Linear Weights

Source: The Book Wiki

With run expectancy, we can determine the expected runs scored of the various base/out states (keep in mind this is outside the context of the inning and score). If we have the base/out state prior to and after a certain event, such as the double mentioned above, we can then attribute the difference in run expectancy to the event. For example, the double mentioned above would have been worth 0.634 runs, the difference in expectancy from the two base/out states.

If we do this for all sorts of events over a long period of time, we can come up with the average run value for each event, from a double to a home run to an out. And with that you get what’s called linear weights of all the events, run values that we can use to quantify batting events and turn them into a common unit of production. This idea was initially popularized by the Pete Palmer in the classic sabermetric tome The Hidden Game of Baseball.

Here are the linear weights for various run environments.

wOBA

Source: The Book

With the possibility of using linear weights to determine value of events, we can easily define run values for players on offense. wOBA, a metric originally defined in by Tom Tango The Book, is the preferred offensive statistic in the saber community. It is a linear weights model that is taken in terms value produced above the run value of an out (i.e. the value of an out, which of course is negative, is subtracted from the linear weights value of an event) and converts it into a rate stat that is on the OBP scale and is taken per plate appearance. wOBA can be found either on FanGraphs or StatCorner in slightly different calculated forms and from slightly different data sources.

wOBA is particularly convenient because of its ease of conversion from rate stat to counting stat in units of runs. This post on FanGraphs by David Appelman explains it well. With wOBA, we can get batting runs pretty easily.

Defensive Metrics

Source: MGL’s original articles (Part 1 and 2) on UZR, Sean Smith’s explanation of Total Zone for Baseball-Reference, and The Fielding Bible site, where you can get samplings of the work John Dewan has done for plus/minus and the classic Derek Jeter vs. Adam Everett article by Bill James

The last few years, work on defensive metrics has exploded, and the fact that MGL’s UZR is now freely available and updated in-season over at FanGraphs is a testament to how far this work has gone. It’s even gotten pub in the mainstream media, though often times it is referred to rather skeptically, in part because it still remains misunderstood to those in the mainstream media. I won’t go into too much detail here, because MGL, Sean Smith, John Dewan, and many others who work in this field are far more knowledgeable, but I will try to explain it simply.

Many of these metrics are the development of a lot of history in defensive metrics, all the way back to Bill James’ Range Factor. These metrics now mostly work on this premise: balls in play are separated into different zones, and each zone is assigned a run value based on the value of events that occur in that zone. Players who make plays in those zones are averaged over the course of a season so that the rate of plays made in the zones for each position is known. Then, the plays individual players make are tallied in their respective zones and are then given run values based on plays made above the average fielder. Other things like outfielder arm, double plays, and in some cases catcher defensive plays, are also measured in a similar method without the use of zones.

There are a lot of adjustments made for things like batter handedness and positioning, but that is the basic gist. It is similar to linear weights, just in a defensive sense. If you want to read more about it, the sources above are a great start.

Defense Independent Pitching

Source: Voros McCracken’s seminal article that first describes DIPS (defense independent pitching statistics), explanations about FIP and tRA

This is perhaps the most difficult aspect of modern sabermetrics to accept when you first see it; it certainly was for me. The gist of the idea is that pitchers have very little control over their balls in play, other than the batted ball type. This means pitchers rarely can control what occurs once the ball has gone into play, whether it lands for a bloop single, is caught by the center fielder, or gets into the gap. Thus, pitchers are more reliant on their defense than it was traditionally accepted, and thus the quality of defenders is important to know in traditional pitcher evaluation.

The research on DIPS was astounding when it first came out, but has held up mostly over the years. It’s been found that pitchers do have control over batted ball type and have less control over home runs than hitters, but the basis of balls in play being out of the hands of the pitcher still stands. This is why batting average on balls in play (BABIP) has become such a critical statistic in understanding why pitchers appear to struggle or play well.

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