Random Thoughts On Statistics in Baseball

After the jump I'm going to put down a couple of my own recent ponderings about statistics, but if nothing else, please check out the links below.  I've learned more about statistics from reading sabermetric articles than I ever did in any class, and these recent articles are all thought-provoking and insightful.  Read them, think about them, and feel free to post any questions you may have in the comments below.

Joe Posnanski - a great read on the Hall of Fame, and how statistics can be used to prove any number of different points.

Tom Tango - The Mike Silva Chronicles, questions from a saber-denier (already linked on DBR before, but amazing)

David Appelman - discussing stat saturation and "statistical scouting"

Dave Cameron - about the overlap between scouting and advanced statistics.  When you think about it, about half of the statistic categories on Fangraphs use scouting data.

Okay, and now for my haphazard thoughts on statistics.  My mind first started down this quasi-existential path a couple of weeks ago while reading the interview here on DRB with Erik Neander, Tampa Bay's Baseball Operations Assistant.  It was a great interview with lots of insight, but one quote in particular got me thinking (emphasis mine):

"E.N.: Blown saves are a useful description of an event that occurs during the course of a game, but like any statistic, they don't tell you everything about a player's performance.  It just depends on what you want to know.  If you're using blown saves to evaluate the quality of a reliever's performance, then they have the potential to be misleading, especially with relievers that aren't always used to record the last three outs of the game."

When you stop to think about it, statistics are a very odd sort of thing.  In short, they're an attempt to describe, through numbers, the actions and events that are happening on the playing field.  That's all that every single statistic is: a description of physical events.  With some statistics, like RBIs and Errors, it's easy to see their relation to physical events, and that's why reading a box score can give you a good basic understanding of what happened in a game.  It describes to you what you could have seen with your eyes at the game.  While books and newspaper articles capture moments through using words, baseball stats do the same thing while using numbers.

With some more advanced statistics, though, that connection becomes lost.  How exactly does wOBA relate to events happening on the field?  What about WAR?  I can't see a player physically add one WAR to their team, but I can see them hit a homerun.  I can see a player make an error, but I can't see a -3 play on the Dewan +/- scale (unless you're trained to do so).  However, all these advanced statistics are based on events happening on the field too, even though they're tougher to actually see.  wOBA is based on the hits and walks that a player accumulates, and UZR is based upon how many balls a player gets to and where they're located.

And that leads me to my second quote, from the DRB interview with James Click, the Rays' Coordinator of Baseball Operations:

"JC: Sometimes people like to draw a line between "advanced" and "regular" statistics, but I don't necessarily see things that way. The difference between different stats can often be explained by the question the metric is attempting to answer. At the end of the day, it's all information and you have to know exactly what that information is telling you and what it isn't."

There are two big things that I get from that quote.  Number one: in short, all statistics are the same underneath.  They all have their own particular strengths and weaknesses, and they all originate from the physical events that are happening on the field.  Different statistics are simply attempting to answer different questions, and so they measure the events on the field...differently.  And that leads to the second big point: you have to understand enough about the statistic to know what specific question it's attempting to answer.  For example, while Errors ask the question, "How many times does a player mess up while attempting to field a ball?", UZR asks, "How good is a player's range, arm strength, and error rate?"  Different questions, different answers, and it's easy to be confused by the more evaluative, less descriptive UZR stat if you don't understand that.

One way that I've been visualizing this concept recently is as a continuum, with descriptive statistics on one end and evaluative statistics on the other:

What I'm trying to show with this picture is that all statistics, no matter if they're considered "advanced" or "traditional", contain varying amounts of both descriptive and evaluative characteristics.  In the example on the chart, ERA is a very descriptive statistic - showing how many earned runs a pitcher let up during the course of a game - but is not very evaluative, meaning it varies much from year to year and is a poor measure of a pitcher's underlying talent level.  FIP, on the other hand, is based on on-field results and attempts to measure how well a pitcher performed, but also goes beyond mere on-field results and attempts to measure the underlying talent level of the pitcher.  It's less descriptive than ERA - what exactly does a 3.00 FIP equate to?  It's not as easy to say as it is with a 3.00 ERA - but it is more stable from year-to-year and a better evaluative tool.

I've been trying to determine how I'd rank of the major statistics on this continuum, but it's a lot tougher than I would have thought.  It may not be a straight line relationship, since certain statistics are very descriptive, but can also be quite predictive (like homeruns and K/BB rate).  Maybe something more like a scatter-plot would make more sense (note: locations of statistics relative to others within the same box not meant to be precise):

Anyway, where would you rank most of the major statistics on a plot like this?  Anything you disagree with?  I could keep on with this subject at great length - there have been multiple books written about baseball stats - but I merely wanted to explore a bit the connections between all baseball statistics.  Like James Click said, there is no such thing as "advanced" stats; there are simply lots of statistics and each of them answers a slightly different question.  There is nothing wrong with using RBIs or BA to make a point, just as long as you are using the statistics with a good understanding of their limitations, strengths, and the questions that they answer.  Any evaluation or discussion about a player, though, requires multiple statistics and looking at the whole picture, since individual stats can only tell you so much. 

All of that said, if you have a question about any statistic that you don't understand entirely, leave a note in the comments and we'll be happy to help.  There are a ton of stats out there and it can be tough to get an understanding of what they all measure and what they don't, so don't feel dumb.  It's a learning process, and one that I know I'm still working on myself.