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. :D
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.