Last week, we took a look at using linear weights to evaluate a player’s performance on offense. Now, one of the things that I explained was why I tend to use linear weights values that ignore situational information.
But there are some plays we can’t treat that way. Let’s look at those. And let’s also look at three ways of presenting offense as a rate. (Two of which will look awfully familiar, I’m sure.)
Situational Hitting
To be clear—I am not talking about clutch here. (If you missed last week’s article, that’s where I explain why. I can certainly take up the topic at a later date, but for now, let’s move along.)
But there are some kinds of especially productive (or unproductive) outs that can only occur in certain situations. You have to have runners on ahead of you to advance a runner on an out, or to get a twin killing and make two outs on one play.
So, for instance, these are the average rates per out of the four “situational” outs, based upon baseout state, for 2009:
Outs 
Bases 
SH% 
SF% 
TP% 

0 
1__ 
0.10 
0.00 
0.17 
0.00 
0 
_23 
0.00 
0.20 
0.01 
0.00 
0 
_2_ 
0.12 
0.00 
0.01 
0.00 
0 
1_3 
0.03 
0.23 
0.16 
0.00 
0 
12_ 
0.14 
0.00 
0.17 
0.00 
0 
__3 
0.00 
0.21 
0.01 
0.00 
0 
123 
0.00 
0.20 
0.19 
0.00 
1 
_2_ 
0.00 
0.00 
0.01 
0.00 
1 
1_3 
0.03 
0.22 
0.21 
0.00 
1 
1__ 
0.03 
0.00 
0.19 
0.00 
1 
_23 
0.00 
0.18 
0.01 
0.00 
1 
__3 
0.01 
0.21 
0.02 
0.00 
1 
12_ 
0.03 
0.00 
0.20 
0.00 
1 
123 
0.00 
0.21 
0.19 
0.00 
I excluded all situations (bases empty, or two outs) where no situational outs were possible, just to keep the chart readable. I also figured the run value (compared to an average out in those circumstances) of each of the situational outs. A sacrifice hit was worth .22 runs more than an average out in similar circumstances that season; a double play was 0.37 runs worse than an average out in those situations.
So then all you have to do is figure out how many, say, double plays a player hit into in a season, as well as how many an average player would have—in other words, multiply DP% by the player’s outs in that baseout state. That gives you double plays above average while accounting for context—so we can now happily mix these values with our context neutral linear weights. Just multiply the double play run value by the double plays above (or below) average to get the run value of a player’s double plays.
This is typically not a big impact, but it can occasionally mean a lot. Here are the top 10 seasons in runs above average on situational outs from 1952 on:
Year 
Name 
SIT_RAA 
1979 
10.4 

1979 
9.4 

1977 
9.2 

1990 
8.1 

2006 
8.0 

2004 
7.0 

1982 
6.8 

1996 
6.6 

1954 
6.4 

2004 
6.3 
It’s an odd list, and as you can see, the best season on record in the category is still only about 10 runs. But it’s certainly important for those players who excel in that category.
Rate of Change
Okay, so that covers runs above average for us. Now what if we want to present these as a rate? I am going to talk about three ways to do this here, although it is possible that only two will be routinely displayed on the website, once we transition to the new stat reports.
I will first detail my preferred method, which is also the method that will serve as the base for the other two. It’s staggeringly simple:
 Take a player’s runs above average (including situational outs), and divide by plate appearances (excluding intentional walks, as discussed last week)
 Take the average runs per plate appearance that year
 Add the two
That’s all you need to get runs per plate appearance. Depending on the run environment that season, you’ll typically get an average value around 0.12.
I prefer it because it’s simple, direct, and can be readily used in the way I tend to use such values (which is to do more math with them). But I understand that most people don’t tend to think it’s very descriptive. So there are two very common ways we can translate our R/PA values to something a bit more palatable.
Before I proceed—all of these values are equally as accurate. They all come to the same conclusion—a player’s ranking in one will be the player’s ranking in the others. I think that sort of unity is important, and it’s been something Baseball Prospectus hasn’t done very well in the past. So we’re taking a step forward here for us, at least.
The first will be very familiar in appearance to BP readers—True Average. It’s a rate stat on the scale of batting average—so .260 or so is average, .300 is exceptional and .200 is flirting with disaster.
In the past, however, our formula for figuring True Average has been rather involved, requiring odd exponents. That’s made it less convenient to use and harder to calculate. So we’re simplifying the formula, while retaining the same basic presentation that BP readers are accustomed to. From 1993 to 2009, you can figure TAv simply as:
Now, we will be tuning those values slightly to match the batting average for that season, but other than that, that’s the formula for TAv we will be using once the new stat reports are rolled out.
The other rate stat we’ll be introducing will be—oh, call it TAv+. It will behave pretty much as you’ve come to expect stats like OPS+ or wRC+ to behave. The calculation is even simpler:
(RPA/lgRPA)*100
Intentional Walks
I’ve been ignoring those, haven’t I?
Well, I plan on continuing to do so. Don’t worry, this isn’t as bad as it sounds.
As it turns out, the decision to intentionally walk a batter is based on two things—the situation, and the quality of the batter relative to the followon batter. (And of course the platoon advantage plays a major role—a lefty pitcher will intentionally walk a righty to get to a lefty far more often than they’ll walk a lefty to get to a righty, for instance.)
Because of this, the run value of the intentional walk in practice is nearly zero, at least compared to the result of the average plate appearance. For instance, from 1993 to 2009, the average plate appearance resulted in .12 runs (in other words, our typical average R/PA value from above). Looking at the runs that score after an intentional walk, and subtracting the starting run expectancy, we get .11.
The intentional walk, though, scales with the player—Barry Bonds will obviously be intentionally walked in more situations than other batters, for instance. So we’ll go ahead and use a player’s own R/PA as his intentional walk value. We can do that simply by excluding IBB totally when we figure R/PA.
What's Next
I have ignored the question of park adjustments; I will tackle those separately.
We also want to be able to figure replacement levels and positional adjustments, so we can use this (as well as our fielding data) to calculate our heavyhitting value stats, VORP and WARP. (And on that note—we’ll be bringing the two of them into unison as well.)
I also anticipate being asked the questions, “How does this compare to wOBA?” and “How does this compare to the old way of figuring TAv?” Allow me to answer briefly here, and I’ll follow up at a later date.
Simply speaking, wOBA is a linear formula for scaling runs per plate appearance to look like OBP. The new TAv formula is a linear formula for scaling runs per plate appearance to look like batting average. Neither is “correct” or “incorrect,” as they’re both just ways of presenting values. One person may find the batting average scale more intuitive, another might find the onbase percentage scale more intuitive. The point of the scale is to make the figures more readily understandable, nothing more or less.
All that matters essentially is the computation of the initial R/PA values. When people ask about wOBA, most of the time what they really care about is the values presented on Fangraphs, derived from this set of linear weights developed by Tom Tango.
TAv—in both, the relative weight of the various events (walks, singles, home runs, etc.) are held constant over time. By availing ourselves of full playbyplay data, we are able to find the relative value of events as they change with the run environment. We’re also able to do a more precise breakdown of certain events, like the situational outs or reaching on an error. All that comes out to a modest but real improvement in accuracy.
There’s actually one great similarity between the weights at Fangraphs and the current formula for