May 19, 2005

Crooked Numbers

Getting Bigger All the Time

by James Click

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It's no secret that ballplayers are bigger now than they were back in the sixties, seventies and eighties. Aside from the goofy uniforms, it's one of the comedic highlights of catching any game on ESPN Classic or the like. Shortstops look like bat boys, designated hitters look like shortstops, Barry Bonds looks like Eriq LaSalle, but Cecil Fielder still looks like David Ortiz after swallowing Nelson de la Rosa. There are many possible reasons for the size increase, including the overall size increase in the population, improved nutrition, expanded talent bases, and, of course, steroids. That's not what I'm looking to discuss. Instead, there are obvious ramifications on the field as a result of the changes.

Nate Silver spent some time talking about how players' projections change based on their body size, noting that Adam Dunn, shrunk to David Eckstein's size, loses about 20 points of slugging in his projection. "Further, the correlation between a players' size and his home run rate is a fairly significant .43, meaning about 18.5% (.43^2) of the variance in home run rates can be explained solely by a player's listed weight." Bigger players, more home runs...no rocket scientists were harmed drawing that connection.

While virtually all players today look bigger than their counterparts from the Biz Markie era, the difference in primarily defensive positions appears the most drastic on the surface. Going from 150 pounds of Ozzie Smith to 210 pounds of Khalil Greene is a much larger percentage difference than Bonds circa 1992 to Bonds circa 2002. Joe Sheehan discussed this recently on Outside the Lines as well as covering it from the pitcher workload standpoint two years ago. Joe also referenced work done by Dan Levitt, co-author with Mark Armour of the highly recommended Paths to Glory: "a 1996 first baseman was 55% more likely to homer than his 1976 counterpart (home run rate of .042 vs. .027), whereas a 1996 middle infielder was 175% more likely to homer than a 1976 middle infielder (.0184 vs. .0067)."

While it certainly appears that more of the late power increase is coming from middle infielders, using percentage increases here distorts the fact that first basemen are hitting an additional .015 home runs per plate appearance while middle infielders increased by a raw total of .0117. Proportionally, there is more power coming from the middle infield spots, but more of the raw increase is coming from a traditional power position: first base.

That said, the theme of Joe's article is still valid: power is now coming from traditionally defensive positions. Power hitters are now coming from all positions, but while the difference between the best and worst individual power hitters may be shrinking, it's unclear if the increase and consolidation encompasses all positions on the diamond or if finding a power hitting shortstop is still the find that it was when Cal Ripken stepped into the limelight.

To help answer this, let's look at positional Marginal Lineup Value Rate (MLVr) for the past few decades to start. MLVr is the total runs a players produces per game more than the league average, thus it's centered around zero, so players who are below league average will have negative values and those above will have positive values. For example, here is the yearly MLVr for AL SSs from 1972-2005:

If the impact of Derek Jeter, Alex Rodriguez, Nomar Garciaparra, and Miguel Tejada wasn't clear, check out that spike from 1996 to 2002. Even so, AL SSs have not had a positive MLVr since before 1972 (and likely never have); the position remains one in which teams are highly likely to have a light hitting player.

Getting back to the question at hand, using each position's MLVr, we can easily estimate the offensive distribution in the league using standard deviations. If every position hit exactly the same, the standard deviation would be zero, but the bigger the standard deviation, the more discrepancy there is between the offensive performance of the various positions around the diamond. Using all non-pitcher and non-DHs since 1972, here's how the standard deviation in each league looks:

For most of the 1980s, the two leagues followed each other pretty closely in the standard deviation of positional MLVr, but then in 1994 and 1995, the AL saw an impressive spike while the NL increased slowly. Since 1999, the two leagues have been reversed: while the NL has seen steadily increasing discrepancy between positional offensive performances, the AL has seen more of a regression to more similar offensive performance across positions.

Knowing that the NL is becoming more divergent and the AL less so, let's see how the various positions have changed. Here's how offensive (first base, third base, left and right field) versus defensive (catcher, second, short, and center) have compared over the past three decades:

Initially, it may appear that something is wrong with the graph because MLVr is supposed to center around zero, but keep in mind that pitchers and DHs have been excluded from the analysis. Thus, when comparing NL players to league average, they're going to look much better because they're being compared to pitchers, but AL players will look worse because they're being compared to DHs. As with overall league offensive discrepancy, we can see in the chart above that the traditionally defensive positions have been diverging from their offensive teammates in the NL since about 1992. The AL saw a spike in discrepancy in from 1994-1998 before slowing regressing over the past six or seven years.

Thus in the NL, the recent increase in power and player size hasn't resulted in a closing of the gap between the game's traditional power positions and the more defensive oriented positions. However, in the AL the trend has been exactly the opposite. Because the leagues are heading in opposite directions, we must concede that the increasing offensive numbers of the past decade haven't been coming from an adjustment of expectations of various positions on the diamond. While there have been individual positional trends (NL catchers and AL centerfielders have been trending dramatically downward; AL shortstops and NL second basemen are going upward), it's tough to pinpoint the offensive surge on one position or even a group of traditionally defensive positions.

Personally, I found this result a little surprising. Much has been made of the rise of players like Ripken, Rodriguez, Jeff Kent, Mike Piazza, and Ivan Rodriguez as a signal that traditionally defensive positions were being overrun with sluggers, new super players who could both handle the defensive rigors of the position and carry a respectable bat in the lineup. Ripken was certainly credited with changing the prototype for his position in the early 1980s and the rise of the trinity of shortstops was billed as the completion of an overhaul of the offensive expectations for normal defensive positions. The offensive contributions of players like Rodriguez, Piazza, and even Jim Edmonds certainly looked much more impressive than their historical counterparts.

Instead, the entire league has progressed offensively at comparable rates rather than being buoyed by a correction of the market for typically offensively weak positions. While those hitters who are playing at more traditionally defensive-oriented positions are putting up numbers significantly more impressive than their counterparts from several decades ago, that fact is true for the entire league and thus we should not consider the offensive explosion of the last decade more a result of defensive positions improving offensively at a faster pace than their slugging teammates. Just like watching those old games on any classic baseball channel, everybody's bigger, not just the shortstops.