NFL Team’s Philosophy

Early Career Production

Production Last Season

Recent Production (Last 2-3 seasons, cumulative)

Career Production / Consistency

Per-game Production

Contract Status

Positional Scarcity

Injury Concerns

Character Concerns

Development Concerns

Fantasy Team’s Strengths and Needs

Workload

College Production

In addition to these factors, there is a high degree of variance and unpredictability as well. Injuries, trades, coaching changes, competition, scheme changes, team makeup, and off the field issues are just a few ways to drastically impact a player’s dynasty value.

The apparent complexity of the modeling process has led some people to conclude that the goal of assigning quantitative dynasty values is folly – an attempt to magically assign a precise numerical value when the situation is so muddled with uncertainty that precision is simply not possible. This criticism is misguided. Insurance companies, banks, and casinos all operate by setting precise premiums, rates of interest, and odds in conditions of uncertainty and change. They make money because they take slightly the better of it on each of these transactions, despite the fact that individual transactions might represent significant risks. How could it be that we can quantitatively model our health, a company’s success, and spins of a roulette wheel but we can’t quantitatively model the careers of running backs? Of course we can quantitatively model them.

There is, perhaps, a grain of truth to the criticism. It is certainly the case that our models aren’t particularly good. Insurance companies, banks, and casinos have been around for a long time and they have been paying smart, dedicated people to set their prices. Those people have come up with more and more sophisticated models that have more and more predictive power. Models for dynasty value are crude and simplistic by comparison. We’re likely to assign values to particular players that are not all that close to the value that the perfect model would assign. That’s the bad news.

 
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The Good News

The good news is that we don’t need great models. We just need better models than the other guy is using. Of course, the better the model we’re using, the better we’ll do. While we’re never going to be able to predict how a particular player will do, we can figure out which factors matter most and start from there. Every owner already considers age, past production, draft pedigree, etc. in evaluating players but most owners are not systematic and don’t have any idea of how these factors should be weighted or how they work together. That means that most owners get lazy and cheat somewhat. Here are a few ways that people cheat:

1. Players are lumped into age tiers instead of considering their actual age.

21-24 year old RBs are “young.” 25-27 year old RBs are “veterans.” 28-30 year old RBs are “old.” WRs are “young” until 25 or 26, “veterans” for another five years or so, and then turn “old” at about age 31 or 32. It seems to work like this: when owners can see the end coming, they start to jump ship. A 27-year-old RB is going to be around for a while but a 28-year-old RB is good this season and maybe next season, after which you’re stuck with a washed up player you can’t trade. The window seems to be about 3 years. If owners don’t anticipate a production drop-off within three seasons, they don’t consider age a problem.

2. Players are projected to keep on doing pretty much what they did last season.

Again, this is just the easiest thing to do. What owners tend to do is look at last season rankings and then adjust somewhat for age. Players who have been solid producers and aren’t too old are penciled in to repeat their recent performances. Some allowances are made for career years, one-year wonders, and injuries but for the most part, where a player is ranked for dynasty purposes is pretty much a function of where he finished the previous season.

3. If a player hasn’t done anything in two seasons, he’s forgotten entirely.

Here are a few players who were productive starters in 2008, then had down years in 2009 and 2010: Steve Smith (Car), Eddie Royal, Anquan Boldin, Marshawn Lynch, Ronnie Brown, Jay Cutler. With the possible exception of Boldin, none of them carries any real trade value at this point. If an owner hasn’t seen production in a few seasons, that player becomes washed up, injury prone, or a flash-in-the-pan and owners are often looking to sell at salvage prices.

4. A rookie gets two years to start producing, then he’s a bust.

The luster of a rookie pick lasts about one season. Owners are generally not worried if a rookie doesn’t see the field much or doesn’t produce when he’s out there. During his second season, he’s supposed to start making an impact. If his sophomore campaign doesn’t indicate signs of life, most owners look to dump dead weight.

5. Owners worry about whether a draft pick was a “reach” or a “steal.”

In 2009, draft pundits shook their heads at the Oakland Raiders’ choice to draft Darrius Heyward-Bey with the 7th selection overall. “Terrible choice!” “Should have been Crabtree!” “Worst pick in the draft!” Later, at 30, the Titans selected Kenny Britt and at 36 the Browns selected Brian Robiskie. Despite DHB being the highest-rated of these prospects according to almost every scout, he was often selected behind them in rookie drafts. The reasoning was pretty clear. All of them were going to anemic passing offenses, but DHB had the “bust” label attached to him the minute he put on the Raiders cap. As soon as that label is stuck on a player, owners shy away.

6. Owners overemphasize a prospect’s similarities with recent players.

Examples abound. When Darren McFadden came into the league and struggled, people compared him to Reggie Bush. Bush never found a foothold as a fantasy-relevant RB, and some owners took away the lesson that top 10 RBs aren’t sure things and dropped McFadden. When McFadden broke out last year, it gave hope to C.J. Spiller owners, who reasoned that if McFadden could put it together in his third year, there was more reason to write of Spiller’s pedestrian rookie campaign. Mike Shanahan’s use of Terrell Davis, Olandis Gary and Mike Anderson led (and, in some cases, leads) owners to think that the next late-round Shanahan RB might have similar success. The recent successes of Andre Johnson, Larry Fitzgerald and Calvin Johnson have led many owners to see A.J. Green as close to a sure thing, now that memories of Charles Rogers, Peter Warrick, Michael Westbrook, and Desmond Howard have faded. Cam Newton and Sam Bradford were both selected 1st overall but Newton is compared to Vince Young while Bradford was usually compared to Matt Ryan or Matthew Stafford. The successes of Ryan and Stafford helped Bradford’s post-draft value while Young’s struggles are clearly tempering enthusiasm for Newton. Comparing prospects to recent players is, to some extent, unavoidable but doing so is likely to introduce an unhelpful bias into the evaluation process.

If you find yourself evaluating players in one of these ways, realize that they are shortcuts to actually doing the work. It is certainly the case that age, past production, early-career production, and player comparisons are factors in evaluating a player’s dynasty prospects but it’s never the all-or-nothing value assessment that most of these shortcuts invite.

 
Adding a Little Complexity

At the outset, I idealized the player transaction process by using VBD points as a medium for exchange. In practice we don’t trade players for VBD points. We trade them for other players and/or draft picks. Despite this additional complexity, the same principle still applies. Rather than worrying about the true value of the players and draft picks in a transaction, we should worry about their values according to the perfect model. The bad news is that this additional layer of complexity makes it even more difficult to gauge player values, since there are two or more values that need to be modeled, rather than just one.

This added complexity doesn’t change the overall approach, but it makes each particular situation more difficult to analyze properly. The process of evaluating and trading players is convoluted and time consuming, but by taking the time to model each player and pick’s estimated future value, you can gain a clear edge over other owners in your league.

Again, apologies on the length of all of this.

 
Lineup Builds Complexity

I think it's interesting to note that the same player can have different values from the same owner depending on the rest of the team. For example, if I own Aaron Rodgers and Michael Vick, I will probably put less of a value on Vick simply because he's not my starter.

 
Let’s say that A’s model deviates 10% from the perfect model and that B’s model deviates 20% from the perfect model. In real numbers, this means that for some player, A assigns a value = the value assigned by the perfect model ± 10%. And, of course, B assigns a value = the value assigned by the perfect model ± 20%. So if the perfect model would set a player’s value at 100, A will value that player at either 90 or 110 and B will value that player at either 80 or 120. There are now 4 possible situations:A = 90 and B = 80: A buys for 90 or lessA = 110 and B = 80: A buys for 110 or lessA = 90 and B = 120: B buys for 120 or lessA = 110 and B = 120: B buys for 120 or lessIf we sensibly assume that A and B meet halfway, we get this configuration:A = 90 and B = 80: A buys for 85A = 110 and B = 80: A buys for 95A = 90 and B = 120: B buys for 105A = 110 and B = 120: B buys for 115A is always underpaying for the player and B is always overpaying, relative to the perfect model. It doesn’t matter whether both overvalue or undervalue the player or if one of them overvalues and one of them undervalues. A always wins.
You lost me here. What the probability distribution for A and B? Is it uniform? Is it Gaussian? Why do you assume that A and B are always sampling the same number of sigma away from the mean in the same direction? For example, why can't you have A = 90 and B = 91, and hence B wins?This is really long, you might want an executive summary in the first post. I got here and was a little bored because I didn't know where you were going with all this.
 
Let’s say that A’s model deviates 10% from the perfect model and that B’s model deviates 20% from the perfect model. In real numbers, this means that for some player, A assigns a value = the value assigned by the perfect model ± 10%. And, of course, B assigns a value = the value assigned by the perfect model ± 20%. So if the perfect model would set a player’s value at 100, A will value that player at either 90 or 110 and B will value that player at either 80 or 120. There are now 4 possible situations:A = 90 and B = 80: A buys for 90 or lessA = 110 and B = 80: A buys for 110 or lessA = 90 and B = 120: B buys for 120 or lessA = 110 and B = 120: B buys for 120 or lessIf we sensibly assume that A and B meet halfway, we get this configuration:A = 90 and B = 80: A buys for 85A = 110 and B = 80: A buys for 95A = 90 and B = 120: B buys for 105A = 110 and B = 120: B buys for 115A is always underpaying for the player and B is always overpaying, relative to the perfect model. It doesn’t matter whether both overvalue or undervalue the player or if one of them overvalues and one of them undervalues. A always wins.
You lost me here. What the probability distribution for A and B? Is it uniform? Is it Gaussian? Why do you assume that A and B are always sampling the same number of sigma away from the mean in the same direction? For example, why can't you have A = 90 and B = 91, and hence B wins?This is really long, you might want an executive summary in the first post. I got here and was a little bored because I didn't know where you were going with all this.
It's way less complex. The only point there is that if A is closer to the perfect model than B in any direction (both high, both low, or one high and one low) then A "wins". I know that's not how it works but if I make this thing any more complex than it already is, 0 people will read it as opposed to the 3 total people that will probably read it at this length.I'd love to summarize and shorten it but don't really know how.
 
I think the same way the OP does, in general. It's more about how many FPs a player still has out there to be harvested, versus anything they've done in the past (their "rep" and historical value). There's only one flaw with this train of thought...however, and it's a BIG one! It's not the total FPs a player has left to produce that is important. It is the distribution of those points over "X" number of seasons that is important.

For example, let's look at two wide receivers: Reggie Wayne, Colts and Josh Morgan, 49ers. Wayne is the "consensus" best player of the two (I at least hope that's not debatable, lol).

Reggie Wayne is 32...a GIANT knock on his value in dynasty. However, he's averaged around 1,300 yards and over 8 TDs a season for the past five seasons...and according to "my" formula(s), he's got two seasons of high productivity left in fantasy before he falls off the cliff. So let's say he's worth 1300/8, 1300/8, 700/4, 500/3

Josh Morgan turns 26 in a month. Excellent age for a dynasty roster...but let's say he's got seven seasons left and that his next four seasons he'll see an uptick of 5% in production, with his final three seasons being more similar to 2010. So we'll say he's worth 735/2, 780/3, 820/3, 860/4, 700/2, 700/2, 700/2

Wayne's value is 3,800 yards and 23 TDs.

Morgan's value is 5,295 yards and 20 TDs.

Morgan's value "wins," right?! Wrong. Because with Wayne, you assume you're getting two more seasons of WR1 type production and two more seasons of WR4 type output. Morgan, by contrast, is never really more than an "okay" WR3. And if I could trade seven years of ho-hum WR3 production for two seasons of WR1? I do that...in a heartbeat. Because it is way, WAY more difficult to find a WR1 than it is a WR3 in dynasty. 16-team leagues, in particular!

So while I do buy into the concept, I think that looking at total future fantasy points versus predicted/assumed FFL output by-season is a giant mistake. FWIW.

 
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I think the same way the OP does, in general. It's more about how many FPs a player still has out there to be harvested, versus anything they've done in the past (their "rep" and historical value). There's only one flaw with this train of thought...however, and it's a BIG one! It's not the total FPs a player has left to produce that is important. It is the distribution of those points over "X" number of seasons that is important.For example, let's look at two wide receivers: Reggie Wayne, Colts and Josh Morgan, 49ers. Wayne is the "consensus" best player of the two (I at least hope that's not debatable, lol).Reggie Wayne is 32...a GIANT knock on his value in dynasty. However, he's averaged around 1,300 yards and over 8 TDs a season for the past five seasons...and according to "my" formula(s), he's got two seasons of high productivity left in fantasy before he falls off the cliff. So let's say he's worth 1300/8, 1300/8, 700/4, 500/3Josh Morgan turns 26 in a month. Excellent age for a dynasty roster...but let's say he's got seven seasons left and that his next four seasons he'll see an uptick of 5% in production, with his final three seasons being more similar to 2010. So we'll say he's worth 735/2, 780/3, 820/3, 860/4, 700/2, 700/2, 700/2Wayne's value is 3,800 yards and 23 TDs.Morgan's value is 5,295 yards and 20 TDs.Morgan's value "wins," right?! Wrong. Because with Wayne, you assume you're getting two more seasons of WR1 type production and two more seasons of WR4 type output. Morgan, by contrast, is never really more than an "okay" WR3. And if I could trade seven years of ho-hum WR3 production for two seasons of WR1? I do that...in a heartbeat. Because it is way, WAY more difficult to find a WR1 than it is a WR3 in dynasty. 16-team leagues, in particular!So while I do buy into the concept, I think that looking at total future fantasy points versus predicted/assumed FFL output by-season is a giant mistake. FWIW.
datonn,I'm using VBD points (points above the baseline) as opposed to FPs to somewhat counteract this.Still, even using VBD, I do agree that concentrated seasons of high VBD are usually preferable.Sorry, datonn, this was very much unclear in the OP. Editing now.
 
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I think the same way the OP does, in general. It's more about how many FPs a player still has out there to be harvested, versus anything they've done in the past (their "rep" and historical value). There's only one flaw with this train of thought...however, and it's a BIG one! It's not the total FPs a player has left to produce that is important. It is the distribution of those points over "X" number of seasons that is important.For example, let's look at two wide receivers: Reggie Wayne, Colts and Josh Morgan, 49ers. Wayne is the "consensus" best player of the two (I at least hope that's not debatable, lol).Reggie Wayne is 32...a GIANT knock on his value in dynasty. However, he's averaged around 1,300 yards and over 8 TDs a season for the past five seasons...and according to "my" formula(s), he's got two seasons of high productivity left in fantasy before he falls off the cliff. So let's say he's worth 1300/8, 1300/8, 700/4, 500/3Josh Morgan turns 26 in a month. Excellent age for a dynasty roster...but let's say he's got seven seasons left and that his next four seasons he'll see an uptick of 5% in production, with his final three seasons being more similar to 2010. So we'll say he's worth 735/2, 780/3, 820/3, 860/4, 700/2, 700/2, 700/2Wayne's value is 3,800 yards and 23 TDs.Morgan's value is 5,295 yards and 20 TDs.Morgan's value "wins," right?! Wrong. Because with Wayne, you assume you're getting two more seasons of WR1 type production and two more seasons of WR4 type output. Morgan, by contrast, is never really more than an "okay" WR3. And if I could trade seven years of ho-hum WR3 production for two seasons of WR1? I do that...in a heartbeat. Because it is way, WAY more difficult to find a WR1 than it is a WR3 in dynasty. 16-team leagues, in particular!So while I do buy into the concept, I think that looking at total future fantasy points versus predicted/assumed FFL output by-season is a giant mistake. FWIW.
datonn,I'm using VBD points (points above the baseline) as opposed to FPs to somewhat counteract this.Still, even using VBD, I do agree that concentrated seasons of high VBD are usually preferable.Sorry, datonn, this was very much unclear in the OP. Editing now.
No worries! I actually did get your train of thought related to points above the baseline. I just did a poor job of typing out all of my thoughts late last night.The general point remains the same though. If you think the typical "WR48" in FFL (last WR3 in a 16 team league) is good for about 650 yards and 3 TDs/year (as was the case in a few of my leagues in 2010), then is it better to have two seasons 600-700 yards and 5 TDs over that "baseline," or is it better to have seven seasons of 200-300 yards and 0-1 TDs over that "baseline?" I think the answer is obvious: the two big seasons out of a WR1. But I just had to make sure and say it...as while I agree with your general premise, it *HAS* to be evaluated within the context of per-season production. IMHO. Good work though! :thumbup:
 
I enjoyed the read -- probably have to go back and read it a couple more time before I fully understand it but it looks like a solid concept/strategy.

How you account for draft picks? Seems like this would be simple enough to apply to players "I can get player A by trading player B and come out 10% above my VBD so I make the trade" but how do you factor rookie draft picks?

 
'datonn said:
'Aabye said:
'datonn said:
I think the same way the OP does, in general. It's more about how many FPs a player still has out there to be harvested, versus anything they've done in the past (their "rep" and historical value). There's only one flaw with this train of thought...however, and it's a BIG one! It's not the total FPs a player has left to produce that is important. It is the distribution of those points over "X" number of seasons that is important.For example, let's look at two wide receivers: Reggie Wayne, Colts and Josh Morgan, 49ers. Wayne is the "consensus" best player of the two (I at least hope that's not debatable, lol).Reggie Wayne is 32...a GIANT knock on his value in dynasty. However, he's averaged around 1,300 yards and over 8 TDs a season for the past five seasons...and according to "my" formula(s), he's got two seasons of high productivity left in fantasy before he falls off the cliff. So let's say he's worth 1300/8, 1300/8, 700/4, 500/3Josh Morgan turns 26 in a month. Excellent age for a dynasty roster...but let's say he's got seven seasons left and that his next four seasons he'll see an uptick of 5% in production, with his final three seasons being more similar to 2010. So we'll say he's worth 735/2, 780/3, 820/3, 860/4, 700/2, 700/2, 700/2Wayne's value is 3,800 yards and 23 TDs.Morgan's value is 5,295 yards and 20 TDs.Morgan's value "wins," right?! Wrong. Because with Wayne, you assume you're getting two more seasons of WR1 type production and two more seasons of WR4 type output. Morgan, by contrast, is never really more than an "okay" WR3. And if I could trade seven years of ho-hum WR3 production for two seasons of WR1? I do that...in a heartbeat. Because it is way, WAY more difficult to find a WR1 than it is a WR3 in dynasty. 16-team leagues, in particular!So while I do buy into the concept, I think that looking at total future fantasy points versus predicted/assumed FFL output by-season is a giant mistake. FWIW.
datonn,I'm using VBD points (points above the baseline) as opposed to FPs to somewhat counteract this.Still, even using VBD, I do agree that concentrated seasons of high VBD are usually preferable.Sorry, datonn, this was very much unclear in the OP. Editing now.
No worries! I actually did get your train of thought related to points above the baseline. I just did a poor job of typing out all of my thoughts late last night.The general point remains the same though. If you think the typical "WR48" in FFL (last WR3 in a 16 team league) is good for about 650 yards and 3 TDs/year (as was the case in a few of my leagues in 2010), then is it better to have two seasons 600-700 yards and 5 TDs over that "baseline," or is it better to have seven seasons of 200-300 yards and 0-1 TDs over that "baseline?" I think the answer is obvious: the two big seasons out of a WR1. But I just had to make sure and say it...as while I agree with your general premise, it *HAS* to be evaluated within the context of per-season production. IMHO. Good work though! :thumbup:
Using net present value of future seasons could assist here, potentially combined with an absolute time horizon, e.g every thing after x seasons is valued at zero. Finding the 'inflation' level for net present value will be tricky though
 
'datonn said:
No worries! I actually did get your train of thought related to points above the baseline. I just did a poor job of typing out all of my thoughts late last night.The general point remains the same though. If you think the typical "WR48" in FFL (last WR3 in a 16 team league) is good for about 650 yards and 3 TDs/year (as was the case in a few of my leagues in 2010), then is it better to have two seasons 600-700 yards and 5 TDs over that "baseline," or is it better to have seven seasons of 200-300 yards and 0-1 TDs over that "baseline?" I think the answer is obvious: the two big seasons out of a WR1. But I just had to make sure and say it...as while I agree with your general premise, it *HAS* to be evaluated within the context of per-season production. IMHO. Good work though! :thumbup:
Using net present value of future seasons could assist here, potentially combined with an absolute time horizon, e.g every thing after x seasons is valued at zero. Finding the 'inflation' level for net present value will be tricky though
That would be pretty tricky.As far as a general comment, it looks like there are two things that are getting mixed:(1) the objective value of a player(2) the subjective value of a player (how valuable is a player to my team specifically?)The "buy low" stuff only deals with (1).The desirability of some distribution of those remaining points seems to me like a subjective measure of value. Assuming we have a known quantity of VBD points, an owner may want those points concentrated over a two year period or he may want points spread out over a longer period (e.g. if you're rebuilding, Wayne's immediate production probably doesn't help you much).So I think that while the distribution of remaining points is an important factor in making decisions, it can be completely separated from the concept of "buying low." They're just doing two separate things. "Buying low" is about maximizing the objective value of a player and sensitivity to point distributions is about maximizing subjective value.This is not to say that subjective value is unimportant or less important than objective value (it may be that subjective value is actually much more important). But I think that they are two different animals.
 
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There does seem to be an "objective" value to shorter, more concentrated production. If a player (A) has a value of 100 over 2 years, after which he retires and another player (B) has a value of 100 over 10 years, then A actually gives you the hidden benefit of 8 years of an open roster space.

The open roster space itself has value in terms of objective VBD points, so A's value is actually > B's value by the value of the 8 seasons of an empty roster spot.

I have no idea how to calculate the value of an empty roster spot, though.

 
There does seem to be an "objective" value to shorter, more conceantrated production. If a player (A) has a value of 100 over 2 years, after which he retires and another player (B) has a value of 100 over 10 years, then A actually gives you the hidden benefit of 8 years of an open roster space.

The open roster space itself has value in terms of objective VBD points, so A's value is actually > B's value by the value of the 8 seasons of an empty roster spot.

I have no idea how to calculate the value of an empty roster spot, though.
I always considered the easier method of "X # of FF value years". For example, Ovie Mughelli might have another 6 years and 300 ff points left in his career, but he's irrelevant in FF. Tomlinson might have 2 years and 250 points left, but in large PPR leagues he might make a fair RB3 and is worth more.

 
There does seem to be an "objective" value to shorter, more conceantrated production. If a player (A) has a value of 100 over 2 years, after which he retires and another player (B) has a value of 100 over 10 years, then A actually gives you the hidden benefit of 8 years of an open roster space.

The open roster space itself has value in terms of objective VBD points, so A's value is actually > B's value by the value of the 8 seasons of an empty roster spot.

I have no idea how to calculate the value of an empty roster spot, though.
I always considered the easier method of "X # of FF value years". For example, Ovie Mughelli might have another 6 years and 300 ff points left in his career, but he's irrelevant in FF. Tomlinson might have 2 years and 250 points left, but in large PPR leagues he might make a fair RB3 and is worth more.
Well, that's the reason to use VBD numbers instead of just fantasy points scored: they automatically confer objective fantasy value on the player. If we just aggregate fantasy points scored over the course of a career, then we'll get all sorts of problems along the lines of Mughelli vs. Tomlinson. But if we use aggregate VBD numbers, I don't think we get the same sorts of problems.
 
I think the reason this has never been done is that an expert level of knowledge is required in multiple facets to pull it off. You'd almost need to lock Aabye, Bloom/Waldman and an absolute datbase wizerd (MySQL or Access) in a room for 80-160 hours to create a functioning framework. As Aabye was saying, ANY values even in the ballpark of the Perfect Model would be infinitely better than anything that exists currently in the industry. You just need to set your values and create a database capable of running (here's the tricky part) hundreds, if not thousands of historical calculations and tweaking the values from there.

I appreciate the work and I do believe a MUCH better model of quantifying dynasty values is possible. It's just never been done because you're talking about an incredible amount work.

 
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'mancrush said:
I enjoyed the read -- probably have to go back and read it a couple more time before I fully understand it but it looks like a solid concept/strategy. How you account for draft picks? Seems like this would be simple enough to apply to players "I can get player A by trading player B and come out 10% above my VBD so I make the trade" but how do you factor rookie draft picks?
You account for rookie draft picks the same way you account for vets: you create a model that best approximates their value in terms of remaining career VBD. In fact, I think it's considerably easier to model rookie values since we know less about them (and so there are less things that we have to worry about in our model).As far as how to do that, I don't know of a sophisticated way of sorting it all out.
 
I think the reason this has never been done is that an expert level of knowledge is required in multiple facets to pull it off. You'd almost need to lock Aabye, Bloom/Waldman and an absolute datbase wizerd (MySQL or Access) in a room for 80-160 hours to create a functioning framework. As Aabye was saying, ANY values even in the ballpark of the Perfect Model would be infinitely better than anything that exists currently in the industry. You just need to set your values and create a database capable of running (here's the tricky part) hundreds, if not thousands of historical calculations and tweaking the values from there. I appreciate the work and I do believe a MUCH better model of quantifying dynasty values is possible. It's just never been done because you're talking about an incredible amount work.
I've screwed around with quantitative models and created one that uses age, recent performance, benchmarks (how quickly a player started performing) and draft status to estimate a player's remaining VBD based on similarity with all players drafted between 1985 and 2000. It took forever.A big problem is that there are a huge number of holes in it. It doesn't account for things like injury, situation, job security, etc. at all so it's still pretty far from usable. I don't know enough about compiling and sorting databases to research efficiently and I don't know enough about statistics to make good sense of the information I do have, unfortunately.
 
No offense, but I don't understand your point. You are saying to buy low and sell high. I think we all know that. Did you really just write the War and Peace edition to tell us not to overstate how age affects a players' dynasty value?

 
Great ideas. I totally agree with the misconceptions of how "dynasty scores" work now. That being said...The need for a model is not anything new (to me at least). The way you lay it out is incredible, and very informing, and nicely done. However:

That doesn't get us anywhere. What matters would be actually having a model. I've tried before using Access and Excel, alternatively, but it's practically impossible. It seems, in the end, as though you're simply saying that the models we have don't weigh certain factors correctly. That's not groundbreaking. That's what we are all trying to do. What would matter would be if you actually had a model that you thought was better.

And even when you create a solid model (which I feel I have done once or twice in all my attempts) you get screwed because one very important factor is practically unquantifiable: TALENT.

 
Great ideas. I totally agree with the misconceptions of how "dynasty scores" work now. That being said...The need for a model is not anything new (to me at least). The way you lay it out is incredible, and very informing, and nicely done. However:

That doesn't get us anywhere. What matters would be actually having a model. I've tried before using Access and Excel, alternatively, but it's practically impossible. It seems, in the end, as though you're simply saying that the models we have don't weigh certain factors correctly. That's not groundbreaking. That's what we are all trying to do. What would matter would be if you actually had a model that you thought was better.

And even when you create a solid model (which I feel I have done once or twice in all my attempts) you get screwed because one very important factor is practically unquantifiable: TALENT.
I'm unaware of the attempts at modeling dynasty value that work by assigning actual remaining VBD scores to individual players. I assumed that people had tried to do it, but I've just never seen one. I'm basically saying that we don't have models at all (well, you have a model but I didn't know that). We have bits and pieces of information which get cobbled together in haphazard fashion.I think that it's possible to construct a usable model like this:

(1) We start by finding players about whom we know the least. This group is obviously the rookies.

(2) We look for factors that we can quantifiably correlate with fantasy success. Here I know of only one: draft status. A 1st round RB is more likely to be a fantasy success than a 2nd round RB and so forth. ZWK did something with this and I did something similar, although mine was less comprehensive.

(3) Once we get a decent handle on rookie values, we move on to look at how players with one year of experience tend to do. We now have more information about a player, which we have to incorporate into the model. Etc.

So we start bootstrapping our previous information, adding pieces as we go along. Since every separate piece is just one more factor that correlates to remaining fantasy value (expressible in remaining VBD points), we can add new factors in without messing with the others. We might need to change how we weigh the various factors as we go along, but we won't have to start from scratch.

Every new piece makes the model a little bit stronger. We don't ever reach the perfect model, but I think that the process of modeling dynasty values at least offers the potential for progress, while the old way just amounts to fumbling around in the dark.

As far as being unable to quantify talent, I agree to some extent. We certainly can't quantify heart or leadership or dedication, so we can't use that stuff in a model. We can quantify stuff like draft status, prior performance, height, weight, 40 times, etc. and use those factors as proxy for "talent", which seems like what we mostly do anyways. I can vividly remember that after the 2008 season, this board was awash with people claiming that DeAngelo Williams was one of the most "talented" backs in the NFL. I don't recall hearing any of that kind of talk in 2007, although I can't imagine that Williams somehow became more talented between 2007 and 2008.

I hear, fairly often, that the secret to fantasy success is evaluating talent. I wish I had this ability but I just don't. I'd imagine that most of the folks on this board don't know the first thing about it either. Since I'm stuck in the position of being unable to evaluate talent, heart, leadership, dedication, etc. based on interviews and youtube clips, I have to mostly stick with quantifiable factors.

 
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I appreciate the effort here, and I think it's a good description of the definition of value in a fantasy football context, similar to VORP in a baseball sabermetric context. One thing I would note is that VBD numbers vary based on what baseline you use, so to create The Perfect Model you have to prove that the VBD baseline you're using actually represents value over replacement. PFR uses worst-starter for its VBD calculation, but there are a number of issues with that. Some include:

[*]You need to look at per-game VBD, not season-ending VBD. Austin Collie in 2010 finished as WR#33, with zero VBD points relative to worst-starter. But he did it in just 9 games. Since owners were able to slot in at least a replacement-level player for the other 7 games, Collie's value was more like +30 or +40 VBD for the time he was in the lineup.

[*]Your best backup will play 2 games per year, per lineup position backed up. In a 3-WR league, your WR#4 will play up to 6 games based solely on bye weeks, and can play more than that based on injuries. So it's important to have players on your bench who are better than replacement-value, which means that the VBD baseline in The Perfect Model should be lower; median #1 backup or worst #1 backup or something.

[*]Point 2 notwithstanding, there are a limited number of lineup spots, so the utility of a player's VBD points is dependent on the roster makeup of the team he's on. This is one reason why trades happen; even if two owners value players identically, their utility may be different based on the rest of each owner's lineup.

 
I appreciate the effort here, and I think it's a good description of the definition of value in a fantasy football context, similar to VORP in a baseball sabermetric context. One thing I would note is that VBD numbers vary based on what baseline you use, so to create The Perfect Model you have to prove that the VBD baseline you're using actually represents value over replacement. PFR uses worst-starter for its VBD calculation, but there are a number of issues with that. Some include:

[*]You need to look at per-game VBD, not season-ending VBD. Austin Collie in 2010 finished as WR#33, with zero VBD points relative to worst-starter. But he did it in just 9 games. Since owners were able to slot in at least a replacement-level player for the other 7 games, Collie's value was more like +30 or +40 VBD for the time he was in the lineup.

[*]Your best backup will play 2 games per year, per lineup position backed up. In a 3-WR league, your WR#4 will play up to 6 games based solely on bye weeks, and can play more than that based on injuries. So it's important to have players on your bench who are better than replacement-value, which means that the VBD baseline in The Perfect Model should be lower; median #1 backup or worst #1 backup or something.

[*]Point 2 notwithstanding, there are a limited number of lineup spots, so the utility of a player's VBD points is dependent on the roster makeup of the team he's on. This is one reason why trades happen; even if two owners value players identically, their utility may be different based on the rest of each owner's lineup.
I agree with all of these, but do you know just how much more difficult that makes things? Trying to do a game by game VBD is similar to the idea that we need to value one 100 VBD season more than two 50 VBD seasons, but even more tricky. I have no issue with all of these ideas, they all make a ton of sense - but we also have to take feasibility into account.Also, Re: my post:

That all makes a lot more sense. Not much to disagree with. It's gonna be a huge project - I can only assume my attempts continually fail not because of an error in idea, but rather due to time constraints.

 
I appreciate the effort here, and I think it's a good description of the definition of value in a fantasy football context, similar to VORP in a baseball sabermetric context. One thing I would note is that VBD numbers vary based on what baseline you use, so to create The Perfect Model you have to prove that the VBD baseline you're using actually represents value over replacement. PFR uses worst-starter for its VBD calculation, but there are a number of issues with that. Some include:

[*]You need to look at per-game VBD, not season-ending VBD. Austin Collie in 2010 finished as WR#33, with zero VBD points relative to worst-starter. But he did it in just 9 games. Since owners were able to slot in at least a replacement-level player for the other 7 games, Collie's value was more like +30 or +40 VBD for the time he was in the lineup.

[*]Your best backup will play 2 games per year, per lineup position backed up. In a 3-WR league, your WR#4 will play up to 6 games based solely on bye weeks, and can play more than that based on injuries. So it's important to have players on your bench who are better than replacement-value, which means that the VBD baseline in The Perfect Model should be lower; median #1 backup or worst #1 backup or something.

[*]Point 2 notwithstanding, there are a limited number of lineup spots, so the utility of a player's VBD points is dependent on the roster makeup of the team he's on. This is one reason why trades happen; even if two owners value players identically, their utility may be different based on the rest of each owner's lineup.
Per-game VBD is almost certainly better than yearly VBD but the amount of work it would take to calculate this stat over decades is just too staggering to attempt, at least for me.
 
Nice topic Aabye.

I think your on the right track. Personally what I would try to do is project VBD #s for my league for the next 3 years. If your goals are longer term then perhaps you should give more weight to potential production beyond 3 years but the further out you project them the more wrong your projections will be. For me that was not useful but I am not saying it can't be done.

In general for me selling high and buying low has more to do with the perceived value of players and finding those specific players who may be under/over valued by the other owners in your league. That takes a lot of communication to find out Owner X is higher on player Y than the rest of the league owners. The more you talk to fellow owners in the league the more you can find out what the market values on players for them might be.

 
Per-game VBD is almost certainly better than yearly VBD but the amount of work it would take to calculate this stat over decades is just too staggering to attempt, at least for me.
Actually it's probably not that bad if you're willing to make some assumptions. Start with a Mendoza Line equivalent for each position; say, 3 receptions for 40 yards and 0.2 TDs for a WR (numbers pulled out of thin air). Don't try to track VBD baselines on a per-year basis; it's probably the wrong thing to do anyway. Then you at least have a fighting chance calculating VBD per game; just look at game logs for any games with more than the baseline production, and add them up.
 
Per-game VBD is almost certainly better than yearly VBD but the amount of work it would take to calculate this stat over decades is just too staggering to attempt, at least for me.
Actually it's probably not that bad if you're willing to make some assumptions. Start with a Mendoza Line equivalent for each position; say, 3 receptions for 40 yards and 0.2 TDs for a WR (numbers pulled out of thin air). Don't try to track VBD baselines on a per-year basis; it's probably the wrong thing to do anyway. Then you at least have a fighting chance calculating VBD per game; just look at game logs for any games with more than the baseline production, and add them up.
You've got to do that for every game of a player's career (for hundreds and hundreds of players) before you can even start to work with the data. It's maybe 50,000 individual calculations. If I could do it automatically, it would probably be worth it. But right now, I'd have to do all of those calculations manually, which is nuts.
 
I agree with all of these, but do you know just how much more difficult that makes things? Trying to do a game by game VBD is similar to the idea that we need to value one 100 VBD season more than two 50 VBD seasons, but even more tricky. I have no issue with all of these ideas, they all make a ton of sense - but we also have to take feasibility into account.
I'm not sure a 100 VBD season should be valued more than two 50 VBD seasons (assuming your baseline is set reasonably). Think about a dynasty expansion team that starts with waiver-wire (replacement level) players, and gets the first overall pick in the draft. Say that player's 5-year career will be 10, 10, 100, 10, 10 VBD points, and you can trade him for two players who will have 10, 50, 50, 10, 10 and 10, 10, 50, 50, 10 seasons. Those players will provide similar value to your team over time, in terms of points scored in the lineup. The only reason why the 100 VBD player might be more valuable is because our payouts are non-linear; we get a greater payout for finishing first once and last once than for finishing sixth twice. Even so, starting with a baseline team, it's not clear that it would be worth paying a lot more for the 100 VBD player.
 
Per-game VBD is almost certainly better than yearly VBD but the amount of work it would take to calculate this stat over decades is just too staggering to attempt, at least for me.
Actually it's probably not that bad if you're willing to make some assumptions. Start with a Mendoza Line equivalent for each position; say, 3 receptions for 40 yards and 0.2 TDs for a WR (numbers pulled out of thin air). Don't try to track VBD baselines on a per-year basis; it's probably the wrong thing to do anyway. Then you at least have a fighting chance calculating VBD per game; just look at game logs for any games with more than the baseline production, and add them up.
You've got to do that for every game of a player's career (for hundreds and hundreds of players) before you can even start to work with the data. It's maybe 50,000 individual calculations. If I could do it automatically, it would probably be worth it. But right now, I'd have to do all of those calculations manually, which is nuts.
I don't know anything more about Microsoft Access than how to spell it, but I gotta believe there's a way to set up a database where these values can be automatically calculated once you set the parameters. Hence, my previous post. The entire thing is too daunting to even think about calculating manually. I have a hunch it's too robust for even an Excel guru to design.
 
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Per-game VBD is almost certainly better than yearly VBD but the amount of work it would take to calculate this stat over decades is just too staggering to attempt, at least for me.
Actually it's probably not that bad if you're willing to make some assumptions. Start with a Mendoza Line equivalent for each position; say, 3 receptions for 40 yards and 0.2 TDs for a WR (numbers pulled out of thin air). Don't try to track VBD baselines on a per-year basis; it's probably the wrong thing to do anyway. Then you at least have a fighting chance calculating VBD per game; just look at game logs for any games with more than the baseline production, and add them up.
You've got to do that for every game of a player's career (for hundreds and hundreds of players) before you can even start to work with the data. It's maybe 50,000 individual calculations. If I could do it automatically, it would probably be worth it. But right now, I'd have to do all of those calculations manually, which is nuts.
I don't know anything more about Microsoft Access than how to spell, but I gotta believe there's a way to set up a database where these values can be automatically calculated once you set the parameters. Hence, my previous post. The entire thing is too daunting to even think about calculating manually. I have a hunch it's too robust for even an Excel guru to design.
Anyone know how to do this? I also know nothing about Access.
 
You'd have to create a form, but the most daunting part of using Access for it would be inputting all your data. You'd better hope to find it all in some form that was easily delineated for input, or you'd have to put every player's stats in over and over.

It might (well, probably would) be better to do it in Excel and then just import the values into Access to see them in an organized manner.

EVen then, regardless of which one you use, the thousands of lines of data and calculations the program will have to run each time you open it is insane. Might take well over a half hour or more just to have it ready for manipulation once the size gets big. You'd for sure have to do a separate file for each position, and even then they might get really large.

 
It wouldn't be hard to crunch the numbers if you have per-game data for every player. The hard part is getting per-game data for every player in a format that's importable. PFR used to have that but had to turn it off due to licensing of the data set.

 
It wouldn't be hard to crunch the numbers if you have per-game data for every player. The hard part is getting per-game data for every player in a format that's importable. PFR used to have that but had to turn it off due to licensing of the data set.
How many players are we talking? 60? 100? Per position? 16 games each? Which would take 17 rows...QB, perhaps less, as with TE. But let's talk just WRs and RBs. That's, say, 160 players. 17 data points each. That alone is 2720 cells of data that you need to input, plus whatever your baseline is for each position, so really 2722 cells of data. Now, not only are you having to input all of that, but you have to have your worksheet do the calculations for each one of those cells to turn them into Fantasy Points, or some sort of game-by-game VBD point system. So you have 2720 calculations that your spreadsheet is going to run each time you open it.In addition to that, you want to know if those VBD points or Fantasy points or whatever each game is and whatever you use to value the game by game stats. So you're going to compare every cell of data you already have to those baselines in order to find out if each game (each cell of stats/points) is better than your baseline. That's another 2720 calculations.Now, that's assuming you only do 60 RBs and 100 WRs. And you're already up to a little over 2720 cells of inputting data, as well as 5440+ calculations.Add in QBs, TEs, and IDPs if you do them, and a deeper set of RB/WRs (I mean, you haven't even gone two deep for every NFL team at RB yet, and you barely cover all the starting WRs - I'm sure we all want to include guys who aren't yet starting but have potential as well...You're probably going to be looking at over 12000 calculations of data every single time you open your workbook...FOR OFFENSE ONLY. The time it takes bugs me when I do simple redraft "projections" and have to calculate the yardage/rec/TD projections into fantasy points just one time. To have to do that not only once, by game by game for each and every player, and deeper because it's dynasty.It's a great idea, but you need to have quite an impressive amount of computing power for it not to be a pain in the ###.
 
A much more simple way to say what you just did (I think):

RBA:

Points/year: 300/180 baseline

Years remaining: 3/2 baseline

RBA VBD = 900/360 baseline or 250% over replacement.

You would add other variables as you see fit.

You are right, in your thought process. But you don't really do much to establish a value calculation, nor provide examples. What I got from all that you typed was: use projected VBD points, instead of a player names.

 
A much more simple way to say what you just did (I think):RBA:Points/year: 300/180 baselineYears remaining: 3/2 baselineRBA VBD = 900/360 baseline or 250% over replacement. You would add other variables as you see fit. You are right, in your thought process. But you don't really do much to establish a value calculation, nor provide examples. What I got from all that you typed was: use projected VBD points, instead of a player names.
I don't know what RBA is.I certainly didn't establish a value calculation because I don't know what it would look like. I'd imagine that it would take most of the variables from post #3 into account and assign a unique weighting system for players in different situations (e.g. draft status matters way more for a 22-year-old than it does for a 28-year-old).I do think that rather than doing player-to-player comparisons, we'd be better of modeling players based on groups that player belongs to (e.g. Adrian Peterson belongs to groups such as: 26-year-old RBs, RBs drafted in the top 10, RBs who scored more than 100 VBD points during the prior season, etc.) and then figuring out how to weight these groups appropriately to arrive at a reasonable VBD projection.It's quite simple to say "use projected VBD points" but a real bear to actually figure out how to proceed from there.
 
A much more simple way to say what you just did (I think):RBA:Points/year: 300/180 baselineYears remaining: 3/2 baselineRBA VBD = 900/360 baseline or 250% over replacement. You would add other variables as you see fit. You are right, in your thought process. But you don't really do much to establish a value calculation, nor provide examples. What I got from all that you typed was: use projected VBD points, instead of a player names.
I don't know what RBA is.I certainly didn't establish a value calculation because I don't know what it would look like. I'd imagine that it would take most of the variables from post #3 into account and assign a unique weighting system for players in different situations (e.g. draft status matters way more for a 22-year-old than it does for a 28-year-old).I do think that rather than doing player-to-player comparisons, we'd be better of modeling players based on groups that player belongs to (e.g. Adrian Peterson belongs to groups such as: 26-year-old RBs, RBs drafted in the top 10, RBs who scored more than 100 VBD points during the prior season, etc.) and then figuring out how to weight these groups appropriately to arrive at a reasonable VBD projection.It's quite simple to say "use projected VBD points" but a real bear to actually figure out how to proceed from there.
RBA simply means the RB in the example that I used: Running back A.I don't know that tiers should be invited into the conversation. If we are hypothesizing a calculation, draft status is far too subjective to include. I don't know why would want a variable that suggests that we rank Felix Jones ahead of Arian Foster. Tiers only hamper the search for a perfect calculation. We know that LeSean McCoy is younger than Jamaal Charles. Tiering them together removes that pertinent information from our calculation. We need to use the same variables we do for re-draft, then invite a new set, to account for dynasty settings. The difference between re-draft and dynasty is the number of years. Bringing us to projected points scored and years of production.It gets tricky projecting years out. I understand that and personally believe that is the ONLY reason we can't have a VBD calculator as relative and valuable as the re-draft version. But, that doesn't mean adding more subjective variables will fix that.
 
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I have $ to invest in this project if a small group of people are serious about getting this off the ground. I think it's worth the money/time just to find out if a set of dynasty rankings (driven solely by measurable factors) is really more accurate than what people or generating on the fly currently.

 

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