Risk-adjusted future value - lessons from finance

[Hey Robbie]

Sorry for resurrecting an old thread, as I assume that is not standard under forum etiquette. However I cannot believe I missed this at the time, and find it fascinating and something I've grappled with for the last couple of years. Thanks HPG for drawing the apt financial parallel.

One comment I have is that the modeling described above was revised to take into account total value as accumulated over the years leading up to a potential breakout, but does not account for any value that might accrue blow the maximum potential target. An idea I fiddled with last year was the idea of a potential distribution rather than a single percentage of reaching maximum potential. Imagine in any given year that we can estimate a probability that a given player scores in some range of points; eg a 5% chance of scoring from 41-50, 10% between 51-60, 21% between 61-70, 32% from 71-80, 25% from 81-90, 5% 91-100. This describes a potential distribution which could be used to assess value. While it is fair to use a discount rate of approximately 75% to a prospect of hitting the maximum (realistic) potential of ppg+, this player will still have great value if he misses that mark but does turn into a low 70s player, which is more likely, and some value if he maxes out in the 60s.

Of course the idea of utilizing this information is probably mere theoretical noodling (the province of science guys like your humble author) than a practically applicable method that might be fashioned by an engineer (eg our esteemed OP). But given that we've resigned ourselves to the fact that this is more of an art than a science, perhaps some element could be taken into consideration when assigning discount rates.

Of course if we believe the general shape of the curve is similar for all prospects, the idea may be simple to apply as a general correction factor, and this is probably part of what FHG meant in, "So, we do what engineers do: look for allegories!" But I think we have all pondered that due to some players combination of skill set, situation, style of play, etc., they will likely be a super-elite scorer in the 90+ range or a 60s type player, while others, who maybe don't have the hands or speed to ever hit 90, but have vision, work ethic, and surrounding talent, are a very solid bet to score in the 70s and low 80s for years. Which is the more valuable prospect?

If we believe the above is relevant, and still want to apply some quantitative thinking to the process, I could envision a model based on simulations. At the most basic levels a simple sim could be run, but the interaction between the potential value and performance in the various years would probably served best using some Markov Chain Monte Carlo (MCMC) simulations. Software (including freeware) exists for setting this kind of thing up, and I've used it for genetic analysis, but I can't fathom the work it might take to adapt it to the current exercise.

In the end, it's probably absurd to try to apply such a quantitative approach, given the uncertainties in devising the probabilities in the first place (however that could be approached quantitatively as well by applying Bayesian methods to the past performance of prospects). As Metal Dude has reminded me in previous discussions, "garbage in, garbage out." After that the extent to which we would want to lean on the model's predictions would not be absolute, as Penguin7 has well elucidated with, "Don't get married to the model."

[fantasyhockeygeek]

blah blah blah... years. Thanks HPG for drawing the apt financial parallel.

First off, it's FHG, not HPG! I understand the confusion, but come on it's been more than a year!

I found this a really interesting subject so I'm happy to revisit it, forum etiquette be damned!

One comment I have is that the modeling described above was revised to take into account total value as accumulated over the years leading up to a potential breakout, but does not account for any value that might accrue blow the maximum potential target. An idea I fiddled with last year was the idea of a potential distribution rather than a single percentage of reaching maximum potential. Imagine in any given year that we can estimate a probability that a given player scores in some range of points; eg a 5% chance of scoring from 41-50, 10% between 51-60, 21% between 61-70, 32% from 71-80, 25% from 81-90, 5% 91-100. This describes a potential distribution which could be used to assess value. While it is fair to use a discount rate of approximately 75% to a prospect of hitting the maximum (realistic) potential of ppg+, this player will still have great value if he misses that mark but does turn into a low 70s player, which is more likely, and some value if he maxes out in the 60s.

Of course the idea of utilizing this information is probably mere theoretical noodling (the province of science guys like your humble author) than a practically applicable method that might be fashioned by an engineer (eg our esteemed OP). But given that we've resigned ourselves to the fact that this is more of an art than a science, perhaps some element could be taken into consideration when assigning discount rates.

Of course if we believe the general shape of the curve is similar for all prospects, the idea may be simple to apply as a general correction factor, and this is probably part of what FHG meant in, "So, we do what engineers do: look for allegories!" But I think we have all pondered that due to some players combination of skill set, situation, style of play, etc., they will likely be a super-elite scorer in the 90+ range or a 60s type player, while others, who maybe don't have the hands or speed to ever hit 90, but have vision, work ethic, and surrounding talent, are a very solid bet to score in the 70s and low 80s for years. Which is the more valuable prospect?

I think what you're talking about in terms of probability (Player A is a full 90 point boom or bust... he'll either make it big or flame out vs Player B has an upside of 85 but is pretty much a lock for 70) is just another way of looking at the risk profile or volatility of the future uncertain event. The way to capture that is to play with the discount rate within the ranges they sit based on the perceived risk of achieving it... if you see more production certainty you could assign a lower discount rate.

Another approach could/would be to use "expected" production values, which could be assigned based on a Monte Carlo simulation of probabilistic result distributions of various forms, or more likely just taking an average between the player's low-end and high-end production scenarios -- ie analyzing based on a 3-year-peak figure rather than an upside.

I love me some Monte Carlo, but I think that would be a complete "garbage in, garbage out" approach -- you'd be looking at something more-or-less equivalent to a completely stopped watch: absolutely and perfectly precise for just two fleeting moments in a day.

[Hey Robbie]

Firshttp://forums.dobbersports.com/images/editor/menupop.gift off, it's FHG, not HPG! I understand the confusion, but come on it's been more than a year!

Well, I did get it right farther down in the post, at least. A shooting percentage of 50% would be pretty good in the NHL...

[cappy76]

Funny how I am working on stuff very similar to this in my Econ class right now and was just taking a break from it to come and check some stuff out here and see this thread bumped from last year.

Scary how where I was confused as hell looking at my text book then all of a sudden some things clicked while reading this......

[fungchen3]

What an amazing thread. A true reminder of how brilliant and informative FHG is when it comes to this stuff. Although I am an "anti-stats" guy at heart, I always love digging into threads like this. When it comes to fantasy hockey, I steer my ship with intuition and unconscious reasoning and/or "chunking." I always go with my gut and follow my instincts which has been very beneficial in nabbing talent before it's too late. There are so many outside influences that go into a player's success, I think intuition is a must. Stats are good until one day a team/player gets a new coach and his mojo is stifled. Would Erik Karlsson be a fantasy hockey immortal if he was playing under Ken Hitchcock or Darryl Sutter instead of the Monopoly Man? I think not (although he would still be top-tier). Karlsson has been encouraged to take risks and learn from his mistakes in Ottawa's system - this type of thinking must be factored in when making pivotal decisions about your club. And, of course, the criteria always changes, which makes it constantly tricky. Fantasy hockey is a 24/7 gig for those willing to take the plunge.

[dongjohnson]

I like the idea but the problem is that this is not (and cannot be) a linear calculation because of at least a half dozen external factors in play. You don't know what team a guy will be on 3 or 4 years down the line, how much ice time he will receive, how his game will change, who the coach will be etc. It's more "If X then Y, but if V then Z" with 4 or 5 other factors at play.

I suppose it just goes to show that certainty is the most expensive commodity of all.