Adam thanks for the explanation about why you do not think the percentage of discount cannot become 100% that is reasonable, I just don't happen to agree with this.
If the player gets injured, loses their job, gets traded to Dallas then cut, performs below replacement level ect. that player will have zero value in the season that this occurs from the point that it occurs. In the case of this ending the players career that player will never have value again. So I cannot agree with your premise that player values do not become zero.
I'm not saying that players can never have zero value. I'm saying that *production* can never have zero value. Obviously when players cease to have production, they cease to have value.
Let's put it this way: you play with a three-year window. Let's say I had a perfectly accurate crystal ball, and I told you that Larry Fitzgerald would score 600 points over the next three years. You go through and you calculate what his value is today from that information.
Now let's say that I tell you four years from now, Larry Fitzgerald is going to have the single greatest season by any player at any position in the history of the NFL, finishing the year with 3,000 receiving yards and 37 touchdowns. Armed with this new knowledge, does Larry Fitzgerald's value go up, stay constant, or go down?
If you said "go up", then you are saying production in year N+4 has positive value. If you said "remains constant", then you are saying production in year N+4 has zero value. If you said "goes down", then you are saying that production in year N+4 has negative value.
Now, I get that year N+4 is super-uncertain, and that uncertainty is going to discount how much we value that year. But this doesn't change the fact that we still assign some sort of value to what happens in year N+4. If we expect positive production in year N+4, then that carries some degree of positive value today, no matter how minor.
The problem with accelerating discounts is they quickly pass 100%. Let's use an accelerating, compounding 33% discount. We'd say that the discount in year N+1 is 33%, and in N+2 is (1 + 0.33)^2, or 77%, and in year N+3 is (1+0.33)^3, or 135%. That's the discount rate, which means the value of each of those seasons is one minus the discount rate. So production in year N+1 is 67% as valuable as production in year N, production in year N+2 is 23% as valuable as production in year N, and production in year N+3 is -35% as valuable as production in year N. That's an accelerating discount.
Now, let's say we assumed a player would provide 100 "points of value" in year N. His value today should be 100. All well and good.
Let's say we predicted he'd provide an extra 100 points of value in N+1. That value gets discounted to 67 due to uncertainty, and the player's value today is 167. That's great.
Let's say we predicted he'd provide an extra 100 points of value in N+2. That value gets discounted all the way down to 23 due to compounded uncertainty, and the player's value today is 190. Fantastic.
Let's say we predicted he'd provide an extra 100 points of value in N+3. That value gets discounted to... -35. And now, because we expect he's going to be very productive still in three years, his value has fallen down to 155. Ummm...
Let's say we predicted he'd provide an extra 100 points of value in N+4. That value gets discounted down to -113, and the player's total expected value today has fallen all the way to 42.
Let's say we predicted he'd provide an extra 100 points of value in N+5. That value gets discounted down to -216 as this accelerating discount has careened off the rails entirely. Suddenly, this amazing stud of a player who we expect to remain consistent and productive for six more years is coming out with *NEGATIVE* total value today, (-174 total, in fact). We're essentially saying that if the player retired after year N+2, he'd have 364 more points of total "present value".
In fact, a player having negative value tells us we'd be better off cutting him outright, since an empty roster space has 0 value, and 0 is greater than -174.
This is clearly a nonsensical outcome. Production should never have negative value. If I told you that a guy was going to have a great season in X years, that should never cause you to value him *less* today.
Now, I totally get saying that production six years out is very, very uncertain, and our expectations should carry very little weight. If we use that 33% time discount the way I'm doing it, where it decelerates, that 100 points of value in year N+5 only increases his expected total value today by 13.5 points, because it's so heavily discounted.
Here's the side-by-side comparison of expected total value using a decelerating time discount and an accelerating time discount on a player who adds 100 points of value every year:
N+0: 100 , 100
N+1: 167, 167
N+2: 212, 190
N+3: 242, 155
N+4: 262, 42
N+5: 275, -172
N+6: 284, -525
N+7: 290, -1061
N+8: 294, -1858
N+9: 297, -2960
N+10: 299, -4691
So the decelerating time discount tells us a guy who gets us 100 points in perpetuity is a pretty nice guy to own, while the accelerating time discount tells us a guy who gets us 100 points in perpetuity would be the single biggest drag on our roster imaginable.
Even if we "sanity-cap" the discount at 100%, (which is just a post-hoc solution to a faulty process), we quickly reach a point where a guy continuing to be productive carries literally no weight. And I don't think that's tenable either. Future production needs to be discounted because of the uncertainty, but that doesn't mean that production ceases to have value past some certain threshold. Production always has value. That's why you make some exceptions on your 3-year window for certain players; because you anticipate a better-than-normal chance for them to be productive past the three-year window, and you recognize that that production has value.
As far as your position on years in the future having equivellent value as the current season I cannot agree with that either. I think owners should be focused on winning now. Winning now is more valuable that winning two years from now at least to the point where you have won. Once the season is over then it has zero value. You could look at this on a game to game basis as well. A player who was a top scorer in week 14 will never have that value again, it is over, the value is now gone, however those points were the most important points of that particular game/week.
I think you're misreading me. I've never said that years in the future have equivalent value to the current season. In fact, quite the opposite! The reason I am time discounting is because I explicitly believe that future years do *NOT* have as much value as present years. Otherwise why am I discounting them?
What I'm saying is that the time discount should be consistent from year to year. 2026 is as much less valuable compared to 2025 as 2025 is compared to 2024. Further, the discount between 2025 and 2026 should be the same today as it is five years from today.
The reason someone will take $10 today instead of $20 next year is because they have bills to pay or other purposes for that money right now. While being able to get a 100% return on the investment is great, what if that $10 was used to buy some rice and vegetables which was then prepared and served and earns the person $30 that week? It would make sense for them to take the $10 then instead of $20 a year from now because the $10 made them more money and sooner because the capital can be utilized right away.
Yup. I get that. That's why I explicitly stated that I'm not saying either taking the $10 or the $20 was the wrong decision. I'm saying that it's weird that they changed their mind on it. If I gave you the choice between a dollar today or two dollars tomorrow, and then I also gave you the choice between a dollar tomorrow and two dollars two days from now, your choice for each should generally be the same. Because it's the same choice- wait a day to make an extra dollar.
(Yes, I'm aware there can be extenuating circumstances. Perhaps there's a loan shark who will break your knees if you don't give him exactly one dollar by today at sun-down, so you're super-impatient on the first choice, but happy to wait on the second. But we're not talking about rare exceptions; study after study demonstrates that these sorts of preference reversals are the standard state of affairs for intuitive internal time discounts.)
There seems to be an issue with the point of origin when you say " being more productive in 2018 makes him less valuable in 2015" you seem to be saying that this cannot happen. But it happens all the time. Lets say the player in question does not play in 2015 therefore their value in 2015 was zero regardless of what the player does in following seasons. You may want to value that player in 2015 for the value they will provide in 2018, that is reasonable to assign some value to that possible outcome, I do that with rookie players especially who are known to progress and grow over the first few years before reaching their peak level of performance, maintaining that for a period of time and then declining.
A players value in 2018 is not equal to a player performing at a similar level for you now. Even if you could be 99% sure that this player will be that valuable in 2018 you still have two years to try to acquire that production. In the mean time you may just keep selling your rice and vegetable dish until you have built enough capital to afford that 2018 season.
Again, I think you're misreading me. I'm not saying "production in 2018 shouldn't be less valuable than production in 2015". It should! That's why I time discount.
I'm saying "production in 2018 should not make a player less valuable today". In other words, if I told you Larry Fitzgerald was going to retire after the 2017 season, let's say you would value him at "X" right this moment. Now let's say I told you instead that Larry Fitzgerald would *NOT* retire after 2017, but would instead hang around for another year and make the pro bowl. You process this information, and you value Larry Fitzgerald at "Y" right this moment.
All I'm saying is that, whatever Y is, it should never be less than X. Additional production in 2018 should not make a player less valuable overall in 2015. That should never happen.
So this is the crux of our disagreement. The current season is more valuable to me than following seasons are. Once the current season is over it no longer has any value at all. It is a depreciating asset with each game, but it is still more valuable than games in 2016 because owners will have 6 months to make trades, draft picks, free agents to improve their teams for 2016 once the 2015 season was over and before the 2016 season begins.
How is the best way to quantify these differences in value? I am not sure. That is largely what the 3 year window idea is about, how to balance the values of now to the values of things in the future. I think if companies shared the perspective that money 3 years from now is the same as today would quickly bankrupt themselves if they do not follow the free cash flow to limit their long term investments and maintain capital for operational activities.
Again, this isn't the crux of our disagreement. I 100% agree with you on this. This is exactly why I'm time discounting, to specifically ensure that next year is less valuable than this year, and the year after that is less valuable still, and the year after that is less valuable still.
We're discussing the form such a time discount should take, not disagreeing over whether it should exist in the first place.
Yep. No one's recommending trading Randy Moss for Jacoby Jones here.
Bracie yeah Randy Moss didn't score 23 TD again. That is still the record I believe?
