There's a discussion that piques my interest going on over at The Book Blog involving the economics of fantasy valuation. I haven't chimed in at this point, but it's certainly a problem I've also thought about when doing my fantasy valuations. I talked to my adviser about this yesterday at the bar and convinced him that this is an interesting and worthwhile topic, but fantasy sports--once the forecast is made--is simply a linear programming problem. The one who spends the most time solving that optimization problem usually wins. But, of course, the question is: what is the answer? And I think the answer in the context of fantasy is: it depends.
There's plenty of game theory that goes on. Depending on who you play with, there's a good chance that each of the other owners' behavior needs to be an input in the optimization problem. Because you don't know what others will do, in theory you should be bidding your valuation (assuming a second price blind auction). In an English auction it's a little different (the standard fantasy auction), as you get information about other owners during the process. But passing up buying someone now is not independent of what happens later on. And that's where the difficulty comes in with solving the problem.
Assuming everyone has exactly the same valuations, there is still room for zigging and zagging. Ultimately, if everyone pays exactly what the same price guide says each player is worth, then in the end the winner of the league simply results from luck. Essentially, if you really want to win fantasy and win some money, you should prey on fans of specific players who take them for the sake of this, those who think they just have a 'knack' for knowing what is going to happen, etc.
The institution of a keeper league, minor leaguers, contracts, etc. simply make this optimization problem more complex and more difficult to solve and adds to the variability, given the need for long-term risk assessment (or, forecasting). At this point, if everyone simply uses some variant of the z-score method with replacement at $1, then it doesn't matter much what the exact answer to the problem is unless you only know it yourself. Otherwise, the equilibrium just shifts to that method, and everyone does the same thing. What we do know (or at least from my experience) is that at this point, the z-score method seems sufficient in roto leagues to win. But that's because the majority of people use it. I haven't seen any place give drastically different valuations for the same projections (in fact, they're all almost exactly the same...except for ESPN with their insane premium for stolen bases).
I suspect there is someone who knows something close the answer to the optimization problem with the game theory and psychological aspect included: Eriq Gardner at Fantasy Ball Junkie and Bloomberg Sports. I only say this because playing with him in our 20-team, H2H, 8x8 league for a few years, he won the league in the first 3 straight, and came in 2nd this last year. An incredible feat, considering this is a keeper league and others recharged their keepers each year, and H2H in the playoffs can be extremely variable. Perhaps me and my buddies in the league just aren't very good, but it's certainly the most competitive league I've played in. I'll likely join another league with Eriq this year, so we'll see if I really know my stuff this time around.
One thing I have learned from Eriq is that the best way around a complex linear optimization is to find gaps in insufficient rule structures. Always look for inefficiencies that are based on the rules. If you can do this, you'll probably increase your chances of winning anywhere from 50% to 100% of what they were to begin with (and possibly much more). This is the best way to get close to the optimal answer to the problem. Standard leagues are well-known, so this is more difficult. However, I think the discussion at Tango's blog gets to the extreme inefficiency I saw in valuations this past year: Starting Pitching. While not discussed directly, the sums spent on the likes of Tim Lincecum and other established starters put a lot of people in a hole to begin their auctions. I discussed this a lot this past fantasy season, putting together a staff of:
ALL for the price that Lincecum went for in that same league. So, I guess my answer to the question is: look for loopholes. Solving the question of the perfect fantasy roster using z-scores may not give you a look into this. My own adjusted z-score method did some of this. Other places tend to use some sort of exponent for the top level players, then do the valuations. I think that in a lot of cases this is incorrect. This can be very true for relievers as well, as their ERA and WHIP help in daily lineups is invaluable for how amazingly cheap they go.
One last addition as to why the z-score method can falter: it is not dynamic. Remember that in a rank-based Roto system, you have diminishing returns to adding to a category. If you already have 320HR on your team, then Adam Dunn isn't worth as much as he would be if you have 100 HR. Same goes for every category. This is the theory behind my simulations for H2H roto league over at FBJ (and cross-posted here). My hope is to still come up with full valuations based on that method if I have the time to do so.
Here's the link. I'm also interested to hear what people say: