In my previous post on 15 tenets of sabermetrics, my response to one tenet received the bulk of the comments. I showed that the talent of the league is distributed normally, and the assumption that there is an abundance of similarly-skilled players on the margin of the majors—the underlying assumption of replacement—is wrong. Replacement-level metrics themselves do just fine at measuring player skill relative to one another, it’s the implication of that these metrics tell us something about the objective value of players that bothers me.
I’ve written quite a bit about my dislike of replacement level over the years. You can see posts that I have written on the subject here, here, and here. But, I thought I’d briefly summarize my reasons for rejecting replacement-level theory in a single post.
— If there was an abundance of talent at the bottom of the league, then the frequency of poor play on the inferior side of the talent distribution should be evident. But as the distributions below indicate, the distribution of talent is bell-shaped.
(UPDATE: Some people don’t like the 100 PA/BFP cutoff, so I’ve replaced the histograms with 30 PA/BFP cutoffs. As I’ve said, it doesn’t make much difference. These distributions have the basic bell-shape, but are negatively skewed, not positively skewed as would be expected if there was an abundance of near-equal talent around replacement level.)
There is no grouping of poor talent on the edge of the league, which means that when seeking replacement who are not in the league, teams must select from a scarce talent pool where some players are better than others. This means there will be price differences between players, with teams willing to pay more for better players and less for worse players according to their marginal revenue products. Now, this doesn’t mean that inferior players don’t serve as competition for superior players, by offering their inferior services for a lower price, but they are not simply worth the league minimum.
— Even if there was an abundance of talent in this range, it is not freely available. Talent outside of 25-men major-league rosters is not a collection of free agents. Each team has a farm system with five or six minor-league clubs, full of players whose playing rights are owned by other clubs. That means that the next-best few thousand non-major-leaguers are off limits for clubs to choose from freely.
So, let’s say a bench player goes down and the team needs a replacement to serve in his place, the team has a few options. It can bring up the most-talented player in its minor-league system that can play the vacated position. This player will be paid a pro-rated share the league minimum while he is in the league. The value of having that player on the roster will be equivalent to his marginal revenue product, which is almost certainly worth more than the league minimum. But just playing the player isn’t free, because there is an opportunity cost to playing him. If it starts his major-league service-time clock prematurely, the team will lose future value from the player. If another team was also seeking a similar player—and given the scarcity of talent, there almost always is—the team forgoes the value it could get from selling his surplus vale (MRP – wage) to another team. And if you want to acquire a player from another minor-league roster, you have to pay the team for the opportunity cost of a player.
— The next step is to put a dollar-value on players based on their contribution beyond replacement level. (I should also add that the linear dollar-per-win estimates often used are biased by estimating a non-linear function with a linear estimator and neglecting to include a y-intercept in the estimate.) If we assume that replacement-level players are worth only league minimum, then players who play worse than replacement level are costing their teams money, because supposedly there is a superior player available for the league minimum. Sounds good in theory, but in practice, about 1/3 of the league—eight players per team—are identified as below replacement-level by the popular sabermetric website Fangraphs.
And this isn’t just some random error involved here: 16% of players cost their teams $1 million or more in 2009. This assumes quite a bit of ignorance on the part of general managers, which is doubly problematic because when free-agent salaries are used to measure the value of players, there is an implicit assumption made that GMs are making rational decisions. Paying $4 million per team for below-replacement players (16% * 25-man roster = 4 players; 4 players * $1 million = $4 million) that should be available for under $1 million is irrational.
Of course, we could respond by saying that replacement-level is being set too low. But, why bother saving a metric that has too many other problems.
— Replacement-level terminology is unnecessarily complicated. If the sabermetric community wants to continue spreading influence beyond its small sphere of influence it can express all its important concepts in terms familiar to all baseball fans. When I played little league, we talked about on-base percentage and slugging percentage. It’s easy to explain DIPS through discussing strikeouts, walks, and homers (“see, the pitcher does these things all on his own, without fielding help”). But replacement level, why not just bring up quantum physics? This is baseball, it’s supposed to be fun. Replacement-level language is complicated and it adds no useful additional information to concepts that can be expressed more simply, especially in reference to league average. Replacement-level terminology should be rejected for parsimony alone. As I previously stated,
I read a lot of dumb things by established baseball writers who deserve to be called out. But when you start inundating people who have lived and breathed baseball for much of there lives—no less than active sabermetricians—with new acronyms that are not in their lexicon, don’t be surprised when they are confused. And getting snooty about it doesn’t help. Baseball already has a language, and there is nothing too complex in sabermetics that cannot be explained through terms and statistics understood by little-leaguers.