Introduction
It seems like such a logical, straightforward argument. For decades, people interested in the rating and ranking of Major League Baseball players have been adjusting their findings to account for the offensive deficiencies of certain positions (Catchers, Shortstops, Second Basemen, and to a lesser extent, Center Fielders). In fact, as sabermetricians began developing comprehensive tools to rate the players, one of the first things they did was use position specific averages and performance margins as the basis for comparison with each individual player. Value Over Replacement Player (VORP), Runs Created Above Position (RCAP) and position-relative OPS+ have been buzzing around the internet and widely accepted as a good way to see which players were truly great. Top ten and fifty lists everywhere are loaded with catchers, shortstops, and even third basemen who wouldn't be there according to their providers if it weren't for the position they played.
Here, in a nutshell, is why so many folks believe in positional adjustment for offensive statistics. Think of it from the perspective of a general manager. When building a team you are charged with finding enough offense between the nine line-up spots to win ballgames. If you have a shortstop or second baseman who is producing runs at a much higher rate than you generally expect from that position, then you don't need to spend as much on offense from one or two of the "non-skill" positions (1B, DH, LF and RF are commonly thought of as non-skill positions because a team can usually get away with a sub-par defensive player at one or more of those positions without crippling its ability to prevent runs), and you can concentrate on finding value on defense, in your pitching staff, and maybe at other skill positions. Put another way, the question was put to me once, would I as a general manager ever trade an average defensive shortstop who hit like an average first baseman for an average hitting first baseman who was a great fielder?
To answer that question, and to get at the heart of the larger question of whether we should be accounting for position when evaluating a player's offense, we need to understand what makes players good fielders at their respective positions, how scouts and coaches guide players to the position where they end up when they get to the majors, and how it all relates to the real-world choices general managers must make when they go about building a team. We'll start this exploration by examining some well known shortstops who embody the different archetypes we've come to know at that position. Then we'll take a look at what makes them successful at the position and why they ended up there as opposed to somewhere else on the diamond. Before we do that, I want to take a moment to explain some of the terminology I'll be using in laying out the statistical evidence I intend to provide in this article so that we don't have to spend too much time on the sabermetrics and can focus on good solid seat-of-the-pants logic. The second article will cover the question in detail, but let's dive into the theory a little more.
PCA Defensive Analysis
I don't want to get too hung up on explaining the intricacies of fielding analysis with Pythagorean Comparative Analysis (PCA), because this is a subject that is best discussed from the point of view of a talent scout. However, because traditional fielding statistics don't really properly see the ins and outs of fielding skill, obscured behind too many variables, and I don't have the in depth tools scouts have had when analyzing some of these players, when I go to lay out some of the evidence that supports my claims, I'll need to rely on a compromise. PCA is similar to Bill James' Win Shares in that the value of individual players follows from the value of the tam as a whole. A number of very different choices were made in the formulation of my methodology, but for now, the important thing to remember about the system is that in order to rate individual hitters, pitchers, and fielders, we need to know something about how successful the team was overall. James uses a slightly different currency than I do to describe value. His Win Shares are each worth 1/3 of a win whereas I describe performance in terms of wins (directly), so while a 12 WS score represents 4 wins contributed to the team, if you see a 12 presented by me here, that's twelve wins.
It's important to remember as well that PCA wins shouldn't necessarily be compared directly with Win Shares (even if you divide win shares in thirds). This is because James chooses a more conservative margin of performance than I do. The margin in sabermetrics is defined as the lowest threshold of productivity that carries any significance in the creation of wins. Without knowing it, James selected a margin that is the equivalent of making the claim that a player, defensive unit or team offense would win no major league baseball games without producing at minimally a .200 W% clip. This is because James defines the margin as one half the league average production rate, and since winning is pretty well predicted by the Pythagorean theorem, we can infer from the formula that:
Marginal W% = Run Scoring Margin ^ 2 / (Run Scoring Margin ^ 2 + Average Runs ^ 2)
But we know that the run scoring margin is always half of the average runs so when you square the terms, you end up with a ratio of 1/5 or a .200 W%. Using the Pythagorean Theorem as the basis of PCA marginal analysis, I was able to determine that, at the team level, the margin actually had to be .250, not .200, and the result is significantly more aggressively extreme ratings. By this I mean that ratings tended to be pulled more toward higher and lower values. An average player scores as being less valuable by PCA than he does by WS, sub-zero PCA Wins Created are more common, and great players end up being worth more in the PCA framework.
When I present data in the second portion of this article, I'll present wins created alongside averages (based on the player's playing time) so it is clear what those wins represent.
Now...I need to give an editorial note here. PCA is not being presented here under any illusion that it is perfect or that the ratings should be trusted as though they were gospel truth. I'm actually in the process of creating a more complete version of PCA that will (I believe) represent a significant step forward in terms of accuracy and reliability of the ratings, but until that time, I am satisfied that, on the whole, the system is "close enough for government work" and can be used to illustrate my main points at least loosely. Since I'm not giving the reader every single detail about how the system works, I don't expect you to take the ratings I provide too literally, but I do believe they serve as useful guidelines, particularly when I look at the total results and see a lot of conclusions in the data that make sense.
For more information on PCA, contact the author at the e-mail address provided at bottom of this article. Let's list here some of the PCA acronyms you'll see below and explain what they mean.
-
OWC -> Offensive Wins Created
-
XOWC -> Expected Offensive Wins Created (The offensive wins an average player would create in the plate appearances occupied by the player in question)
-
PA -> Plate Appearances
-
ADWC -> Defensive Wins Created (Adjusted to account for the era in which they occurred...certain time periods were more favorable for infielders, and others were more favorable for outfielders due to the normal distribution of balls in play...I correct for these differences in positional scoring rates)
-
XDWC -> Expected Defensive Wins Created (The Defensive wins an average fielder would create in the PRG occupied by the player in question)
-
PRG -> PCA Real Games (A measure of the amount of actual playing time each fielder had, determined by calculating the number of plays made by the player's position on his team, and the plays made by the player, finding the ratio and multiplying that ratio by the games played by the team)
The PCA Greatness Index
One last bit of statistical ground to cover before the analysis begins. Sabermetricians have spent years attempting to define the term "greatness" and everyone has their own ideas. Bill James, for instance, uses a six-category system that includes career win shares, average win shares per season, win shares scored in three top seasons, win shares scored in a consecutive range of seasons, best individual effort, and a subjective component designed to account for the player's qualities as a leader, manager, or - in the negative -clubhouse cancer. I've seen folks propose any number of ideas on how to capture greatness in a quick numerical methodology, but there a few qualities that everyone agrees are part of what makes a player great.
-
Longevity - It's hard to be great if you don't stay on the field long enough to earn value and become a long term solution for the franchises that own you. Pretty much everyone agrees that the real value of longevity is measured by career wins created (or runs created or whatever you choose to use to account for a player's contribution).
-
Efficiency - Rarely do I hear anyone actually describe this quality using the word efficiency, but most everyone I've spoken with seems to agree that there is value in scoring wins more rapidly than normal (per playing time increment), because not only do you benefit from more production while the player is in his prime, but he gets out of the way and you have the chance to replace him (he doesn't waste a lot of PA or Games Played not producing and thus lowering his career scoring rates).
-
Peak Dominance - Everyone has a different way to explain what they mean here, but the idea is that a player who is truly dominant in his prime is more likely to contribute significantly to a championship and makes a bigger difference between a winner and a loser.
Some ascribe other qualities, like consistency, public image and leadership skills. It's certainly up for debate how best to consider non-quantifiable elements involving a player's character, and it's important to know that I don't argue against considering such qualities, but a numerical analysis cannot claim to incorporate such things truthfully so I tend to leave such things to individual opinion of the readers. However, I want to briefly address the question of consistency.
The argument for the need to consider year to year stability goes something like this. If a player's peak is interrupted by bad seasons, his team is forced to field a weaker player (him) than they might otherwise if they could predict when he was going to decline and make the necessary moves to replace him. Add to that the fact that if a player has a down year, he might scare his team into committing draft picks, trades, or finances toward finding his replacement only to have him come back and make those commitments a waste, and you wonder whether there is significant value in being consistently productive.
There's a major problem with this logic, however. All players are inconsistent. It's exceedingly rare to find a player who is as bankable as A-Rod (and even he has had a down year every so often by his standards). That inconsistency occurs for a variety of reasons, namely injuries (which a team can never predict for), random clustering of slumps (also not predictable, nor do teams tend to alter their management strategy just because a player has a bad slump), and changes in the environment that aren't presently measured by our best sabermetric analysis tools (which teams are commonly aware of). Of course there are players who are more inconsistent than others, but it does not follow that because a player doesn't produce at his usual best, the team is suffering a drop in production that would be avoidable otherwise. After all, the most optimistic assumption you can truly make is that if the player in question weren't there, you would expect league average production from an average replacement.
I feel it's important to define statistics that go to the heart of what you're trying to quantify. It seems to me that other attempts to define greatness have circled around the issue rather than really focusing on what exactly it means to have a great peak, what the real value of efficiency is, and how best to account for things like lengthy declines and inconsistency. The Greatness Index (GI) is my attempt to define greatness (excluding the subjective elements) more exactly.
Components of the GI method include career wins, prorated wins, upward win variability, and peak wins. What follows is a brief description of each of those components.
I) Career Wins - This is the element that addresses the virtue of longevity. Players with longer careers will tend to do well accumulating wins over the long haul.
II) Prorated Wins - Many statistical method for player evaluation include a prorated term (wins per season in win shares, or wins prorated to a standard career length), but I think this is a little bit of an oversimplification. The virtue of efficiency is that you get more production in a shorter period of time and then you step out of the way are are replaced before you become an albatross. A player who wins 200 games in 20 years is not worth as much as a player who wins 200 games in 10 years because in the other 10 years, the second player's team probably reaped some positive value from his replacement. The trick is to quantify some fair assumption about what that replacement is. Systems that rely exclusively on scoring rates make the assumption that a player's replacement once he's out of the way is someone who produces at the same exact level as he does. I feel that the only fair assumption is that the average replacement for a player whose career is short will be average. The GI element I'm calling prorated wins is actually a method whereby a player's career is assumed to be a standard length and if he lasts longer than the standard, his win total is prorated down at his scoring rate, and if his career is shorter than the standard, wins are added at the average scoring rate to account for the missing time.
Peak Wins - Most methods I've seen account for this by grabbing a player's best seasons (individually) and combining that with his best range of consecutive seasons. The problem is that the final rankings are significantly influenced by how many years you choose to focus on, and by things like ill-timed injuries in the middle of a player's peak. Can the case really be made that a player who happened to cluster his best seasons closely together was more valuable than a player who was consistently good but his best seasons were scattered more evenly throughout his career? Rather than biasing the results with arbitrary numbers of years or the false claim that a cluster of good seasons is more valuable than a scattering, I have chosen to simply credit players for wins scored above twice the league average. The peak level is chosen arbitrarily, but choosing it differently would only have the effect of changing how important the peak element is in the ratings. It would not change how players scored relative to each other in the peak element.
Upward Variability - This is a bit of a new invention used in the GI method to correct the efficiency rating to account for uncharacteristically bad seasons that have the effect of displacing the player's career scoring rate and casting him inaccurately as a less efficient player than he actually was. The way upward variability is calculated is by determining a player's career scoring rate (per PA for offense or PRG for defense), and then comparing each season to that scoring rate. All wins created above and only above the average line are counted as being upwardly variable. Seasons during which the player scored at below his career rate are not counted. All players have some amount of upward variability, but players who suffered from inconsistency due to prolong growth or decline phases, injury problems or general inconsistency are given a little more credit to mitigate (slightly) the downward pull bad seasons had on their prorated wins category.
Each of the four elements is calculated for every player with enough playing time to be considered in the rankings and for both offense and defense individually, and the element scores are simply added together to arrive at GI rankings.
With that out of the way, let's make use of the GI Method and of PCA to put some figures to the stories and explore the question of whether it's appropriate to adjust a player's offensive statistics to account for his position.
Questions, comments, or suggestions? E-mail the author at m_souders@yahoo.com
