FAAB Budgets and the Discount Factor

The following comes from my latest article for The Hardball Times.

Every year, big names fall on the waiver wire. Be it a prospect call-up, a frustrated owner prematurely cutting ties (e.g., what I did with Madison Bumgarner this year), a move of desperation in light of shallow benches and deep injuries (e.g., the "perfect storm" league where I own Hanley Ramirez, Joe Mauer, David Wright, Pablo Sandoval, Jason Heyward, Ike Davis, Brandon Beachy, Josh Johnson and former DL pains Brian Matusz and Geovany Soto, or some other occurrence, an economic game of how much to spend on whom and when inevitably results.

So how much do you spend on Eric Hosmer, an early elite prospect call-up? Or Jerry Sands, a supposed impact player of a less-elite level? Or what do you do if Anthony Rizzo and Mike Moustakas are both sitting on waivers after their call-ups last week (some leagues play where you cannot own or bid on a player until they have one game under their belt)? Do you wait for Brett Lawrie and Dustin Ackley?

The answer is never a clear one, and I cannot give you a simple answer. FAAB bid recommendations are a lot like snowflakes. Value is infinitely complex and unique, and it depends on the size of the league (12 teams? Five outfielders?), the format of the league (mixed? AL-only?), the depth of benches and DL spots, and your team's current standing in your league.

What I can tell you, however, is that the timing of the FAAB bid makes a major impact on the expected return of the player, and that timing is rarely considered a factor.

One of the more distinct concepts I can still recall from my days as an undergrad studying economics is the discount factor. Put simply, a discount factor, often an interest rate, accounts for the difference between present and future value. A dollar now is never (okay, maybe almost never, as deflation/stagflation does exist sometimes) worth a dollar in the future.

Let's say, for example, the bank pays five percent interest on your CD account, and that you can open a CD account with any balance. If you begin in year N with X amount of money, and you put that money in the beginning of year N into that CD account, it will grow in value to X*1.05 dollars. In other words, the future value of X is 1.05X.

Conversely, we can evaluate the value of future money now by looking at the same interest rate. Instead, suppose that you will have Y dollar in the future, say because of an impending lawsuit settlement. You cannot have the money from the source now, but will have to wait one year.

If you want to figure out either how much money you would need now to attain Y in one year by putting said money into the CD account noted above (or alternatively how much you should sell the rights to collect on your settlement for), you just need to do the math from above in reverse. If present value (P) times interest rate (R, here five percent) equals future value (again, Y), then Y = 1.05P, or the present value is Y/1.05.

As you will notice, with the denominator being larger than one, present value is lower than the future value. That may seem simple enough, but it is a powerful thing to note that is often ignored in trading and FAAB budgets.

It is to say, alternatively, that a transaction worth Z today is more valuable than a transaction worth Z in the future; that trading for Prince Fielder today is more valuable than doing so in two weeks, and that bidding on Hosmer now is better than bidding the same amount on Anthony Rizzo in the future, even if you think both players are equally valued.

So what does this all mean? It means that shelling out FAAB money on Hosmer in the beginning of May is more valuable than shelling out a similar sum on Rizzo in the beginning of June. The season is only 162 games long, and every day you wait, your opportunity cost is approximately 0.6 percent of potential value.

This 0.6 percent figure could and should be thought of as a discount rate applied to a player's expected production in evaluating FAAB money. It means that a worse player today could be worth more than, or equal value to, a better player who will not be on waivers until some period in the future.

Let's use Rizzo and Hosmer as an example in comparative bidding, and begin by assuming that the two are roughly equal in rate value (production per game). Both are highly-touted, power-hitting prospects that play in offense-suppressing parks with comparable-enough 2010-2011 minor league numbers.

Hosmer was called up about 35 days earlier than Rizzo. If each player, over a comparable sample of plate appearances, is roughly equal to X dollars of production, Rizzo's late call-up induces a penalty value of -15.4 percent. In other words, if you think Rizzo is worth a FAAB bid of X, then your bid on Hosmer should be approximately 15 percent larger than what you would bid on Rizzo.

As the expected waiver pool thins, there is also a scarcity premium that should be considered. Imagine that by the All-Star Break, all of Domonic Brown, Hosmer, Rizzo, Moustakas, Ackley, and Desmond Jennings have been called up.

That could leave Lawrie as the lone "impact" hitting prospect of great consideration that you can count on to be on the big league roster getting a healthy series of playing time. If Lawrie is worth X to you at his call up time, then you better bet more than X, particularly if it is a hard-to-fill position like second, shortstop or third.

This might all seem simple in form, but timing truly is an overlooked value concept in fantasy baseball, where we preach patience.

On one hand, we say "ride out his slump" and caution blowing all your FAAB budget on the first day of the season to acquire a huge prospect like Heyward or Michael Pineda. On the other hand, as noted above, every day you wait is another day the impact of the move you seek to make loses some gravity of impact.

A lot of owners bid conservatively on Hosmer in my leagues, whom I won on every FAAB bet I could place for under $70, because, as they relayed to me, why overbid now when there are comparably valuable players looming out there, some who play premium positions, such as Rizzo, Moustakas, Lawrie, and Ackley (who, in my eyes, is just Kelly Johnson with less power and a bit more batting average). "Why throw away $70 on Hosmer when I know I can probably win Rizzo for less?" one owner relayed to me.

The answer is all of the things I have said above. With Hosmer off the board, there is one less prospective impact player on the waiver wire. You also get Hosmer, even if inferior to Rizzo, a whole month earlier. Particularly if you were employing Luke Scott or Ike Davis at first entering May, having Hosmer today over Rizzo in the future could mean the difference between a league title and another disappointing finish.