Hit Rate Observer

This column is about an idea that didn’t pan out.

The imminent debut of THTF’s “Trading Post” column got me thinking. We talk a lot about a player’s “value.” And we do our best to put a dollar figure on that value, both in generating the underlying stats and in setting players against their brethren.

That’s a very artificial process, though, even apart from the vagaries of projecting human beings. One monkey wrench is the value of replacement players. We can make a good guess of replacement value from looking at recent history, but if there’s an unusually high or low number of productive call-ups, our baselines are junked. We’re also seeing early shifts in value this season from the lively baseball and from the Yankees’ new park; temporary, possibly, but unforeseen all the same.

Any property tied to reality will fluctuate unpredictably. In the real world, most investments don’t have a price that’s fixed from above. At heart, a good is worth only what someone is willing to pay for it. (This notion will be familiar to anyone trying to sell a house.)

For the “truest” player prices, then, rather than imposing a value on a player, we would deduce the player’s value by looking at the sorts of things he was exchanged for. This method would be both more elegant and more accurate. And we could generate updated values whenever we felt like it, at any point in the season.

If only we had a market for fantasy players… if only….

But, of course, we do have fantasy markets. Most online leagues permit trades between owners. And many of those leagues advertise recent trades for the player. For example, I can head to CBSSportsline right now and get a list of deals involving Jayson Werth.

There are a lot of names there. Mathematically speaking, though, a trade is just an equality: The sum of the things on the left equals the sum of the things on the right. So the idea was to record many, many of these trades. What we would end up with is a (big) set of simultaneous equations, in which each player represents a different variable. If Alfredo Amezaga, Burke Badenhop, and Chris Carter were represented by A, B, and C, then a trade of Amezaga for Badenhop would be A=B, and a trade of both for Carter would be A +B=C.

If you have many more equations than you do variables, you can run a solver to pin a value on each player that best fits the observed trades. Voila! Instant player valuation.

Sounds cool in theory. Unfortunately, reality didn’t cooperate. The main problem is that the bulk of fantasy trades are of equal numbers of players. This is a problem because, if every trade is of the form A+B=C+D, then the simplest solution is:

(1) All players have the same value; and
(2) That value is 0.

This constraint is a consequence of the structure of fantasy, where every owner must field a team of the same number and types of players and purchased for the same sum. It’s like a stock market where everybody has to be in for exactly $10,000.

One way to make trading more flexible is to allow teams to accumulate differing numbers of players. If one team wants to trade a mega-star for three B-level prospects, why must they jettison two other guys? Go on, let somebody corner the market on Double-A third basemen.

Also, in most other markets, you don’t have to buy a good with the same kind of good—you needn’t pay for a car with a car, or a house with a house. In particular, we use currency. Currency is ultra-flexible—you can dispense it in virtually any fraction.

It would be easier to equate players to dollars if we actually traded players for dollars. Maybe leagues should let owners purchase some, or even all, of a traded player with cash (the same currency, after all, with which they pay entry and transaction fees). Admittedly, this would make fantasy baseball more about trading (where you are always on the make for the good deal) and less about investing (where you’re pretty much saddled with the team that you have). But there’s always a fine line between the two. And a league with more trading could be more competitive.

Perhaps the biggest difficulty with our plan, though, was the enormous variation in needs. Consider these players who have recently been dealt one-on-one for Jayson Werth:

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  • Cristian Guzman
  • Aaron Hill
  • Trevor Hoffman
  • Edwin Jackson
  • Clayton Kershaw
  • Adam LaRoche
  • Geovany Soto
  • Ryan Theriot
  • Jose Valverde
  • Brandon Wood

And this is a list just from non-keeper leagues. Record enough trades, and you’ll probably find an example in which each player was traded for each other player! Forget about solving for X there.

Trying to impose some sense on this madness will be one of the aims of Trading Post. Still, there is a lesson here. Player valuation is a spongy business. It’s only a small stretch to say that no owner actually gets “sticker price” from a player—if you have too little of the resource in question, then the player is more dear to you; if you have too much, he’s less dear. The flip side is that probably every owner in your league has a player who would fit much better in your lineup than theirs.

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Even if you could identify market value it will put you no closer to your goal of building a superior team without knowing the real value of the player in terms of your scoring system.  You must acquire players at market value who have higher real value in order to gain advantage.

Couple of quick things (this probably should have been in a personal email but i can’t find author emails on this site!): 1. The precise type of problem you describe has actually been studied to great length already. I can’t give you a quick solution, but you can find a lot of information on it using Generalized Method of Moments as your reference; if you’d like more details, feel free to email me. 2. The issue you raised about everybody having 0 estimated value is not specific to having trades with equal numbers of players on each side; that will… Read more »
John Burnson
John Burnson
KY, gotowarmissagnes: I agree that average market values are not perfect guideposts (and we’ll end up somewhere else with Trading Post). But saying that their utility is essentially zero may be overstating the case—are NO teams like the “average” team? (That’s something to study.) Market prices are valuable because they reflect the tussle of human beings engaged in the same activity as you. We all play in a market—one small in scope (maybe just 12 people), but very aware of, and influenced by, the wider world. In today’s netlinked world, it’s the rare commodity whose offered price I would not… Read more »

Cool idea! I’ll be looking forward to the follow up.


I think the fundamental problem has nothing to do with replacement value.  It has to do with the fact that players have different values to different teams.  If I lead my league by a ton in HRs and am last in SBs, then a 50 HR/0SB guy may have much less value to my team than a 0 HR/50 SB guy.  Summarizing a player’s value through trades gives you a sense of the average player value, but tells you little to nothing about the value of that player to your team, given its existing make-up.