If you've ever taken a class in economics, one of the first things you learned about was the difference between accounting costs and economic costs. Accounting costs are the nominal price of object--you can think of this as the sticker price. Economic costs are also known as opportunity costs, and I'll leave it to Harvard economist Greg Mankiw to define the term:

The opportunity cost of an item is what you give up to get that item.

And that must include the value of all the other options that are now precluded. The concept of opportunity cost is at the heart of the sabermetric concept of "replacement level." As important as the concept is, are there aspects of it that need refining? Today's box score looks at the concept of replacement level, as well as the related concepts of average players and player peaks.

Table of Contents

The Waiver Wire
The Shallow End of the Talent Pool
Whence the Talent Comes
The All-Average Team and Player Peaks
Discussion Question of the Day

The Waiver Wire

A replacement level player is defined to be the level of freely available talent at a given position. Whether that talent is acquired via the Rule 5 draft, waivers, free agency, or the minor leagues, it is typically the sort of player who bounces back and forth between Triple-A and the major leagues. Because they are freely available, the reasoning goes, no team should do worse than replacement at any position. Conversely, all players ought to be judged by their contributions above and beyond replacement level. That is to say, the replacement level player represents the opportunity cost of acquiring any other player. In equation form, it looks like this

Benefit - Cost = Surplus

And renaming the terms gives (roughly speaking):

Total production - Replacement level = WAR

But many people (including some smart ones) argue that replacement level misses a crucial aspect of the market for baseball talent: the fact that ballplayers are not perfectly fungible. Here's Christina Kahrl, writing about Alex Rios:

Players aren't freely available in the way that, say, sofas are; one start-worthy sofa's value over a replacement-level sofa can be easily resolved by just going out and buying that quality sofa. (And no, you do not have to wait for Ikea to put it on waivers.) Unlike sofas, there is not a limitless supply of ballplayers, and they're not all freely available at the same time. If, between the trickle of off-season free agents at the position where you have a specific need, your own farm system, and the mish-mash of journeymen sloshing around the minor league free agency pool, there's nothing and nobody that grabs you when it comes to filling that specific need, you might understandably go after the best player at the position available at any price to try and help yourself, and hang the expense.

Put slightly differently by Mike Silva:

Who is the typical average minor leaguer? Anderson Hernandez? Nelson Figueroa? Sergio Mitre? Josh Towers? Fernando Martinez? Shelley Duncan? Do you Get the point?

(Just for fun, their 2009 WARs are 0.2, -0.1, 0.2, n/a, -0.5, n/a, respectively, which suggests to me that perhaps he understands the concept better than he is letting on).

In any event, this is an important criticism. Teams to do not seek upgrades over a theoretical replacement level but rather over whatever it is that they've already got. So, in context, each team has an individual replacement level that represents its opportunity cost for any given transaction.

If we are looking at the value of, say, Alex Rios, we ought to compare his expected production to the expected production of the in-house options, and value the difference in wins at $4.5 million (or whatever the correct number is) per win. Of course, as the time horizon lengthens from a few months to several years, the market for talent does in fact become more fungible and the granularity of the world approaches the efficiency of the model.

(Besides, no market is perfect--I speak from experience in saying that while you don't have to wait for Ikea to put a sofa on waivers, you do have to wait until you've given yourself a few gashes before the thing is completely assembled.)

The Shallow End of the Talent Pool

It is the very nature of replacement level that it depends on the pool of freely available talent. Therefore, it is sensitive to changes in the makeup and quality of the available talent. Recently, Kevin Goldstein has suggested that there is currently a drought in the availability of talent on the left side of the infield (particularly shortstops):

The reasons for the decline are numerous. The loss of athletes to sports like basketball, football, and soccer continues to be an issue, and there's also now a mindset for many teams that tells them that up-the-middle players are better sourced from the international market, specifically Latin America. However, one scouting director noted that there's more of a lack of focus on the position itself when in comes to player development for young players in North America. "Part of the problem is that the kinds of players that play shortstop in college and high school aren't the kind of players that we see as playing there in the big leagues," one scouting director explained. "Often it's not the best athlete as much it's it's the steadiest fielder playing there; we see that all the time, even in college, so often what teams are doing doesn't match what we're looking for."

According to his data, in the period 1965 to 1969, an average of 16.1 shortstops were drafted in the first 100 picks. By the period 2000 to 2009, the number was 10.6. Given that replacement level is a fluid concept, we can infer that the value of shortstops has likely increased as the number drafted has decreased. Of course, this is not surprising--given a fixed demand and a limited supply, the value of a good tends to rise.

However, what is surprising is not that the value of shortstops has risen, but rather that there has not been a related increase in the supply of shortstops. If the price that can be fetched by a shortstop has gone up as teams are willing to pay more, we would expect more high school/amateur baseball players to work hard so they might be able to stick at shortstop. And yet Goldstein's data suggest this has not been happening.

Whence the Talent Comes

I have made no secret of my dislike of the current draft structure. That's why my attention was piqued when I saw this post by the Kansas City Star's Sam Mellinger:

Baseball’s CBA is scheduled to end after the 2011 season. Many baseball insiders on both sides of the negotiation say the players are willing to institute some sort of slotting system for draft picks, but need to get something back from owners in return.

He argues that any changes will be the direct result of the strength of the MLBPA, and the MLBPA is the most successful labor union in the history of the United States. Craig Calcaterra thinks this could result in hard-slotting:

It won't take much in return, I'd wager.  Most people don't realize this, but draftees aren't union members -- you don't become eligible to join the union until you're on a 40-man roster -- yet the members have the power to negotiate the terms of the draft.  As such, giving the owners a hard slotting system doesn't truly take anything off the union's plate.

It is difficult to say what consequences this might have on the quality of the talent pool. On the one hand, lowered upfront compensation might deter some players from choosing to play baseball (perhaps choosing football or basketball instead). On the other hand, hard-slotting might rationalize the talent market, ensuring dollars went to players who actually contributed wins a major league level, which in turn might guarantee greater fungibility.

The All-Average Team and Player Peaks

One compounding issue in assessing the quality of the talent pool as a whole is the related concept of a league average player. The easiest way for sabermetricians to calculate replacement level is in reference to the average production at each position. How do we know what average production looks like? Why, we ask wezen-ball.com, of course!

I broke every player into their primary position (ie, the position that they played the most that season) and found the average across each position.

I won't spoil the surprise too much by listing the whole team, but I can't resist sharing with you that the most average season EVER by a second baseman was turned in by Tony Bernazard, in 1985. Honestly, I might be afraid to challenge him for that honor.

One thing to keep in mind is that average production is very valuable. By definition, average value must be at least equal to replacement level. That means sustained but average production is worth keeping around. But not all players contribute this way--some burn fast and bright. The difference, writes Lincoln Mitchell, is the difference between Eddie Murray and Willie McCovey:

The practical question this raises is which is more valuable.  The question, while somewhat abstract, because career paths cannot be predicted with great certainty, is still important when thinking about building teams, particularly when making decisions about free agents.  

If it were possible to predict which types of players would have more stable peaks, I think all other things being equal, teams would be wise to choose the most stable. That way, they are better able to gauge how much talent they need to be a playoff-bound team.

Discussion Question of the Day

For a little fun, I'd like to point your attention to this North County Times article about one of the greatest fights baseball has ever seen. It includes a Tony Gwynn bodyslam and a DL player suiting up just to participate. 

For discussion, though, I'd like to get your opinions about replacement level. It is certainly a useful concept, and provides a common baseline for analysis. However, it also clearly has limitations. So, then, when is the concept of replacement level most useful? Least useful?

What do you think?