Smathers WR dynasty rankings (1 Viewer)

[Adam Harstad]

Ok I think I misunderstood your point about $20 value a year from now compared to $10 today and similarly your point about 100 points in 2018 being equal to 100 points in 2015.

I completely agree the discount should never be negative. It can drop to zero, and zero will be below replacement level (so we could view that as a negative) but aside from the opportunity cost of using a roster spot on that player for that current year, the player is not causing you to lose points in your line up. The player just isn't contributing anything that season.

So I think I have a better understanding of why the discount percentage cannot fall to zero or a negative number.

Cool, glad we're on the same page.

Player careers are not perpetual however. There are limits to the length of players careers and even more limits to a player actually having value in any given season (or game). So you would be using the annual (or by game) basis, not a perpetual (infinite) basis for the discount (I think?).

I'm using two separate discount factors. The first is my flat 10% time discount. This represents the "time-value" of production. 100 points of value today is simply worth more than 100 points of value next year, in much the same way that $100 today is worth more than $100 next year.

The factors represented by this discount are varied. For one, if I play fantasy for 20 years and win a title in year 1, I have nineteen additional years to enjoy it. If I win a title in year 20, I have no more years to enjoy it. As a result, all else being equal, I'd rather win titles sooner than later.

For another, there's a non-zero chance that I'm just not playing in the league five years from now. Maybe the league folds. Maybe something comes up in my life and I have to drop it. Maybe I die. Production today is certain to be realized, whereas future production is uncertainty. Time discount helps capture this uncertainty.

That 10% time discount factor is completely static. It is the same from year to year, from position to position, and from player to player. Everyone's production gets discounted by 10% year over year.

My second discount factor deals with how likely that production is to happen in the first place; that's my "mortality tables" and "death rate" stuff. If I have a 32 year old wide receiver, how likely is it that he's still providing me positive value at age 35? It's not 100%. It's not 0%, either. Let's say that I calculate a 33% chance that he's still valuable in year N+2.

Now, year N+2 is only 81% as valuable as this year, because of the aforementioned time discount. And if the WR only has a 33% chance of producing any value that year, then I'm only valuing his particular year N+2 as worth 33% * 81%, or 27% of his season this year. That's a substantial discount.

For a younger receiver, such as Odell Beckham, my discount isn't going to be nearly that steep. The odds that Beckham is still productive in year N+2 are probably more like 90%. In this case, I'm taking the flat 81% discount, multiplying it by his 90% survivorship chances, and I'm valuing Beckham's N+3 as worth 73% as much as the current year.

So as you see, there's no window. Each player gets a personalized discount that reflects their own specific circumstances. With a young player, I'm going to value the future more highly. For an older player, a proportionally larger percentage of their current value will be made up by the current season. For someone like DeAngelo Williams last year, about 99% of his fantasy value would have been made up of his 2015 fantasy value.

Because the total discount is based on the interplay of these two separate factors, sometimes it will be accelerating and sometimes it will be decelerating. (More rarely, sometimes it will be decreasing linearly from season to season, at least over short stretches.) But because the two discount factors operate within closed systems, (i.e. are tightly controlled within a range of 0-100%), the resulting product also operates within those bounded rules, (i.e. a player's discount for any given season always falls in a range of 0-100%.)

This, to me, makes much more intuitive sense than a blanket one-size-fits-all value system with perhaps a few post hoc exceptions. (Post hoc exceptions are, to me, a sign that the underlying system has failed, and should ideally be replaced with structural improvements rather than quick patches.)

I believe it more accurately models actual player value. Additionally, one of the advantages of my "mortality tables" approach is that I think it really represents the risk better. I'm not saying "Player X is going to be worth Y in year N+3". I'm saying "There's an X% chance that he's worth Y in year N+3, and a (1-X)% chance that he's just fallen off a cliff". I think that naturally highlights the need for contingency plans, while best representing the ever-changing field on which we compete.

 

[Slapdash]

Wow, great thread here.

 

[Biabreakable]

I came across another section from my finance class that details the increasing risk over time.

"[SIZE=14pt]Our ability to forecast accurately diminishes as we forecast farther out in time. As the time horizon becomes longer, more uncertainty enters the forecast. The decline in oil prices sharply curtailed the search for petroleum and left many drillers in serious financial condition in the 1980s after years of expanding drilling activity. Conversely, the users of petroleum products were hurt in 1990 when the conflict in the Middle East caused oil prices to skyrocket. Airlines and auto manufacturers had to reevaluate decisions made many years ago that were based on more stable energy prices. September 11, 2001, coupled with the Iraqi war of the mid-decade dealt another blow to the already fragile economy. The collapse of the housing market caused a terrible shock to the economy in 2007–2009. The inability of Congress to agree on tax reform and spending cuts lingered throughout 2011, 2012, and into early 2013 and caused a great deal of uncertainty for all businesses. These unexpected events create a higher standard deviation in cash flows and increase the risk associated with long-lived projects.[/SIZE]

[SIZE=14pt]Even though a forecast of cash flows shows a constant expected value, the range of outcomes and probabilities increases as we move from year 2 to year 10. The standard deviations increase for each forecast of cash flow. If cash flows were forecast as easily for each period, all distributions would look like the first one for year 2. Using progressively higher discount rates to compensate for risk tends to penalize late flows more than early flows, and this is consistent with the notion that risk is greater for longer-term cash flows than for near-term cash flows.[/SIZE]

[SIZE=14pt]Qualitative Measures[/SIZE]

[SIZE=14pt]Rather than relate the discount rate—or required return—to the coefficient of variation or possibly the beta, management may wish to set up risk classes based on qualitative considerations."[/SIZE]

[SIZE=14pt]The risk classes range from six percent (low risk) to twenty percent (high risk) there are six of these categories, the first four increase by 2 percent each starting at six (6,8,10,12) then the discount rate doubles to four percent for the last two categories (16,20)[/SIZE]

[SIZE=14pt]So this would be an example from finance of what I was trying to describe as an accelerating level of uncertainty the further out you project.[/SIZE]

[SIZE=14pt]All of these calculations are tricky as well because of the compounding effects of using multiple percentages in the formulas. Those errors can be more costly in the long run from using a long term form of valuation of the asset.[/SIZE]

[SIZE=14pt]Going back to the Reggie Wayne vs Larry Fitzgerald example.[/SIZE]

[SIZE=14pt]I am glad this did not happen, but what if Fitzgerald had a career ending injury immediately after you paid the value of two Reggie Waynes because of the potential for Fitzgerald to have a longer productive career than Wayne will have. That assumption turns out to be wrong and you paid a premium for value 4 to 5 years from now that never were realized.[/SIZE]

[SIZE=14pt]If you are projecting out the value of the players potential career using historical patterns of progression and decline then that is going to be a lot more value for a projected 10 year career that never would be realized. [/SIZE]

[SIZE=14pt]If you valued both players based on the next 3 years it would still hurt your positon losing a quality player to career injury, but at least you only paid for 3 years of value compared to 10.[/SIZE]

[SIZE=14pt]What would be worse than the injury would be career replacement level production. Just enough good games to keep you starting the player but inconsistency that causes you to take a lot of dud games along with watching the player go off on your bench. The value you paid for the player was still high based on the length of the possible career performance, but in reality the player struggles for [/SIZE][SIZE=18.6667px]ancillary[/SIZE][SIZE=14pt] reasons such as poor QB and offensive line play, getting in the coaches doghouse, not being focused, any number of unpredictable things that cause the performance of that player to be different than your projected value for them. Then subsequently your projections for that player will change with that new data and those seasons five years from now keep being valued but never realized as each update is made.[/SIZE]

 

[Baeddel Moon]

I came across another section from my finance class that details the increasing risk over time.

"[SIZE=14pt]Our ability to forecast accurately diminishes as we forecast farther out in time. As the time horizon becomes longer, more uncertainty enters the forecast. The decline in oil prices sharply curtailed the search for petroleum and left many drillers in serious financial condition in the 1980s after years of expanding drilling activity. Conversely, the users of petroleum products were hurt in 1990 when the conflict in the Middle East caused oil prices to skyrocket. Airlines and auto manufacturers had to reevaluate decisions made many years ago that were based on more stable energy prices. September 11, 2001, coupled with the Iraqi war of the mid-decade dealt another blow to the already fragile economy. The collapse of the housing market caused a terrible shock to the economy in 2007–2009. The inability of Congress to agree on tax reform and spending cuts lingered throughout 2011, 2012, and into early 2013 and caused a great deal of uncertainty for all businesses. These unexpected events create a higher standard deviation in cash flows and increase the risk associated with long-lived projects.[/SIZE]

[SIZE=14pt]Even though a forecast of cash flows shows a constant expected value, the range of outcomes and probabilities increases as we move from year 2 to year 10. The standard deviations increase for each forecast of cash flow. If cash flows were forecast as easily for each period, all distributions would look like the first one for year 2. Using progressively higher discount rates to compensate for risk tends to penalize late flows more than early flows, and this is consistent with the notion that risk is greater for longer-term cash flows than for near-term cash flows.[/SIZE]

[SIZE=14pt]Qualitative Measures[/SIZE]

[SIZE=14pt]Rather than relate the discount rate—or required return—to the coefficient of variation or possibly the beta, management may wish to set up risk classes based on qualitative considerations."[/SIZE]

[SIZE=14pt]The risk classes range from six percent (low risk) to twenty percent (high risk) there are six of these categories, the first four increase by 2 percent each starting at six (6,8,10,12) then the discount rate doubles to four percent for the last two categories (16,20)[/SIZE]

[SIZE=14pt]So this would be an example from finance of what I was trying to describe as an accelerating level of uncertainty the further out you project.[/SIZE]

[SIZE=14pt]All of these calculations are tricky as well because of the compounding effects of using multiple percentages in the formulas. Those errors can be more costly in the long run from using a long term form of valuation of the asset.[/SIZE]

[SIZE=14pt]Going back to the Reggie Wayne vs Larry Fitzgerald example.[/SIZE]

[SIZE=14pt]I am glad this did not happen, but what if Fitzgerald had a career ending injury immediately after you paid the value of two Reggie Waynes because of the potential for Fitzgerald to have a longer productive career than Wayne will have. That assumption turns out to be wrong and you paid a premium for value 4 to 5 years from now that never were realized.[/SIZE]

[SIZE=14pt]If you are projecting out the value of the players potential career using historical patterns of progression and decline then that is going to be a lot more value for a projected 10 year career that never would be realized. [/SIZE]

[SIZE=14pt]If you valued both players based on the next 3 years it would still hurt your positon losing a quality player to career injury, but at least you only paid for 3 years of value compared to 10.[/SIZE]

[SIZE=14pt]What would be worse than the injury would be career replacement level production. Just enough good games to keep you starting the player but inconsistency that causes you to take a lot of dud games along with watching the player go off on your bench. The value you paid for the player was still high based on the length of the possible career performance, but in reality the player struggles for [/SIZE][SIZE=18.6667px]ancillary[/SIZE][SIZE=14pt] reasons such as poor QB and offensive line play, getting in the coaches doghouse, not being focused, any number of unpredictable things that cause the performance of that player to be different than your projected value for them. Then subsequently your projections for that player will change with that new data and those seasons five years from now keep being valued but never realized as each update is made.[/SIZE]

I have a hard time seeing how the ins and outs of real world finance really have anything to do with dynasty. To start, from year to year, dynasty is a zero sum game. There is only one winner. If an investment club all does well, one might do the best but they will all profit. There are also very few fixed costs to running a team. The players all age a year, you pay an entry fee and that is the sum of it. Whereas a business man cannot declare his intention to rebuild, sell his machines and wait for the new models to come out. He still has to eat, that goes for the family as well. Capital, as Marx says, is the sum of life unlived. Dynasty owners do not make the choice of foregoing a trip to the movies to improve their starting line up. They do not save capital to try and achieve goals, other than the goal of winning the title.

That brings me to the crux of my argument. I find that league swinging transactions are rare and usually happen at inflection points that do model crisises of capital (OH my god what happened to the Running Backs!?!? etc.). An owner usually decides they need to take a radical course of action, like to rebuild or push their chips in the center. Players will be available at discount and only to the players who can make the trade happen at the right time. They are paying a premium to move this piece now. Most owners will have most of their assets dedicated to the title chase, and that is why this is the time to buy. Studs can be had, particularly if they are injured. I moved Calvin Johnson and a 1st (that of the league winner) to the league winner in late October for Le'Veon Bell/Jamison Crowder. This is the key. He won the league, but Calvin was not at all the difference. We are very very bad at predicting the future, and that includes the current year. Or in the example above, Larry Fitz and Reggie Wayne do not have the same rate of career ending injuries. It would have definitely hurt more to lose Larry considering the price paid for him, but they are not an equal likelihood. Heck, if that player is young enough, even if they are most likely done, they can still carry considerable trade value. (Consider the Gordon or the Marcus Lattimore who was drafted in the late 1st of rookie drafts even with the knowledge of said injury.) You would have a window to get rid of Fitz in that example that Wayne wouldn't have had. Maybe you could have even swapped the two even knowing about Fitz's likely career ending injury. Whereas if Wayne went down, you do not get that leeway. In a similar way, if both players under perform the younger one usually maintains an edge in perceived value.

How I see it then is this. If you failed to win the title your players did not produce any use value for you that year. They might have changed their perceived value but that has no bearing on next season, unless you cash them in.

 

[Adam Harstad]

I came across another section from my finance class that details the increasing risk over time.

"[SIZE=14pt]Our ability to forecast accurately diminishes as we forecast farther out in time. As the time horizon becomes longer, more uncertainty enters the forecast. The decline in oil prices sharply curtailed the search for petroleum and left many drillers in serious financial condition in the 1980s after years of expanding drilling activity. Conversely, the users of petroleum products were hurt in 1990 when the conflict in the Middle East caused oil prices to skyrocket. Airlines and auto manufacturers had to reevaluate decisions made many years ago that were based on more stable energy prices. September 11, 2001, coupled with the Iraqi war of the mid-decade dealt another blow to the already fragile economy. The collapse of the housing market caused a terrible shock to the economy in 2007–2009. The inability of Congress to agree on tax reform and spending cuts lingered throughout 2011, 2012, and into early 2013 and caused a great deal of uncertainty for all businesses. These unexpected events create a higher standard deviation in cash flows and increase the risk associated with long-lived projects.[/SIZE]

[SIZE=14pt]Even though a forecast of cash flows shows a constant expected value, the range of outcomes and probabilities increases as we move from year 2 to year 10. The standard deviations increase for each forecast of cash flow. If cash flows were forecast as easily for each period, all distributions would look like the first one for year 2. Using progressively higher discount rates to compensate for risk tends to penalize late flows more than early flows, and this is consistent with the notion that risk is greater for longer-term cash flows than for near-term cash flows.[/SIZE]

I *do* use progressively higher discount rates to compensate for risk. Each year's discount is higher than the discount from the year before. Your earlier criticism was that the rate of increases is decelerating rather than accelerating, but increasing at a decelerating rate is still increasing.

Further, while the *absolute* discount increases at a decelerating rate, the *relative* discount remains completely flat. Each year is worth exactly the same relative to the year before as every other year is.

Again, a truly accelerating discount like you're describing will quickly surpass 100%, meaning future years eventually have negative value and you'd rather score fewer points, (or make fewer dollars), than more. That's an untenable outcome, so by reductio ad absurdum, such an accelerating discount is likewise untenable. I suppose you could use some sort of fancy sigmoid-shaped discount rate which initially accelerates, but eventually your discount is going to have to start decelerating as it approaches 100%. There's really no way around that.

Going back to the Reggie Wayne vs Larry Fitzgerald example.

I am glad this did not happen, but what if Fitzgerald had a career ending injury immediately after you paid the value of two Reggie Waynes because of the potential for Fitzgerald to have a longer productive career than Wayne will have. That assumption turns out to be wrong and you paid a premium for value 4 to 5 years from now that never were realized.

If you are projecting out the value of the players potential career using historical patterns of progression and decline then that is going to be a lot more value for a projected 10 year career that never would be realized.

If you valued both players based on the next 3 years it would still hurt your positon losing a quality player to career injury, but at least you only paid for 3 years of value compared to 10.

What would be worse than the injury would be career replacement level production. Just enough good games to keep you starting the player but inconsistency that causes you to take a lot of dud games along with watching the player go off on your bench. The value you paid for the player was still high based on the length of the possible career performance, but in reality the player struggles for ancillary reasons such as poor QB and offensive line play, getting in the coaches doghouse, not being focused, any number of unpredictable things that cause the performance of that player to be different than your projected value for them. Then subsequently your projections for that player will change with that new data and those seasons five years from now keep being valued but never realized as each update is made.

Career-ending, (and season-ending), injuries are essentially stochastic, which means they're randomly distributed, but not evenly distributed. We cannot predict where they will strike with any precision, but we can model it probabilistically.

The cost of a catastrophic loss to Larry Fitzgerald would be higher, but the likelihood of a catastrophic loss to Reggie Wayne would be higher to offset, (assuming you valued them appropriately). Put simply: older players are more likely to suffer career-ending injuries than younger players. If a Fitz injury wiped out twice as much value, but a Wayne injury was twice as likely to happen, the two assets are in equilibrium. (Note: this is actually a simplification just to illustrate; mathematically, it's not that simple.)

Also, given the way my discount rate increases year by year, the seasons further out naturally represent an ever-smaller fraction of the player's total value, so there's less at risk in the present valuation. The cost of being wrong is something you can, (and should), incorporate into player values. It doesn't mean "don't buy expensive assets", though. It means an asset should only be expensive if the blend of risk and reward warrants it.

 

[Gandalf]

Adam,

If we accept the premise that each additional year from now becomes less certain than our projections for one year than now (which also have high levels of uncertainty) then it seems clear to me that the level of uncertainty should be increasing with each additional year.

What I see in your example is an increase of that uncertainty, but at a declining rate. You state 2016 = 10% 2017 19% 2018 28% ect. the total rate of decline here is increasing, however the rate of change is not increasing. In your example this first year is 10% the second year is +9% and the third year is +9% in my opinion even using an arbitrary starting point of 10% there should be an increase of this each year after that (more uncertainty) so the 10% rate should be increasing each year. If this were by the rate of the first percentage (10%) this would mean the rate would be 11% in year two 12.1% is year two and so on or 10% year one 21% year two 33.1% year three. You are correct that once this gets extended out to year five then we would be looking at a discount that is over 50% by year five if you were using an increasing rate of uncertainty.

In statistics the issue of uncertainty is usually handled by calculating the level of uncertainty as a percentage, plus or minus from the "true value" or the mean value that is expected.

This week in my financial management course we are discussing the time value of money is relation to the cost of money in terms of interest rates that can be expected over a specific time frame. There are two main formulas used for these calculations of two different values. The present value and the future value that could be applicable to FF as well.

"Present Value refers to the current value of money either paid or received in the future. It is what investors will pay today for future cash flows.

PV calculations are the inverse of FV calculations. We learned earlier that:

FV = PV (1 + r)n

Dividing both sides by (1 + r)n yields:

FV/(1 + r)n = PV (1 + r)n/(1 + r)n

The interest factors cancel, and the equation is now:

PV = FV/(1 + r)n"

The r = the rate of interest +/- and the n = the number of periods (time frames)

The rate of interest compounds over the time frame as long as it continues in the same direction and therefore the percentage of change increases at an accelerating rate not a decelerating rate as you show in your example.

Now you are also using a career performance path by age in the form of a discount as well. So you have two different elements providing a discount. I can see why you may want to be more conservative in your rate of discount because of this. However I have to question how the discount for uncertainty is related to the discount for players age (based on historical average). This is a problem if the two discounts are not related. This means the level of discounts are not aligned with each other. When I think of calculations not being aligned I see problems with that because of my background in cartography. The projections need to be in the same scale otherwise there will be a lot of noise and error which will be obvious when your icons are not correctly aligned to the physical features.

This concern about alignment is also why I try to do things using a 3 year window. The scale of the time frame gets aligned by always using the same amount of time (as possible).

This discussion leads me to more questions than answers.

Omg. Financial analysis. I love it. The PV of a player is his future points discounted back. We should do an NPV on all players in dynasty.

 

[Adam Harstad]

Omg. Financial analysis. I love it. The PV of a player is his future points discounted back. We should do an NPV on all players in dynasty.

I do this.

http://subscribers.footballguys.com/apps/article.php?article=Harstad_15_Wk16_Value

 

[Biabreakable]

[SIZE=14pt]Baeddel Moon,[/SIZE]

[SIZE=14pt]I agree that the time value of money is not the same as player value in FF. There are no bonds or safe investments in NFL players. The value of a player can go to zero at any time, on any play or even during practice. Perhaps rookie pick values could be considered safe investments that will have a stable value up to the time of maturity. Rookie picks often gain in [/SIZE][SIZE=18.6667px]perceived[/SIZE][SIZE=14pt] value leading up to the NFL draft. Sometimes after the NFL draft but I think often post draft some of the optimism for specific rookies changes based on where they were drafted by NFL teams.[/SIZE]

[SIZE=14pt]What we are discussing and trying to learn more about is the quantification of player values.[/SIZE]

[SIZE=18.6667px]I see player performance in the NFL as the market we as FF players are looking at to form our decisions. These values are quantifiable in terms of yards, TD and there are patterns of historical performance that can be followed to form some realistic guesses or projections from as far as how to price the value of these possible outcomes.[/SIZE]

[SIZE=14pt]The quantification would be based on how your league scores certain events such as gaining yards, scoring touchdowns, making receptions. The value of these numbers when converted into fantasy points. These points also have different values relative to each other based on the number of teams in your league, the starting requirements and the total roster size. These things determine the opportunity cost of a roster spot, the replacement level value of players is the baseline that all player performance is measured against. Similar to the break-even point or the internal rate of return.[/SIZE]

[SIZE=14pt]A rookie pick does not require a roster spot, so the opportunity cost does not apply to the pick, but it will be applied to the player that the pick ends up becoming. Which means that the pick when converted into a player loses value, because it now requires a roster spot.[/SIZE]

[SIZE=14pt]As far as the impact and frequency of injuries go I agree with both of you that an older player may find it more difficult to recover from a significant injury. In fact I have seen some studies that suggest a younger player is more likely to return to their previous level of performance after an ACL injury than an older player is. Another somewhat strange connection was that players who perform at a high level are more likely to be injured at some point than players who do not.Maybe this is just because those players play more, in some cases I think it may be due to the effort the player is putting forth perhaps making them a higher risk of injury. A team is less likely to be [/SIZE][SIZE=18.6667px]patient[/SIZE][SIZE=14pt] with an older player recovering from injury compared to a young player who still has peak years of their career left.[/SIZE]

[SIZE=14pt]The age 30 for RB being an age where many RB historically decline is partly because of team management decisions to not play a RB beyond 30 as much as they will be willing to do so at other positions. Recent history has gone against this in some ways, for example Fred Jackson, Curtis Martin and some other RB having good numbers after the age of 30. This has me leaning towards elite RB being more viable beyond the age of 30 than I once did. However when these players do drop in their performance it is usually something they won't recover from and they do not have enough time remaining in their careers to recover from. When the drop happens it is often very sudden.[/SIZE]

[SIZE=14pt]However this is not the point I was trying to make in regards to Fitzgerald is that if one valued him as being worth 100 points of value each season starting in 2008 (just an example) that there would be different total values for him depending on the number of seasons that you counted this value.[/SIZE]

[SIZE=14pt]If you were using a 3 year view this would be 300 points.[/SIZE]

[SIZE=14pt]If you were using a 5 year view this would be worth 500 points.[/SIZE]

[SIZE=14pt]If you were applying a value for all quality years remaining, the curve may have looked more like 100, 120, 120, 120, 100, 100, 100, 80, 60, 60, 20 which would be worth 900 points.[/SIZE]

[SIZE=14pt]The last one would be based off of the career curve i[/SIZE][SIZE=14pt]n 2008 Fitzgerald was 25 years old. The peak years for a WR are known to be from age 26 to 28 then there is a slight decline from 29-31 when a steeper decline happens from age 32-34 and at age 35 most drop off unless you are Jerry Rice.[/SIZE]

[SIZE=14pt]If I paid 900 value points in resources (players and draft picks) for Fitzgerald and got nothing in return for him that is 3 times the cost I would have paid using the 3 year method of valuation. Simialarly if I used 5 years I would pay 200 more value points than I would have using the 3 year method.[/SIZE]

[SIZE=14pt]The actual points that he scored were different than what these methods would have projected.[/SIZE]

[SIZE=14pt]Using Adams numbers above replacement for Fitzgerald 2008-2014 was [/SIZE][SIZE=14pt]worst-starter baseline in PPR was 185.14, 153.80, 102.50, 129.26, 29.04, 92.12, and 18.30, for a total of 710.16.[/SIZE]

[SIZE=14pt]This would be 400 points more than would be paid using the hypothetical 3 year method.[/SIZE]

[SIZE=14pt]My point is simply that by paying value points for year 4 and beyond can lead to a greater loss on a less than stable investment than using a shorter term valuation will.[/SIZE]

[SIZE=14pt]There are three different kinds of unknowns that we likely should be discounting for.[/SIZE]

[SIZE=14pt]Projections will not be accurate. The further out in time that we project, the greater the likelyhood of those projections being inaccurate.[/SIZE]

[SIZE=14pt]The historical pattern of how a player will perform by their age. Not all players follow the average career path. While I think this is something to be aware of and possibly to help inform your projections, there are always exceptions.[/SIZE]

[SIZE=14pt]Discounting for risk. Different players carry different levels of [/SIZE][SIZE=18.6667px]volatility[/SIZE][SIZE=14pt] in their performance which can make them less usable as starters because of this inconsistency (unless you are playing total points and not H2H). The more volatile the player [/SIZE][SIZE=18.6667px]performance[/SIZE][SIZE=14pt], the greater uncertainty forecasting that performance over time. Some players and situations can be remarkably consistent over time while others seem to be continually changing and there is little consistency in performance from season to season. Some players and teams carry more risk than others.[/SIZE]

[SIZE=14pt]So I can see using all 3 of these things as form of discounting. Some of these combinations should lead to a players value being zero at some point of their career. Valuing years beyond 3 from now can lead to over valuation of the asset in an ever changing marketplace.[/SIZE]

 

[Biabreakable]

I have a hard time seeing how the ins and outs of real world finance really have anything to do with dynasty. To start, from year to year, dynasty is a zero sum game. There is only one winner. If an investment club all does well, one might do the best but they will all profit. There are also very few fixed costs to running a team. The players all age a year, you pay an entry fee and that is the sum of it. Whereas a business man cannot declare his intention to rebuild, sell his machines and wait for the new models to come out. He still has to eat, that goes for the family as well. Capital, as Marx says, is the sum of life unlived. Dynasty owners do not make the choice of foregoing a trip to the movies to improve their starting line up. They do not save capital to try and achieve goals, other than the goal of winning the title.

I agree the ultimate goal should be winning a title this year and every year if possible.

I also agree there isn't a direct correlation between accounting or finance and the market of FF players and how those players performance can help you win that title.

So how do you achieve the goal of winning a title? You need players who can score more points than your opponents players. The more accurately you are able to predict player performance, generally the better informed decisions you will be able to make towards that goal of winning a championship.

Part of the beauty of dynasty leagues is that people may all agree that their goal is to win a championship, owners have different ideas about how to accomplish this goal and those ideas influence the way they value assets (players) in working towards this goal. Some people are not trying to quantify player values in FF points at all. They go off of their real football knowledge about the players to guide their rankings and guesses about how those players will perform and help them towards their goal of winning a championship.

I have seen championship teams formed from all kinds of different strategies and player combinations. There is not one way to construct a team towards the goal of winning a championship. There are several different ways one could try to accomplish this. The market may form these decisions for you. If the members of your league value the RB more than you do for example, you will find it hard to trade for or acquire RB in that market, so you may be better off trying to win by being strong at other positions. In todays environment WR are king and therefore may be over valued by a large portion of the FF community.

Some folks may be so good at daily fantasy that they could use that knowledge and the waiver wire in a dynasty format to excellent results in weekly head to head match ups. Players with this perspective may see 3 years as a long time away much less valuing a player for what you might expect they will do five years or longer from now. The smaller the roster size the better these options become.

I do think there is some useful cross over from the accounting and finance disciplines that can be applied to the market of FF player performance. If you are trying to quantify player values over time for example. There are other ways to try to win of course and I think the ideas about how to win a championship vary from owner to owner, although ultimately this should be the goal they are all working towards.

eta - If the goal is to form the most accurate projections over a players career, then obviously only looking at the next 3 years is less accurate than a longer view on that. The hypothetical value of the useful career remaining is closer to the actual performance for Fitzgerald than only looking at 3 or 5 years is.

But if the goal is winning a championship within the next 3 year starting with this year, which is the basic crux of my strategy, then looking at years beyond 3 is taking away from achieving this goal of winning a championship within 3 seasons.

 

[thriftyrocker]

One of the nice things about the Wayne vs. Fitzgerald comparison is that both were already established as elite and followed through with HOF careers (or a reasonable approximation). Fitzgerald was a once every 5 years WR, and Wayne was an elite player who played most of his career with a once every 5 years QB - we knew that going into 2008 and it held true. There's a purity in the comparison that you wouldn't get with many other players. There was a reason to put higher confidence on those players. However the messy part was all the names after Fitzgerald in the original list. When you look at the current landscape of WRs, it's similarly messy. I believe the middle aged WRs (Julio, Green, Dez, Brown) to be more talented than the young WRs (Hopkins, Cooper, Watkins, Robinson). That's the reason Beckham goes 1.1 in almost every mock I've seen because he's the only one in that age group where talent seems undeniable. You look at Matt Miller's 2020 rankings that were linked here, and there's a conflict there, because you know lower market value is coming for the Julio/Brown group, but the alternative is (arguably) less upside and not as big difference in long term stability (past a three year window) as you'd want. Allen Robinson is 5 years younger than AJ Green. They have very similar ADP, but I don't think Robinson (or Cooper or Hopkins) is twice as valuable. I don't have confidence the younger player's relevant career will be longer.

 

[Adam Harstad]

...

If you were applying a value for all quality years remaining, the curve may have looked more like 100, 120, 120, 120, 100, 100, 100, 80, 60, 60, 20 which would be worth 900 points.

The last one would be based off of the career curve in 2008 Fitzgerald was 25 years old. The peak years for a WR are known to be from age 26 to 28 then there is a slight decline from 29-31 when a steeper decline happens from age 32-34 and at age 35 most drop off unless you are Jerry Rice.

...

The historical pattern of how a player will perform by their age. Not all players follow the average career path. While I think this is something to be aware of and possibly to help inform your projections, there are always exceptions.

...

Just snipping this bit out really quickly to talk about it. The common "aging curves" we're all used to seeing are almost certainly an example of the ecological fallacy; while the group average always produces a nice pretty curve, individual careers are almost never curve-shaped.

For instance, I looked at the top 50 fantasy WRs and the top 50 fantasy RBs from 1985-2014. If NFL careers tended to be curve shaped, you would expect that their last fantasy-relevant season would have been worse than their 2nd-to-late fantasy-relevant season. In short, you would expect them to be declining at the end of their career.

But that's not what we see. Of the 100 players I looked at, 50% performed worse in their final fantasy-relevant season than they had the year before, and 50% performed better. The old players weren't declining. They were bouncing up and down at an equal rate right up until the day they were done.

Extending it out, if improvements and declines were distributed completely randomly, we would expect 25% of those 100 players to decline in each of their final two fantasy relevant seasons, (while 25% improved in both, 25% improved then declined, and the final 25% declined then improved). Based on aging curves, we should expect declines to be more common than improvements, resulting in greater than 25% of the sample who ended their career with consecutive declines.

Instead, only 17% of the top 100 fantasy RBs and WRs over the last thirty years declined in each of their last two fantasy-relevant seasons, a rate even lower than what would be predicted by chance alone.

In short, on an individual basis, "aging curves" are bunk. Players don't gradually improve, peak, and then gradually decline. Instead, they suddenly spike in value, then basically maintain that new level for an indeterminate amount of time before just as suddenly falling from relevance. It's just that the sudden falls from relevance become more common as players age, producing the illusion of a curve when the data is aggregated.

 

[Adam Harstad]

One of the nice things about the Wayne vs. Fitzgerald comparison is that both were already established as elite and followed through with HOF careers (or a reasonable approximation). Fitzgerald was a once every 5 years WR, and Wayne was an elite player who played most of his career with a once every 5 years QB - we knew that going into 2008 and it held true. There's a purity in the comparison that you wouldn't get with many other players. There was a reason to put higher confidence on those players. However the messy part was all the names after Fitzgerald in the original list. When you look at the current landscape of WRs, it's similarly messy. I believe the middle aged WRs (Julio, Green, Dez, Brown) to be more talented than the young WRs (Hopkins, Cooper, Watkins, Robinson). That's the reason Beckham goes 1.1 in almost every mock I've seen because he's the only one in that age group where talent seems undeniable. You look at Matt Miller's 2020 rankings that were linked here, and there's a conflict there, because you know lower market value is coming for the Julio/Brown group, but the alternative is (arguably) less upside and not as big difference in long term stability (past a three year window) as you'd want. Allen Robinson is 5 years younger than AJ Green. They have very similar ADP, but I don't think Robinson (or Cooper or Hopkins) is twice as valuable. I don't have confidence the younger player's relevant career will be longer.

For what it's worth, my method doesn't say Robinson is twice as valuable just because he's five years younger; it accounts for Green's additional security in the short term, and the time discounts eat away the majority of that extra value that Robinson is adding 5+ years down the line. In my final value charts of the year, I had Green valued at 468.4 and Robinson at 592.4, a roughly 25% increase

 

[Biabreakable]

...

If you were applying a value for all quality years remaining, the curve may have looked more like 100, 120, 120, 120, 100, 100, 100, 80, 60, 60, 20 which would be worth 900 points.

The last one would be based off of the career curve in 2008 Fitzgerald was 25 years old. The peak years for a WR are known to be from age 26 to 28 then there is a slight decline from 29-31 when a steeper decline happens from age 32-34 and at age 35 most drop off unless you are Jerry Rice.

...

The historical pattern of how a player will perform by their age. Not all players follow the average career path. While I think this is something to be aware of and possibly to help inform your projections, there are always exceptions.

...

Just snipping this bit out really quickly to talk about it. The common "aging curves" we're all used to seeing are almost certainly an example of the ecological fallacy; while the group average always produces a nice pretty curve, individual careers are almost never curve-shaped.

For instance, I looked at the top 50 fantasy WRs and the top 50 fantasy RBs from 1985-2014. If NFL careers tended to be curve shaped, you would expect that their last fantasy-relevant season would have been worse than their 2nd-to-late fantasy-relevant season. In short, you would expect them to be declining at the end of their career.

But that's not what we see. Of the 100 players I looked at, 50% performed worse in their final fantasy-relevant season than they had the year before, and 50% performed better. The old players weren't declining. They were bouncing up and down at an equal rate right up until the day they were done.

Extending it out, if improvements and declines were distributed completely randomly, we would expect 25% of those 100 players to decline in each of their final two fantasy relevant seasons, (while 25% improved in both, 25% improved then declined, and the final 25% declined then improved). Based on aging curves, we should expect declines to be more common than improvements, resulting in greater than 25% of the sample who ended their career with consecutive declines.

Instead, only 17% of the top 100 fantasy RBs and WRs over the last thirty years declined in each of their last two fantasy-relevant seasons, a rate even lower than what would be predicted by chance alone.

In short, on an individual basis, "aging curves" are bunk. Players don't gradually improve, peak, and then gradually decline. Instead, they suddenly spike in value, then basically maintain that new level for an indeterminate amount of time before just as suddenly falling from relevance. It's just that the sudden falls from relevance become more common as players age, producing the illusion of a curve when the data is aggregated.

Yes obviously the average of a large sample is going to tell us generally what will happen on average by age to the entire group, not how each individual performed within that group.

When the fall does happen, it usually very sudden. Teams do not make a habit of playing players who are under-performing long.

At the same time I do not think the average of player career curves are bunk. They are what they are. If they were bunk this would imply they have no utility at all. I don't think this is what you intend to be saying by this comment.

A lot of player production curve studies include sample sizes larger than your top 50 RB and WR sample. Mixing WR with RB in such a selection of data isn't very helpful because the career curves of players at these two positions is pretty different. The WR sample is likely skewing the overall results. If you look at the RB separately you will see more fall off than the combined sample size suggests.

I hardly think the evidence you have provided proves that the use of player production curves as an ecological fallacy when your sample is pretty small and not on the scale that this fallacy applies to.

 

[ZWK]

As Adam has said, there are 2 sorts of reasons for you to discount future value: because future production is more uncertain (e.g., we can be more sure of what Russell Wilson will do in 2016 than of what he'll do in 2023) and because you care more about the near future (e.g., what happens in 2016 matters more to me than what happens in 2023). The first of these has to do with predicting what players will do, the second has to do with how much value we assign to it.

The second of these is what gets called "pure time preference" and it's where exponential discounting makes sense. That's what Adam & Bia have been talking about (and what's standard in finance) where each year matters N% as much as the previous year (e.g., with a 20% discount rate, each year matters 80% as much as the previous year). If there is no reason to expect a drastic change in any one specific year, and just a general trend for things to get fuzzier farther into the future, then this shape of discounting makes a lot of sense (that's why it's used in finance).

I prefer to think about pure time preference in terms of championships rather than in terms of fantasy points. For example, if you have a 20% discount rate, then the situation where you'll win the championship in 2017 if you're still in the league then is only 80% as good as the situation where you'll win the championship in 2016 if you're still in the league then. (It's important to include the "if you're still in the league then" part because one of the reasons to discount the future is because you might not be in the league.) And a championship in 2018 is only 80% as good as a championship in 2017, which means that it's only 64% as good as a championship in 2016.

I like thinking about pure time preference in terms of championships because it lets you pose questions like this: When would you prefer to win championships over the next 10 seasons (2016-2025)?

Option 1: win 1 championship in 2016 (and no others from 2017-2025)

Option 2: win 7 championships in a row from 2019-2025 (only if you are still in the league for each of those seasons, and you do not win any from 2016-2018)

If you make a hard-and-fast rule of following a "three year window" than you'll prefer Option 1. That might make sense in some special cases, like if you just got to college and started a dynasty league with some classmates, and you expect it to break apart after you all graduate. But I'm guessing that most people would prefer Option 2.

If you prefer Option 2, and you use exponential discounting, that means that your discount rate is below 30%. In other words, each year matters at least 70% as much as the previous year.

If choosing Option 2 was not a close call for you, then we need to narrow things down because your discount rate could be anywhere from 0% to 30%. Consider these two options:

Option A: win 1 championship in 2016 (and no others from 2017-2025)

Option B: win 4 championships in 2020, 2022, 2024, and 2025 (only if you are still in the league for each of those seasons, and you do not win any others between now and 2025)

If you prefer Option A, then your discount rate is 20% or higher. If you prefer Option B, then your discount rate is below 20%.

If you chose options 2 & B, then what about this choice?

Option I: win 1 championship in 2016 (and no others from 2017-2025)

Option II: win 2 championships in 2021 and 2025 (only if you are still in the league for each of those seasons, and you do not win any others between now and 2025)

If you prefer Option I then your discount rate is 10% or higher. If you prefer Option II then your discount rate is below 10%.

You can narrow in on your discount rate by considering several of these sorts of scenarios (although if it's below 8% then we need to start using scenarios that go beyond 10 years, or where both options involve multiple championships). You can also test whether you actually have a robust, consistent discount rate by varying the scenarios up some more (so that the first option is not always "win 1 championship in 2016") and seeing if your preferences still match the same discount rate.

 

[Biabreakable]

ZWK I like your focus on a particular teams goals. For example win in 2016 without concern about 2017 or 2018. Try to win in 2017 through 2020 would be a strategy where the owner decides to sacrifice their ability to compete now in order to put their team in a better position to win in 2017 this goal could be to set up a team that will win or be competitive enough to be in a position to win for many years to come.

This is something gheemoney and I were talking about many years back using the 3 year window as the framework for shifting strategy.

This would start by forming projections for 2016 and then looking at career player curves as a guide to which players may decline in value (real or perceived) in 2017 and 2018 with some modification of your projection for those players. In some cases you may have a player entering the prime years of their career where you expect that player to improve their numbers in 2017 or 2018 compared to 2016.

Then with these projections as a guide you could apply the 3 year window in different ways to fit your strategy.

The default would be valuing each of the years equally.(33% 2016 33% 2017 33% 2018) or you can decide to value to the current season a bit more than the following seasons because you are contending for a championship now. This weighting might be (50% 2016 30% 2017 20% 2018) or it could be more extreme (70% 2016 20% 2017 10% 2018).

If your team is not contending for a title in 2016 then the value of the seasons 2017 or 2018 become more important and you might use a weight like (25% 2016 50% 2017 25% 2018) or if you think your team is two years away from contending then maybe place most of the value on 2018 instead of 16 or 17. That would look something more like (20% 2016 30% 2017 50% 2018) or (10% 2016 20% 2017 70% 2018).

These percentages are not related to the discounting. They would be applied to projections as part of the owners strategy.

Now as we have been discussing, I think the current season is the most important season to try to win. However there are some circumstances, such as a start up draft or if I were taking over a team not able to compete right now where I would shift my strategy towards building a championship team one or two years from today. I will make sacrifices for youth to further this cause. I am doing this with a goal in mind, to build the best team I can for 2017 or 2018. Once the roster becomes competitive then I shift back to a focus that values the current season more than the others again and try to maintain my roster as one of the most competitive teams in the league indefinitely from that point forward.

As much as things change in the NFL I do think you can manage your roster with these goals in mind and thereby maintain your team as highly competitive indefinitely which is a goal of dynasty. Not only to win a championship, but to win many championships over the time of the league.

 

[Adam Harstad]

Yes obviously the average of a large sample is going to tell us generally what will happen on average by age to the entire group, not how each individual performed within that group.

When the fall does happen, it usually very sudden. Teams do not make a habit of playing players who are under-performing long.

At the same time I do not think the average of player career curves are bunk. They are what they are. If they were bunk this would imply they have no utility at all. I don't think this is what you intend to be saying by this comment.

A lot of player production curve studies include sample sizes larger than your top 50 RB and WR sample. Mixing WR with RB in such a selection of data isn't very helpful because the career curves of players at these two positions is pretty different. The WR sample is likely skewing the overall results. If you look at the RB separately you will see more fall off than the combined sample size suggests.

I hardly think the evidence you have provided proves that the use of player production curves as an ecological fallacy when your sample is pretty small and not on the scale that this fallacy applies to.

I believe I wasn't clear enough. I looked at the top 50 RBs, and I looked at the top 50 WRs. Two separate samples producing two separate mortality tables, one for each position. (I also produced one for quarterbacks and one for tight ends; the quarterback sample was even smaller- 30 players, iirc- because the talent fall-off was steeper. I believe the TE one was smaller, too, and I also produced a blended table combining both tight ends and wide receivers to account for the fact that today's TEs are completely different beasts from the TEs of the '80s and '90s and probably closer to WRs in usage and skills.)

I will agree that the sample size is relatively small, all things considered. The problem is creating the largest sample size we can while still maintaining relevance. I could have added in another 50 RBs and another 50 WRs, but the 100th best fantasy WR of the last 30 years isn't necessarily going to be very representative of how someone like Dez Bryant might age. For comparison, the 46th-50th best fantasy WRs of the last thirty years were Anthony Carter, Santana Moss, Terance Mathis, Laveranues Coles, and Antonio Freeman. The 96th-100th best fantasy WRs of the last thirty years were John Taylor, Mike Wallace, Michael Jackson, David Boston, and Fred Barnett.

I had to draw the line somewhere that I felt best balanced my desire to maximize the size of the sample and my desire to maximize the quality of the comparisons. "Top 50" is a pretty arbitrary benchmark, but it's one I felt did a reasonable job of accomplishing that goal.

Also, my evidence that aging curves suffer from ecological fallacy is separate from my work on a mortality table. Most of the former argument can be found in a series of charts and graphs in this article. Part of it can be seen in the stats I posted earlier about what percentage of players decline in their final one and final two fantasy-relevant seasons, (a rate lower than would be predicted by chance alone, whereas aging curves demand a chance higher than would be predicted by chance alone).

 

[Biabreakable]

I couldn't read the article. When you asked me to look at your database all I saw in the link was your twitter feed. Perhaps one of those tweets contained a link to the data base you were referencing, I was not going to dig through your conversations to find it, so I didn't.

You may think you have proven aging curves are an ecological fallacy, without seeing further explanation that becomes impossible for me to evaluate. On the surface I do not think football statistics as a market or population functions in the same way as statistics are applied to micro organisms for example.

When you are talking about statistics on a ecological scale you are talking about parts per million and very large data sets (which might be about very small organisms) which I do not see as comparable to football performance which is not even at baseballs level of robust data from many games over the season.

As we have discussed before, football performance statistics do not have exponential growth rates. Performance occurs in a more bound and predictable range of possible outcomes than this. So I question why you are trying to cross these two disciplines or think it is appropriate to do so? Much less that you have scientifically proven age curves to be a logical fallacy.

I agree you are always going to have a cut off point somewhere in whatever sample size you might choose. Some of the players who are not included in your sample were relevant FF players for a time such as Mike Wallace and I am sure several more players who get cut out of the sample.

Now we may agree more than we disagree in regards to each player being unique and having a career path that is unlike other players or unlike the average of all of the players. I think you evaluate each player on a case by case basis as far as how you think their career performance will change over time and how that players age may affect that.

However if you are going to use a production curve for a value discount (as I believe you mention doing) you would be doing so based on the historical evidence of that occurring. Whatever discount you may apply to one player needs to be applied to all of them, based on the average of the entire sample size. This is done with an understanding that each player is unique, however if you apply the discount fairly to all players then I am not seeing the issue with doing that because the discount would affect all players the same.

Players who play different positions have different career path curves. I wanted to form a sample of the WR that was the same as the data I put together for the RB career averages last year. The reason I did not do so is because the target data does not go back far enough for me to form a sample size of 25 years. So if I did put together a career average production curve for WR, I would need to change what I did for RB so that the sample sizes are aligned in the same time frame. This would make a smaller sample size for the RB and the results of which I have less confidence in than the 25 year sample I already compiled. So I just didn't do the WR. The two positions are so different, maybe I shouldn't be concerned about aligning them at all

 

[Adam Harstad]

I couldn't read the article. When you asked me to look at your database all I saw in the link was your twitter feed. Perhaps one of those tweets contained a link to the data base you were referencing, I was not going to dig through your conversations to find it, so I didn't.

The link was not to my Twitter feed, but to Storify, which is a service that allows you to collect several related tweets and collate them in a single post. It was just thirteen tweets that explained what my databases were, why I was sharing them, and where they could be find. My data is in eight different spreadsheets and it's a lot easier to share just that one link that contains individual links to all eight than it is to share eight individual links every time.

I appreciate that, being behind the paywall still, my article won't be accessible to non-subscribers until the switch gets flipped to offseason mode and everything comes out from behind the wall. I've been doing my best to present a fair and accurate summary where possible, including of the key data, (such as the fact that players aren't actually any more likely to decline at the end of their careers).

You may think you have proven aging curves are an ecological fallacy, without seeing further explanation that becomes impossible for me to evaluate. On the surface I do not think football statistics as a market or population functions in the same way as statistics are applied to micro organisms for example.

When you are talking about statistics on a ecological scale you are talking about parts per million and very large data sets (which might be about very small organisms) which I do not see as comparable to football performance which is not even at baseballs level of robust data from many games over the season.

I think "proven" is a pretty loaded word, and I don't think it fairly represents how I view the fantasy football process, which I think is more of a collaborative back-and-forth. I'd be more comfortable saying that I feel like I've evaluated several of the key claims of the "aging curve" hypothesis and found the evidence lacking or even contradictory. I aimed to shift the burden of proof; instead of being in a place where we needed to demonstrate that aging curves were a poor representation of reality, we're in a place where proponents of them should be required to present evidence that they aren't.

Also, "ecological fallacy" doesn't really have anything to do with ecology. It's merely... well, we'll let Wikipedia take this one:

An ecological fallacy (or ecological inference fallacy)[1] is a logical fallacy in the interpretation of statistical data where inferences about the nature of individuals are deduced from inference for the group to which those individuals belong.

The groups could be millions or even billions of members strong. Or the groups could be just ten members. For example: Imagine there are two classes, each containing 10 students, who are given a test where they can score anywhere between 0 and 10 points. In the first class, one student scores 10 points and the other nine score 5 points each. In the second class, one student scores 0 points and the other nine score 6 points each.

The first class has an average test score of 5.5. The second class has an average test score of 5.4. However, if someone saw those averages stated "I'd expect a student in the first class to have done better than a student in the second class", they would be guilty of the ecological fallacy- taking the group average and from there generalizing out to the individual members of the group. In fact, if you selected a student at random from each class, there would be an 81% chance that the student from the second class outscored the student from the first.

Similarly, even from a sample of fifty receivers we can conclude that none of the individuals behave in a manner consistent with the population average, and therefore generalizing from the average itself is an example of the ecological fallacy. For instance, the population average declines with age, but I've already said that individual players are no more likely to decline at the end of their careers than they are to improve.

However if you are going to use a production curve for a value discount (as I believe you mention doing) you would be doing so based on the historical evidence of that occurring. Whatever discount you may apply to one player needs to be applied to all of them, based on the average of the entire sample size. This is done with an understanding that each player is unique, however if you apply the discount fairly to all players then I am not seeing the issue with doing that because the discount would affect all players the same.

Nope, no curves. I predict a set production value, (a "true mean", if you will), and then estimate odds as to whether the player will still be fantasy-relevant based on historical "death rates", (the observed rate at which productive players have fallen out of fantasy relevance in the past). But I'm not anticipating any decline in performance, I'm just modeling a process where a player will either be productive or he won't. If he's productive, I anticipate him being just as productive as he was before.

Also, I'm not saying that any instance of generalizing from groups to individuals is an example of ecological fallacy. I'm saying that age curves in particular are, in my opinion, an example of ecological fallacy. There's little evidence that they actually apply on an individual level, as opposed to merely being an artifact of aggregation. As I've said, actual individual players are no more likely to decline in their final fantasy-relevant season than they are to improve.

 

[Biabreakable]

Ok I see the data is gathered from 1985 to 2014.

The target data in PFR starts in 1994. How do you compensate for the lack of target data in the years previous to this?

In regards to the career averages I agree each player is different and each has their own unique ending to their career which will be different than what the averages might suggest will happen to the average player based on age is not directly applicable to each individual player.

I can also understand your position of the person developing and using a carer curve to explain its utility or to prove how this may be accurate or useful. From my perspective I understand that each player will be unique but there are general trends, such as a RB facing decline at age 30 that are strong enough that I would not ignore that possibility, even for the best of them to decline from this point.

Where I guess there is some misunderstanding is that earlier when we were discussing discount over time due to uncertainty, you mentioned also applying a discount for a players career curve. However if you think a players career curve cannot be found and that those results are a the product of a logical fallacy, then you likely are not applying a discount based off a player performance curve over time. Is the discount for uncertainty the only discount you use?

What I can do using a player performance curve is to cut off all values after 3 seasons and compare the entire group using this selection of the entire data to meet my goals of informed player value decisions. If you only have one total number accounting for the quality years remaining, I would not know how to reduce this for the purpose of player values over the next 3 seasons.

Adrian Peterson for example just won the rushing title at age 30. However it is a shallow accomplishment because so many other RB were injured and Petersons career average yards per carry fell below 5 for the first time in his career following the 2015 season. Time waits for no one and even Peterson will see a fall off in his production in the years ahead. I expect Peterson to keep playing as long as a coach allows him to. Similar to how I viewed LT when he was reaching this age.

If I have the player I will just keep them until the wheels fall off because I don't think you can get good value for a RB over 30 as most dynasty owners know the end for such a RB is coming soon. It might not happen until Peterson is 33 years old but it is going to happen. I don't think we can accurately predict when specifically that will happen. But we can look at the trends of the general population as an indication of when that window has opened, or where the threshold age is where we should be realistically concerned about a decline that may or may not happen this season, but is expected to happen within the next two to three seasons.

The way I chose my sample size was by looking at top 12 performance (by VBD standard from PFR) of 25 seasons. So this was 300 total possible players. Many players had repeat top 12 performance in multiple years so the number of players is actually smaller than 300. I took the top 150 players (50% of the results) as the baseline of the 300 top 12 years. So like your sample of the top 50 players, it does not include all of the players, we are considering for career averages. It only considers the best of the best at the RB position. This would not be applicable to the entire RB population, but to players who are performing at a high level currently at the position. Players performing at a lower level than this have shorter total careers and even fewer instances of a game where they will put up numbers good enough to be start and when they do that performance is most often short lived. My cut off was a combined total VBD and PPG which I thought worked out to a nice balance because it identified players such as Andre Ellington as having an impact over a short number of games, but mostly what caused players to qualify was by performing at a high level over a longer period of time, which not many RB cannot do longer than two seasons of their career.

 

[Adam Harstad]

Ok I see the data is gathered from 1985 to 2014.

The target data in PFR starts in 1994. How do you compensate for the lack of target data in the years previous to this?

I'm relatively unbothered by it, from a process standpoint. I'm measuring fantasy value, which relies on output statistics, (catches, yards, and touchdowns), so it doesn't really matter if I'm missing any and all input statistics, (such as targets for a WR or carries for an RB). An 80/1200/10 season is worth 260 fantasy points in PPR whether it came on 100 targets or 200.

I can also understand your position of the person developing and using a carer curve to explain its utility or to prove how this may be accurate or useful. From my perspective I understand that each player will be unique but there are general trends, such as a RB facing decline at age 30 that are strong enough that I would not ignore that possibility, even for the best of them to decline from this point.

Where I guess there is some misunderstanding is that earlier when we were discussing discount over time due to uncertainty, you mentioned also applying a discount for a players career curve. However if you think a players career curve cannot be found and that those results are a the product of a logical fallacy, then you likely are not applying a discount based off a player performance curve over time. Is the discount for uncertainty the only discount you use?

My data suggests that players don't decline so much as they fluctuate around a fixed mean unpredictably until they fall off a cliff and out of fantasy relevance. As a result, I'm just projecting that fixed mean and their odds of falling out of fantasy relevance. That fixed mean, (being fixed), doesn't change. If a guy is a 100 VBD player, I predict he'll essentially remain a 100 VBD player, (give or take some random fluctuation), until the day his fantasy-relevant career is over.

As players age, the odds of falling off the cliff and out of relevance go up, (just like a human's odds of dying go up with age). So older players will naturally receive bigger discounts from this factor, as their odds of just going belly up at any given point are higher. But assuming they don't go belly up, I predict business as usual.

What I can do using a player performance curve is to cut off all values after 3 seasons and compare the entire group using this selection of the entire data to meet my goals of informed player value decisions. If you only have one total number accounting for the quality years remaining, I would not know how to reduce this for the purpose of player values over the next 3 seasons.

How the mortality rate works is I calculate a "death rate" at each age individually. So if you're a 24-year-old WR, maybe you have a 3% chance of just imploding, while if you're a 25-year-old WR, maybe it's 5%, and by the time you get up to 35 it's maybe a 50% chance.

Expected years remaining, then, are your chances of surviving this year, plus your chances of surviving next year provided you survived this year, plus the chances of surviving two years from now provided you survived next year, and so on and so forth. Add up all of those possible outcomes to create a weighted average, and that's your total EYR.

It's the same process actuaries use to calculate life expectancies.

In theory, if you really wanted to fit it to a 3-year window, that's easy enough. Just set the estimated death rate for 4 years from now to 100%. But the whole point of doing the life expectancy and time discounting is so you don't have to limit your scope to just three years.

 

[Borden]

Sooooooo, where do I get my $10?