December 8, 1997

How much should a player be worth? How can one assess whether the listed price is relatively cheap or expensive?

At first blush, the answers might seem trivial. Obviously, players that produce more Smallworld Points (SWP's) should be worth more money. But how much more? Should a player with 400 SWP's to-date be worth double the value of a player with only 200 SWP's?

Let's look at some live data, using prices as updated on December 8, along with stats accumulated through 12/7. Rather than using year-to-date SWP's as a pricing benchmark, I prefer to use average SWP's per game. This avoids biases in cumulative points resulting from differences in the number of games played, whether they are due to scheduling or injuries. Since price should only reflect expectations of future value, past differences in games played shouldn't be critical price determinants.

They say a picture is worth a thousand words, so let me take advantage of the following graph to illustrate some relationships. The "dots" on the graph represent a plot of price vs. SWP's per game for the 293 players who had played at least 10 games as of December 7^th. SWP's per game are plotted on the vertical axis, and price is plotted on the horizontal axis. The red line which runs through the cluster of points represents the best fit for all of this data. You might think of this as representing the average of all points. (For a more detailed explanation of this graph, click here.)

Several observations:
1. As expected, there is a distinct relationship between price and performance. Big deal.
2. The dispersion of prices around the average is much greater for low performers than it is for the high performers.
3. The "best fit" line is not perfectly straight. It is somewhat "negatively convex" (that is, it curves down as values rise).
4. In general, you could say that players whose dots are on the left side of the "best fit" line are cheap, while those on the right side are expensive - all other things being equal (which of course, they aren't.)

There are a number of likely explanations for this price dispersion. First, for some players, historical performance may not reflect the market's best estimate of future performance. (This is especially true early in the year, when a few abnormal games - good or bad - can distort an average. Second, players who are currently injured, or who are more likely to be injured, will have depressed prices. And undoubtedly, some of this dispersion is due to market inefficiency. Some player are simply priced too low, and others too high.

The "non-linearity" of the relationship (that is, the downward curve) is probably best explained by supply and demand. There just aren't that many players who will average upwards of 35-40 SWP per game, so managers who are wealthy enough to be able to afford those "premium" players have a limited selection to pick from. In addition, those players tend to be more recognizable - like Karl Malone, David Robinson, Shaq - which probably means they are "in demand" than are the lesser known players.

When I evaluate relative pricing, I focus on buying the players along the left edge of the cluster. If I select the 100 "cheapest" players and plot a best fit line for just those points, I get the green line (superimposed on the original graph).

Players represented by dots in the vicinity of this green line offer the best SWP value for the money. You might think of them as being efficiently priced, or as lying on the "efficient frontier". Not surprisingly, if you look at the rosters of the Smallworld Hoops worldwide leaders, you'll find them chock full of players priced near this efficient frontier.

Notice that the green line is a bit less sloped and a bit more curved than the red line. This has very important implications, especially if you haven't amassed enough wealth to buy all of the high performance players. (If you do have that much money, then just buy them, and relax.) You can generally get more "bang for your buck" by buying efficient players in the mid-priced range than by buying some premium players (like David Robinson) along with some "dirt cheap" players (like Jacque Vaughn). That concept produces some very interesting situational opportunities - which I'll save until the next Hoop Pointers to explore.

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Hoop Pointers is written by Dave Hall (a.k.a. the Guru), an avid fantasy sports player. He is not an employee of any of the fantasy games discussed within this site, and any opinions expressed are solely his own. Questions or comments are welcome, and should be emailed to Guru<davehall@home.com>.