How Do Various Defensive Metrics Relate to Each Other?

This post aims to very generally shed light on how a couple key defensive metrics often applied in baseball circles relate to each other.  Observed will be five such stats, all cumulative scores of entire teams, from the 2018 season. 

The statistics: fielding percentage, team error totals, Def, UZR, and DRS.

All of these cross-sectional data originate from FanGraphs’ delightful statistics leaderboards.  The first two statistics are very obviously of the most traditional nature; they have been around for decades.  The latter three are of a more modern wave of quantification tools.  What follows will include four visualizations (each set of statistics compared to FanGraphs’ Def stat) and a bit of editorializing on some of those plots’ features.  

Additionally, the correlations (or lack thereof) between each of the statistics on those plots will be included.  Correlation, to some the name-brand cousin of causation, features its own set of pitfalls in this type of discussion.  

The drawbacks/limitations are not insignificant though.  Academic circles, for instance, are far more focused on distilling causation from correlation than in correlation itself. For one, correlation hints at causation while unfortunately not always fulfilling promises that a causal relationship between variables is in fact present.  Correlation, while also suggestive of predictive powers, is not always so and too easily provides a platform of conclusions to which humans love to jump to prematurely.  Correlation can also sometimes misspecify the nature of the relationship between variables in question: what might be estimated as a linear relationship could in fact be logarithmic, etc.

Correlation is nonetheless a very valuable tool, if only to better understand how variables might relate.  And contrary a prior point, sometimes correlation can in fact feature some predictive clout.  Causation does not always have to be the finish line, in other words.  Correlation can be provided in a single quick and dirty number to briefly summarize a relationship (essentially what I will be doing here).  It also puts a name (number) to a face (plot), so that people can more effectively understand how clouds of data are sometimes summarized numerically.

Here UZR, DRS, Fielding percentage, and errors will all be compared to Def (Defensive Runs Above Average).  I chose Def to be the key statistic because it normalizes its score for various positions and is additionally a key building block of FanGraphs’ own WAR metric. 

Visualizations!

Here, we find that there appears to be very little in the way of a relationship between a team fielding percentage and that same team’s Def total.  This isn’t particularly surprising given the considerable amount of information baked into a metric like Def. What is more interesting to me is that the lack of relationship highlights the departure of new age statistics from those stats of old.  The correlation between these two variables is just .309, definitely existent, but not particularly robust either.  

The adjusted R-Squared number provided, .062, was generated using simple OLS (a crude tool, but a useful baseline) suggests that fielding percentage is a pretty poor explanatory variable for mapping Def and it furthermore indicates that a theoretical linear regression line would make an underwhelming fit in mapping these data.  Fielding percentage is not a statistically significant variable for predicting Def for any particular team in this case.

The distinction between total errors and fielding percentage is worth making in this case based on the changing number of chances that are available defensively.

There appears to be an even lesser relationship between the two featured variables.  An only slightly perceptible downward trend exists in an otherwise noisy plot of data.  As expected though, that relationship does appear to be negative (highlighted by the slope) given more errors very sensibly would correspond to a lower Def total.  The correlation between Def and Total errors, the only counting statistic featured in this post, is -0.291.  

To go along with a weaker correlation than the first visualization is a smaller adjusted R-Squared to match: just .052.  Errors committed by any particular team do not appear to be a statistically significant indicator of team-wide Def.  

Here a positive correlation between UZR and Def is abundantly clear: as team UZR rises, so too does team Def.  This relationship is a good example of the constraints on this casual use of correlation though.  While there is an obvious relationship between these two variables, that relationship is almost certainly impacted by serial correlation given that UZR in fact is part of what goes into an algorithm for Def, according to FanGraphs.  Were this a discussion of causality, the presence of serial (or auto-) correlation would be a considerable hurdle, but it is not.  

The correlation between these two variables is, based on the plot above, expectedly huge: .982.  The adjusted R-Squared marker also expresses the strong goodness of fit for a simple OLS regression line should it be featured in this plot.  As this evidence might suggest, UZR, based on simple OLS, is considered a strongly statistically significant explanatory variable of Def.

The plot above highlights a positive relationship, though not so closely aligned as in the case of the third visualization.  In this one, the relationship is form fitting but there are a couple outliers.  In particular, the Diamondbacks appear to have a disproportionately high DRS mark compared to their overall Def score.  

While the relationship doesn’t literally appear to be so strong, autocorrelation could definitely be a factor in this case too.  Overall, the correlation between these two variables is .687.   Additionally, DRS is a statistically significant explanatory variable of Def.

In summation, “traditional” defensive statistics do not correspond very much to newer performance estimators.  That said, they do not appear to run in direct contradiction to each other in the limited cases observed here.  More modern estimators do align more closely, but to varying degrees, and that relationship is likely in part due to algorithms cooked with some of the same ingredients.