Risk-adjusted future value - lessons from finance
So here I found myself writing in SeaDawg's "audit my team" thread, mentioning that future value of prospects is pretty uncertain and how many GMs tend to overrate them.
Tonne of bricks on my head: why on earth don't we consider this problem the same way the financial industry evaluates future dollars in the present day? Those principles are used constantly to value what a "future dollar" is worth today... so why can't we do that with future fantasy production? This post will be me exploring that idea to see if it has any merit.
The finance background
The underlying premise of this is the Time Value of Money. Have a read if you're not familiar. To put forward the simple example listed in Wikipedia, if you're looking at getting 5% interest on $100 over the course of a year, then $105 in your hands in May 2013 has the same true value as $100 in your hands today.
The simple formula is Future = Present * (1 + rate)^period or F=P(1+i)^n
The rate is either an interest rate if you're looking forward, or a discount rate, if you're bringing future value into today.
Applying it to fantasy hockey
So 80 points from a player two years from now are worth how many points today? That's what we're trying to answer.
F = 80
n = 2
i... well, this is really the trick isn't it? How on earth do we apply a discount rate to fantasy hockey production? One approach would be to look at year-on-year appreciation of specific "classes" of player when compared to the NHL scoring in general, perhaps evaluating "top-3 F", "top-6 F", etc etc. Well damn, that seems like too much work for my sinus-cold head this morning. Not gonna happen.
So, we do what engineers do: look for allegories! The heart of what we're trying to do here is quantify the risk that the future production will or won't happen, right? Is that appreciably different from an investor trying to determine whether their investment will give them the money they're hoping for, based on the type of investment it is?
For a look at the types on discount rates we see for evaluating companies, we roll on over to QFinance and see what they have to say. They say this:
Startup seeking new money: 50-100% discount rate
Early start-ups: 40-60%
Late start-ups: 30-50%
Mature company: 0-25%
Since financial analysis of future money is really more art than science, I'd think we can use that as a guide to map it over to fantasy hockey players using our intuition.
Prospects with no NHL track record: 50-100%
1st and 2nd year players: 40-60%
3rd and 4th year players: 30-50%
Established veteran: 0-25%
That seems reasonable enough to me, though the ranges are pretty wide. I guess we could further refine each of those, like breaking Established Veteran down into "Marty St. Louis -like consistent veteran" and "typical veteran", but that sounds like too much work.
So it seems like we've got the groundwork. Let's see how it looks by taking a few examples.
2003, when drafted: thought to have an 80-point upside, 2003. Anticipated NHL ETA: 2005/2006 (call that 2006, since he was drafted at the end of the 2002/2003 season). Assuming a "standard" 4-year NHL development window, complete with 4th year breakout, that pegs his 80-point value in 2009, 6 years from his draft. n=6
F = P(1+i)^n
P = F/ ((1+i)^n)
We'll use the low-end of the discount rate for a player with no NHL experience, since he was considered a good prospect at #11 overall.
P = 80/((1+50%)^6)
P = 7 points
2004: Still no NHL resume, so the same 50% discount rate. n=5
P = 80/((1+50%)^5)
P = 11 points
2005: still no real NHL resume, same 50% discount rate. n=4
P = 80/((1+50%)^4)
P = 16 points
2006: first real NHL season. He's now "de-risked" himself by proving he can hang in the NHL. Discount rate now at 40%, n=3.
P = 80/((1+40%)^3)
P = 29 points
Hmmm. He actually scored 42. That implies a discount rate of 24%. Noted!
2007: second NHL season. Continuing to de-risk himself, but still in that first window of discount rates. n=2.
P = 80/((1+40%)^2)
P = 41 points
He scored 37. Not bad!
2008: third NHL season, so the discount rate is down to 30%. n=1
P = 80/((1+30%)^1)
P = 62 points
He scored 53.
Seems like this is a decent guide... not going to hit it bang-on, but it gives you a decent way to evaluate future worth.
A few more examples? Yes please!
Evander Kane: drafted in 2009. I always liked his upside to be 90+, but let's use 80 for a 4th year breakout. NHL ETA, I figured a year more in junior, then 4 NHL seasons to break out. That gets us to 2014, so n=5.
2009: P = 11
2010: cracked the NHL immediately, which drops n to 3. Becoming a 1st year NHLer drops the discount rate to 40%. P = 24 points. Kane's production? 26.
2011: n = 2, rate = 40%. P = 41 points. Kane produced 43.
2012: n = 1, rate = 30% (3rd year player). P = 62 points. Kane produced 57.
Hmmm, this I like! His value is increasing from year-to-year as he reduces the risk. That makes sense... he's becoming a less risky investment, so his value goes up. Intuitively jives.
So far we've only looked at players that have made it though... what about guys who are busting? I guess you'd adjust the F values to get something more realistic as the info gets more realistic. I'm kinda running out of steam though, so I'm not doing it.
Next time I get a trade offer for a 2nd year player who is perceived to have an 80-point upside, I'm gonna go:
P = F / ((1+i)^n)
F = 80
i = 40%
n = 2
... and not pay more than fair value, a 41-point player.
If it's a 3rd year player with an 80-point upside, I'd cough up a 62-point player.
For a 3rd year player with a 100-point upside, like say, oh, I dunno... John Tavares? I'd cough up a proven 77 point player. Maybe because he was a first overall pick, you pick a discount rate lower than 30%? I'd buy that. During last season (ie his 3rd year), I'd have been comfortable with dishing a proven 83 point player. Yup, that jives.
This might be complete bunk, but I'm gonna play with it for a while. Seems promising! It certainly holds together with the idea that production today is worth more than production 2 years from now... and certainly reinforces my long-held belief that people waaaay overvalue future production. Enough with winning 4 years from now!
Ahhh, good ol' confirmation bias.
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Last edited by wendelclark17; 05-25-2012 at 12:09 PM.
I love looking at this kind of stuff...
I could only imagine doing this for a full roto league!!
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I wish it were that easy, wendel... maybe we could develop a value-of-future-production tool, but it would be greasy.
It's an interesting take, for sure.
Very interesting. Its been a while since I've taken a math class but I'm pretty sure I follow what you were doing.
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LW: Kovy(RW), Moulson, Kunitz, _
RW: Eriksson(LW), Clarkson, _, _
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And this folks, is why HPG is pretty easily, considered the best number cruncher on this site. Great stuff, Geek.
ps. Out of curiosity HPG, is your career in the field of mathematics?
Kind words, Rylant - thanks. There are many on these boards who think and crunch like I do.
Ironically, I was always a flop at math, at least in the academic sense. I am an engineer, so it's not about conceptual purity but rather just getting close enough! I'm not doing any technical work anymore, though.
After sleeping on this, I see a whole lot of merit in the concept, but the implementation I slapped together yesterday was a bit rough. The present value calculation I used wasn't considering the production in the years leading up to the 4th year breakout, just the value of the 4th year breakout itself. That doesn't really make that much sense.
To really consider this fairly, we need to look at a Net Present Value calculation of the future years of production with the variable discount rates.
Basically, the NPV is the sum of all the future values, each discounted according to the risk the prospect holds at each stage of production.
NPV = F(year 1) + F(year 2) + F(year 3) + F (year 4) +... etc
So to bring this full circle, let's compare a theoretical prospect that we see as having 90-point upside with an established low-risk veteran who can knock of 60 points each year with relative certainty. We'll consider the prospect to be expected to make the NHL in the year following his draft, and have a "star" growth curve of 50, 60, 75, 90 points over 4 years, then holds that production for 2 years afterwards, so we're comparing a 6-year range.
Using the same assumptions about discount rate as in the previous example, and using 10% for the low-risk veteran, the comparison would look like this before that prospect has played a single NHL game:
NPV (prospect) = 50/((1+50%)^1) + 60/((1+50%)^2) + 75/(1+50%)^3 + 90/(1+50%)^4 + 90/((1+50%)^5 + 90/((1+50%)^6 = 33 + 27 + 22 + 18 + 12 + 8 = 120
NPV (veteran) = 60/((1+10%)^1 + 60/((1+10%)^2 + 60/((1+10%)^3 + 60/((1+10%)^4 + 60/((1+10%)^5 + 60/((1+10%)^6 = 55 + 50 + 45 + 41 + 37 + 34 = 261
That makes sense... before the prospect has played a game, there is still a lot of risk that the projection won't happen. The 60-point vet is lower risk.
After the prospect's 1st NHL season, his discount rate drops to 40% and it looks like this:
NPV (prospect) = 43 + 38 + 33 + 23 + 17 = 154
NPV (vet) = 55 + 50 + 45 + 41 + 37 = 227
Still better off with the 60-point vet. After the 2nd season, the prospect's discount rate drops after he has demonstrated that he can do it, thus de-risking himself as an investment, and it looks like this:
NPV (prospect): 58 + 53 + 41 + 32 = 183
NPV (vet): 55 + 50 + 45 + 41 = 190
The vet still has more value, which intuitively makes sense since the prospect's "good" production still lies a distance in the future. It's close though.
After the 3rd season, the prospect has shown that he can hang in the NHL and that his production is steadily increasing. I'd expect that this is the flex point where his true value is higher since he's "about to break out":
NPV (prospect): 69 + 53 + 41 = 163
NPV (vet): 55 + 50 + 45 = 150
Oh man, this hangs together very well. An established methodology that's used in another industry, ported to fantasy hockey in such a way that it jives with conventional wisdom:
Obviously this analysis assumes that the prospect will occupy a roster spot the whole way along. If you have a farm team that could "stash" them away, it would be reasonable to use the production of the other player that would sit on your roster in the place of the prospect in the NPV calc until the time when the prospect bumps the other player.
Interesting formulation - has me thinking about variable discounts based on: league peripherals beyond points where that applies, environmental factors e.g. prospect belongs to Detroit vs Minn (developmental opportunity) or strength of linemates, proportional games played in a season, etc.
I am neither an economist nor a math guy, but isn't what you are trying to do here is create a method to get a handle on opportunity cost? If that is so, I wonder if environment of the fantasy hockey team being considered isn't very critical in the equation.
Anyway, as always, got me thinking, HPG.
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